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  • 1. FE-501 PHYSICAL PROPERTIES OF FOOD MATERIALS ASSOC PROF. DR. YUS ANIZA YUSOF DEPARTMENT OF PROCESS & FOOD ENGINEERING FACULTY OF ENGINEERING UNIVERSITI PUTRA MALAYSIA
  • 2. INTRODUCTION • Foods are characterized by their physical properties. y p y p p • Physical properties intensely affect the quality of foods  and can be used to classify/identify foods. • Formerly, the quality of a food was given by its  geometric characteristics. • Now quality of food evaluate as total quality and takes Now, quality of food evaluate as total quality and takes  into account the entire spectrum of physical properties  of foods.  • Physical properties should be able to be measured  objectively, quickly, individually, at a low cost and in a  manner that will not destroy the foods.  manner that will not destroy the foods
  • 3. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 4. INTRODUCTION • Size and shape are important physical attributes of foods that are used in screening, grading and quality control of foods. • They are also important in fluid flow and heat and mass transfer calculations. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 5. SIZE • Size is an important attribute of foods used in p screening solids to separate foreign materials, grading of fruits and vegetables, and evaluating the quality of food materials materials. • In fluid flow, and heat and mass transfer calculations, it y p is necessary to know the size of the sample. • Size of the particulate foods is also critical. For example, particle size of powdered milk must be large enough to prevent agglomeration but small enough to agglomeration, allow rapid dissolution during reconstitution. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 6. SIZE • Particle size was found to be inversely proportional to  l f d b l l dispersion of powder and water holding capacity of whey  p protein powders (Resch & Daubert, 2001).  p ( ) • Decrease in particle size also increased the steady shear and  complex viscosity of the reconstituted powder. • The importance of particle size measurement has been widely  recognized, especially in the beverage industry, as the  distribution and concentration ratio of particulates present in  p p beverages greatly affect their flavor. • It is easy to specify size for regular particles, but for irregular  particles the term size must be arbitrarily specified. ti l th t i tb bit il ifi d SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 7. SIZE • Particle sizes are expressed in different units depending on  l d d ff d d the size range involved.  • Coarse particles are measured in millimeters, fine particles in Coarse particles are measured in millimeters, fine particles in  terms of screen size, and very fine particles in micrometers or  nanometers.  • Ultrafine particles are sometimes described in terms of their  surface area per unit mass, usually in square meters per gram  ( (McCabe, Smith & Harriot, 1993). , , ) SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 8. SIZE • Size can b d be determined using the projected area method. In d h d h d this method, three characteristic dimensions are defined: 1. Major diameter, which is the longest dimension of the maximum projected area; 2. Intermediate diameter, which is the minimum diameter of the maximum projected area or the maximum diameter of the minimum projected area; 3. 3 Minor diameter which is the shortest dimension of the diameter, minimum projected area. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 9. SIZE • Length, width, and thickness terms are commonly used that correspond to major, i d j intermediate, and minor di di d i diameters, respectively. • The dimensions can be measured using a micrometer or caliper (Fig. 1). The micrometer is a simple instrument used to measure distances between surfaces. Most micrometers have a frame anvil spindle sleeve thimble and ratchet stop They frame, anvil, spindle, sleeve, thimble, stop. are used to measure the outside diameters, inside diameters, the distance between parallel surfaces, and the depth of holes. Fig.1 SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 10. SIZE • Particle size of particulate foods can be determined by sieve analysis (Fi 2) passage through an electrically charged l i (Fig.2), h h l i ll h d orifice, and settling rate methods. • Particle size distribution analyzers (Fig.3), which determine both the size of particles and their state of distribution, are used for production control of powders. Fig.3 Fig.2 SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 11. SHAPE • Shape is also important in heat and mass transfer calculations, screening solids to separate foreign materials, grading of fruits and vegetables, and , g g g , evaluating the quality of food materials. • The shape of a food material is usually expressed in terms of its sphericity and aspect ratio. • Sphericity is an important parameter used in fluid flow and heat and mass transfer calculations. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 12. SHAPE • According to the most commonly used definition, sphericity is the ratio of volume of solid to the volume of a sphere that has a diameter equal to the major diameter of the object so that it can circumscribe the solid sample. For a spherical particle of diameter Dp, Dp sphericity is equal to 1 (Mohsenin 1970) (Mohsenin, 1970). SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 13. SHAPE • Assuming that the volume of the solid sample g p is equal to the volume of the triaxial ellipsoid which has diameters equivalent to those of the sample, then: SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 14. SHAPE • In a triaxial ellipsoid, all three perpendicular p , p p sections are ellipses (Fig. 4). If the major, , , , intermediate, and minor diameters are 2a, 2b, and 2c, respectively, volume of the triaxial p ellipsoid can be determined from the following equation: • Then, sphericity is SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 15. SHAPE Fig.4 Triaxial ellipsoid SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 16. SHAPE • Sphericity is also defined as the ratio of p y surface area of a sphere having the same j volume as the object to the actual surface area of the object (McCabe, Smith, & Harriot, ) 1993): where, where SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 17. SHAPE • The equivalent diameter is sometimes defined as the d h diameter of a sphere h f h having the same volume h l as the particle. • However for fine granular materials it is difficult However, materials, to determine the exact volume and surface area of a particle. • Therefore, equivalent diameter is usually taken to be the nominal size based on screen analysis or microscopic examination in granular materials materials. • The surface area is found from adsorption measurements or from the pressure drop in a bed of particles. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 18. SHAPE • In general, diameters may be specified for any g , y p y equidimensional particle. • Particles that are not equidimensional that is equidimensional, is, longer in one direction than in others, are often characterized by the second longest major dimension. • For example for needlelike particles example, particles, equivalent diameter refers to the thickness of the particles not their length particles, length. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 19. SHAPE • In a sample of uniform particles of diameter  p p Dp, the number of particles in the sample is: where • Total surface area of particles; SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 20. SHAPE • Another definition of sphericity is the ratio of  p y the diameter of the largest inscribed circle (di )  to the diameter of the smallest circumscribed  circle (dc) (Mohsenin, 1970): • Recently, Bayram (2005) proposed another  equation to calculate sphericity equation to calculate sphericity as: SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 21. SHAPE • Where • According to this formula, equivalent diameter for irregular shape material is accepted as the average dimension. • Differences between average diameter and measured dimensions are determined by the sum of square of differences. • When this difference is divided by the square of product of the average diameter and number of measurements, it gives a fraction for the approach of the slope to an equivalent sphere which is sphericity sphere, sphericity. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 22. SHAPE • According to Eq. (1.9), if the sample sphericity value is close to zero it can be considered as spherical spherical. • The aspect ratio (Ra) is another term used to express the shape of a material. It is calculated using the length (a) and the width (b) of the sample as (Maduako & Faborode, 1990): • Certain parameters are important f the d for h design of conveyors f for particulate foods, such as radius of curvature, roundness, g p p and angle of repose. Radius of curvature is important to determine how easily the object will roll. The more sharply rounded the surface of contact, the greater will be the stresses developed developed. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 23. SHAPE Where • The minimum and the maximum radii of curvature for larger objects such as apples are calculated using the larger and smaller dial indicator readings, respectively. • For smaller objects of relatively uniform shape, the radius of curvature can be calculated using the major diameter and either the minor or intermediate diameter. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 24. • Where SHAPE • Roundness is a measure of the sharpness of the corners of the solid. Several methods are available for estimating roundness. The most commonly used ones are given below (Mohsenin, 1970): where SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 25. SHAPE Fig. 5 Roundness  definitions. • Roundness can also be estimated from Eq. (1.15): where SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 26. SHAPE • Angle of repose is another important physical property used g p p p y p p y in particulate foods such as seeds, grains, and fruits. • When granular solids are piled on a flat surface, the sides of the il th pile are at a d fi it reproducible angle with th t definite d ibl l ith the horizontal. • This angle is called the angle of repose of the material. The g g p angle of repose is important for the design of processing, storage, and conveying systems of particulate material. • Wh When the grains are smooth and rounded, the angle of h i h d d d h l f repose is low. For very fine and sticky materials the angle of repose is high. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 27. PARTICLE SIZE DISTRIBUTION PARTICLE SIZE DISTRIBUTION • The range of particle size in foods depends on the cell g p p structure and the degree of processing. • The hardness of grain is a significant factor in the particle size distribution f flour. Th particle size di t ib ti of fl di t ib ti of fl The ti l i distribution f flour i is known to play an important role in its functional properties and the quality of end products. • The relationship between the physicochemical properties of rice grains and particle size distributions of rice flours from different rice cultivars were examined (Chen Lii & Lu 2004) (Chen, Lii, Lu, 2004). • It was found that physical characteristics of rice grain were the major factors but chemical compositions were also important in affecting the particle size distribution of rice flour. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 28. PARTICLE SIZE DISTRIBUTION PARTICLE SIZE DISTRIBUTION • Particles can be separated into fractions by using one of the  p y g following methods: 1. Air elutriation method: In this method, the velocity of an air stream is adjusted so that particles measuring less than a given diameter are suspended. After the particles within the size range are collected, the air velocity is increased and the new fraction of particles is collected The process continues until the particulate collected. food is separated into different fractions. Air classifier SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 29. PARTICLE SIZE DISTRIBUTION PARTICLE SIZE DISTRIBUTION 2. Settling, sedimentation, and centrifugation method: In settling and sedimentation, the particles are separated from the fluid by gravitational forces acting on the particles. The particles can be solid particles or liquid drops. Settling and sedimentation are used to remove the particles from the fluid. It is also possible to separate the particles into fractions of different size or density. Particles that will not settle by gravitational force can be separated by centrifugal force. If the purpose is to separate the particles i t f ti ti l into fractions of diff f different sizes, particles of uniform d it b t t i ti l f if density but different sizes are suspended in a liquid and settle at different rates. Particles that settle in given time intervals are collected and weighed. Centrifuge SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 30. PARTICLE SIZE DISTRIBUTION PARTICLE SIZE DISTRIBUTION 3. Screening: This is a unit operation in which various sizes of g p solid particles are separated into two or more fractions by passing over screen(s). A dispersing agent may be added to improve sieving characteristics Screen is the surface characteristics. containing a number of equally sized openings. The openings are square. Each screen is identified in meshes per inch. Mesh is defined as open spaces in a network. The smallest mesh means largest clear opening. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 31. PARTICLE SIZE DISTRIBUTION PARTICLE SIZE DISTRIBUTION • A set of standard screens is stacked one upon the other with p the smallest opening at the bottom and the largest at the top placed on an automatic shaker for screen analysis (sieve analysis). analysis) In screen analysis the sample is placed on the top analysis, screen and the stack is shaken mechanically for a definite time. The particles retained on each screen are removed and weighed. Then, the mass fractions of particles separated are calculated. Any particles that pass through the finest screen p are collected in a pan at the bottom of the stack. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 32. PARTICLE SIZE DISTRIBUTION PARTICLE SIZE DISTRIBUTION • Particle size analysis can be done in two different ways: l l b d d ff – differential analysis  – cumulative analysis. y • In differential analysis, mass or number fraction in each size  increment is plotted as a function of average particle size or  particle size range. The results are often presented as a  ti l i Th lt ft t d histogram as shown in Fig. 6 with a continuous curve to  approximate the distribution. If the particle size ranges are all  equal as in this figure, the data can be plotted directly. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 33. PARTICLE SIZE DISTRIBUTION PARTICLE SIZE DISTRIBUTION Fig. 6 Particle size  g distribution using  differential analysis. • However it gives a false impression if the covered range of particle However, it gives a false impression if the covered range of particle  sizes differs from increment to increment. Less material is retained  in an increment when the particle size range is narrow than when it  is wide. Therefore, average particle size or size range versus is wide Therefore average particle size or size range versus should be plotted, where       is the mass fraction and                          is the particle size range in increment i (McCabe et al., 1993). SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 34. PARTICLE SIZE DISTRIBUTION PARTICLE SIZE DISTRIBUTION • Cumulative analysis is obtained by adding consecutively the adding, consecutively, individual increments, starting with that containing the smallest particles and plotting the cumulative sums against the maximum particle diameter in the increment. In a cumulative analysis, the data may appropriately be represented by a continuous curve. p y • Table 1 shows a typical screen analysis. Cumulative plots are made using the second and fifth columns of Table 1 (Fig. 7) SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 35. PARTICLE SIZE DISTRIBUTION PARTICLE SIZE DISTRIBUTION Fig. 7 Particle size distribution using  cumulative analysis SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 36. PARTICLE SIZE DISTRIBUTION PARTICLE SIZE DISTRIBUTION • Calculations of average particle size, specific surface area, or g p , p , particle population of a mixture may be based on either a differential or a cumulative analysis. In cumulative analysis, the assumption of “all particles in a single fraction are equal in all size” is not required. Therefore, methods based on the cumulative analysis are more precise than those based on differential analysis. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 37. PARTICLE SIZE DISTRIBUTION PARTICLE SIZE DISTRIBUTION • The specific surface area is defined as the total surface area of p a unit mass of particles. • For constant density (ρp) and sphericity , specific surface area (A ) of th mixture i (Aw f the i t is: where SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 38. PARTICLE SIZE DISTRIBUTION PARTICLE SIZE DISTRIBUTION • If the cumulative analysis is used, specific surface area of the y , p mixture is found by integrating with respect to mass fraction between the limits of 0 to 1 (McCabe & Smith, 1976): • Average particle diameter of a mixture can be calculated in Average particle diameter of a mixture can be calculated in  different ways. The most commonly used one is the volume  surface mean diameter (Sauter mean diameter). It is used if  the mass fraction of particles in each fraction is known. For  h f i f i l i hf i i k F differential analysis: SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 39. PARTICLE SIZE DISTRIBUTION PARTICLE SIZE DISTRIBUTION • For cumulative analysis: y • Mass mean diameter can also be calculated if the mass fractions of particles in each fraction are known For known. differential analysis: • For cumulative analysis: SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 40. PARTICLE SIZE DISTRIBUTION PARTICLE SIZE DISTRIBUTION • If the number of particles in each fraction is known,  p , arithmetic mean diameter is used. For differential analysis: where • For cumulative analysis: For cumulative analysis: SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 41. PARTICLE SIZE DISTRIBUTION PARTICLE SIZE DISTRIBUTION • The number of particles in the mixture can be calculated from  p either differential or cumulative analysis using Eqs. (1.25) and  (1.26), respectively: • where  is the volume shape factor, which is defined by the  p , y ratio of volume of a particle (Vp) to its cubic diameter: SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 42. PARTICLE SIZE DISTRIBUTION PARTICLE SIZE DISTRIBUTION • Dividing the total volume of the sample by the number of  g p y particles in the mixture gives the average volume of a particle.  The diameter of such a particle is the volume mean diameter,  which is found from: which is found from: For the cumulative analysis, volume mean diameter is  determined by integrating with respect to mass fraction between  the limits of 0 and 1: SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 43. VOLUME • Volume is defined as the amount of three‐dimensional space p occupied by an object, usually expressed in units that are the cubes of length units, such as cubic inches and cubic centimeters, centimeters or in units of liquid measure such as gallons and measure, liters. • In the SI system, the unit of volume is m3. • Volume is an important quality attribute in the food industry. • It appeals to the eye, and is related to other quality parameters. F For i instance, i i i it is inversely correlated with l l d ih texture. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 44. VOLUME • Volume of solids can be determined by using the following  y g g methods: 1. Volume can be calculated from the characteristic  dimensions in the case of objects with regular shape. di i i th f bj t ith l h 2. Volumes of solids can be determined experimentally  by liquid, gas, or solid displacement methods. y q ,g , p 3. Volume can be measured by the image processing  method. An image processing method has been recently  developed to measure volume of ellipsoidal agricultural  d l d l f lli id l i l l products such as eggs, lemons, limes, and peaches  (Sabliov, Boldor, Keener, & Farkas, 2002). SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 45. VOLUME Liquid Displacement Method • If the solid sample does not absorb liquid very fast the liquid If the solid sample does not absorb liquid very fast, the liquid  displacement method can be used to measure its volume.  • In this method, volume of food materials can be measured by  y pycnometers (specific gravity bottles) or graduated cylinders. • The pycnometer has a small hole in the lid that allows liquid  to escape as the lid is fitted into the neck of the bottle (Fig. 8). to escape as the lid is fitted into the neck of the bottle (Fig 8) Fig. 8 Pycnometer (specific gravity  bottle) SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 46. VOLUME Liquid Displacement Method • The bottle is precisely weighed and filled with a liquid of The bottle is precisely weighed and filled with a liquid of  known density.  • The lid is placed on the bottle so that the liquid is forced out  p q of the capillary.  • Liquid that has been forced out of the capillary is wiped from  the bottle and the bottle is weighed again.  the bottle and the bottle is weighed again • After the bottle is emptied and dried, solid particles are  p placed in the bottle and the bottle is weighed again.  g g • The bottle is completely filled with liquid so that liquid is  forced from the hole when the lid is replaced.  SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 47. VOLUME Liquid Displacement Method • The bottle is reweighed and the volume of solid particles can The bottle is reweighed and the volume of solid particles can  be determined from the following formula: where SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 48. VOLUME Liquid Displacement Method • The volume of a sample can be measured by direct measurement of volume of the liquid displaced by using a graduated cylinder or burette. • The difference between the initial volume of liquid in a graduated cylinder and the volume of liquid with immersed material gives us the volume of the material. • That is the increase in volume after addition of solid sample is is, equal to the solid volume. • In the liquid displacement method, liquids used should have a low  surface tension and should be absorbed very slowly by the  surface tension and should be absorbed very slowly by the particles.  • Most commonly used fluids are water, alcohol, toluene, and  tetrachloroethylene. For displacement, it is better to use a  tetrachloroethylene For displacement it is better to use a nonwetting fluid such as mercury.  SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 49. VOLUME Liquid Displacement Method • For larger objects a platform scale can be used (Mohsenin objects, (Mohsenin, 1970) (Fig. 9). The sample is completely submerged in liquid such that it does not make contact with the sides or bottom of the beaker. Weight of the liquid displaced by the solid sample is divided by its density. The method is based on the Archimedes p principle, which states that a body immersed in a fluid will p , y experience a weight loss in an amount equal to the weight of the fluid it displaces. That is, the upward buoyancy force exerted on a body immersed in a liquid is equal to the weight of the displaced liquid. Fig. 9 Platform scale for  measurement of volume of large  objects. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 50. VOLUME Liquid Displacement Method where SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 51. VOLUME Liquid Displacement Method • Liquids having a density lower than that of sample should be used if partial floating of the sample is observed. The sample is forced into the liquid by means of a sinker rod if it is lighter or it is suspended with a string if it is heavier than the liquid. If the sample is forced into the fluid using a sinker rod, it should be taken into account in the measurement as: SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 52. VOLUME Gas Displacement Method • Volumes of particulate solids and materials with irregular shape can be determined by displacement of gas or air in pycnometer (Karathanos & Saravacos, 1993). • The most commonly used gases are helium and nitrogen. • The pycnometer consists of two airtight chambers of nearly equal volumes V1 and V2,that are connected with small volumes, that small‐ diameter tubing (Fig. 10). Fig. 10 Gas comparison  pycnometer. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 53. VOLUME Gas Displacement Method • The material to be measured is placed in the second chamber chamber. • The exhaust valve (valve 3) and the valve between the two chambers (valve 2) are closed. ( ) • The inlet valve (valve 1) is opened and the gas is supplied to the first chamber until the gauge pressure is increased up to a suitable value (e g 700 1000 Pa) (e.g., 700–1000 Pa). • Then, the inlet valve is closed and the equilibrium pressure is g g y recorded. Assuming that the gas behaves ideally: SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 54. VOLUME Gas Displacement Method where • After the equilibrium pressure is recorded the valve between recorded, the two chambers is opened (valve 2) and the gas within the first chamber is allowed to fill the empty spaces (pores) in the second chamber. d h b • The new pressure (P2) is recorded. When valve 2 is opened, total mass of gas (m) is divided into two, one of which fills the first tank (m1) and the other fills the pore space of the second tank (m2). SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 55. VOLUME Gas Displacement Method • Assuming that the system is isothermal: • where Va2 is the volume of the empty spaces within the second chamber and can be expressed as: • where Vs i the volume of the solid ( 3) and can b calculated h is h l f h lid (m d be l l d from the following equation: SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 56. VOLUME Gas Displacement Method • The errors in this method may come from not taking into account the volumes of the tubing connecting the chambers. • M Moreover, although the calculation assumes an id l gas, the lh h h l l i ideal h air does not exactly follow the ideal gas law. • In addition, the equalization in pressures between the two chambers is not isothermal. • To eliminate these errors, the instrument should be calibrated by i b using an object of precisely k bj f i l known volume. l SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 57. VOLUME Solid Displacement Method • The volume of irregular solids can also be measured by sand sand, glass bead, or seed displacement method. • Rapeseeds are commonly used for determination of volume p y of baked products such as bread. • In the rapeseed method, first the bulk density of rapeseeds is determined by filling a glass container of known volume uniformly with rapeseeds through tapping and smoothing the surface with a ruler. • All measurements are done until the constant weight is reached between the consecutive measurements. • Th d iti of th seeds are calculated f The densities f the d l l t d from th measured the d weight of the seeds and volume of the container. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 58. VOLUME Solid Displacement Method • The sample and rapeseeds are placed together in the container. The container is tapped and the surface is smoothed with a ruler. Tapping and smoothing are continued until a constant weight is reached between three consecutive measurements. The volume of the sample is calculated as follows: where SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 59. VOLUME Expressions of Volume • Volume can be expressed in different forms The form of the forms. volume must be well defined before the data are presented. The most commonly used definitions are: – Solid volume (Vs ) is the volume of the solid material (including water) excluding any interior pores that are filled with air. It can be determined by the gas displacement method in which the gas is capable of penetrating all open pores up to the diameter of the gas molecule. – A Apparent volume (Vapp) i the volume of a substance i l di all pores l is h l f b including ll within the material (internal pores). Apparent volume of regular geometries can be calculated using the characteristic dimensions. Apparent volume of irregularly shaped samples may be determined by solid or liquid displacement methods. – Bulk volume (Vbulk) is the volume of a material when packed or stacked in bulk. It includes all the pores enclosed within the material (internal pores) and also the void volume outside the boundary of individual particles when stacked in bulk (external pores). SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 60. POROSITY • Porosity is an important physical property characterizing the texture and the quality of dry and intermediate moisture foods. • Porosity data is required in modeling and design of various heat and mass transfer processes such as drying, frying, baking, heating, cooling, baking heating cooling and extrusion extrusion. • It is an important parameter in predicting diffusional properties of cellular foods. • Porosity (ε) is defined as the volume fraction of the air or the void fraction in the sample and expressed as: SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 61. POROSITY SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 62. POROSITY • There are different methods for determination of porosity, which can b summarized as f ll i hi h be i d follows: 1. Direct method: In this method, porosity is determined from the  difference of bulk volume of a piece of porous material and its  volume after destruction of all voids by means of compression.  volume after destruction of all voids by means of compression This method can be applied if the material is very soft and no  attractive or repulsive force is present between the particles of  solid. 2. Optical method: In this method, porosity is determined from the  microscopic view of a section of the porous medium. This method  is suitable if the porosity is uniform throughout the sample, that  is, the sectional porosity represents the porosity of whole  , p y p p y sample. Pore size distribution can be determined if a suitable  software is used to analyze images. 3.  Density method: In this method, porosity is calculated from the  measured densities: measured densities: SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 63. POROSITY DENSITY METHOD • Porosity due to the enclosed air space within the particles is named apparent porosity (εapp) and defined as the ratio of total enclosed air space or voids volume to the total volume. It can also be named internal porosity. Apparent porosity is calculated from the measured solid (ρx) and apparent density (ρapp)data as: pp y ) • or from the specific solid and apparent volumes as: SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 64. POROSITY DENSITY METHOD • Bulk porosity (εbulk) which can also be called external or Bulk porosity (ε ), which can also be called external or  interparticle porosity, includes the void volume outside the  boundary of individual particles when stacked as bulk and  calculated using bulk and apparent densities as: • or from the specific bulk or from the specific bulk  volumes as: and apparent  and apparent • Then, total porosity when material is packed or stacked as  bulk is: SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 65. POROSITY DENSITY METHOD • Pores within the food materials (internal pores) can be divided into three groups: closed pores that are closed from all sides, blind pores that have one end closed, and open or flow‐ through pores where the flow typically takes place (Fig. 1.11). Fig. 11 Different kinds  of pores. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 66. POROSITY DENSITY METHOD • Since the apparent porosity is due to the enclosed air space within the particles and there are three different forms of pores within the particles, it can be written as: where • Then total porosity can also be written as: Then, SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 67. POROSITY GAS PYCNOMETER METHOD 4. 4 Gas pycnometer method: Porosity can be measured directly by measuring the volume fraction of air using the air comparison pycnometer. Remembering Eq. (1.49): Porosity can be calculated from Eq. (1.49) as: 5. 5 Using porosimeters: Porosity and pore size distribution can be determined using porosimeters, which are the instruments based on the principle of either li id i i h liquid intrusion i i into pores or li id extrusion liquid i from the pores. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 68. POROSITY GAS PYCNOMETER METHOD • For extrusion porosimetry, wetting liquids are used to fill the pores in the porous materials. Liquid is displaced from the pores by applying differential pressure on the sample and volume of extruded liquid is measured. • Extrusion methods can be categorized as capillary flow porosimetry and liquid extrusion porosimetry. Capillary flow porosimetry is a liquid  extrusion method in which the differential gas pressure and flow rates  g p through wet and dry samples are measured (Fig. 12). Capillary flow  porosimetry can measure pore size between 0.013 and 500 μm (Jena &  Gupta, 2002). Fig. 12 Principle of  capillary flow  capillary flow porosimetry SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 69. POROSITY GAS PYCNOMETER METHOD • For large pore sizes, liquid extrusion porosimetry is preferred.  g p , q p y p Liquid extrusion porosimetry can be used for pore sizes of  0.06 to 1000 μm. Fig. 13 Principle of liquid  extrusion prosimetry SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 70. POROSITY GAS PYCNOMETER METHOD • In intrusion porosimetry, as intrusion liquid mercury, oil, or water is used. • In intrusion porosimetry, liquid is forced into pores under pressure and intrusion volume and pressure are measured. • Mercury intrusion porosimetry can measure pores in the size range of 0.03 to 200 μm while nonmercury intrusion porosimetry can measure pores in the size range of 0.001 to 20 μm. • This method can detect pore volume, pore diameter, and surface area of through and blind pores. g p • Since very high pressures are required in mercury intrusion, the pore structure of the samples can be distorted. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 71. POROSITY • Porosity may show a maximum or minimum as a function of y y moisture content. • It may also decrease or increase exponentially during drying without showing an optimum point. ith t h i ti i t • The porosity of the apple rings increased linearly when moisture content decreased during drying and then reached a g y g constant value (Bai, Rahman, Perera, Smith, & Melton, 2002). • A linear increase in the bulk porosity was also observed during drying f h d i of the starch samples (M h l (Marousis & S i Saravacos, 1990) 1990). SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 72. POROSITY • The drying method is also important in affecting porosity. y g p gp y • Freeze drying was found to produce the highest porosity, whereas in conventional air drying the lowest porosity was observed as compared t vacuum, microwave, and osmotic b d d to i d ti drying of bananas, apples, carrots, and potatoes (Krokida & Maroulis, 1997). • Rahman (2003) developed a theoretical model to predict porosity in foods during drying assuming that volume of pores formed is equal to the volume of water removed during drying. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 73. POROSITY • The presence of pores and degree of porosity affect the p p g p y mechanical properties of food materials. • It has been shown that mechanical properties of extruded food f d products are affected b porosity (G d t ff t d by it (Guraya & T l d Toledo, 1996). • Mandala and Sotirakoglou (2005) mentioned that crumb and g ( ) crust texture of breads could be related to porosity. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 74. POROSITY • Porosity is also important in frying, since it affects oil uptake  y p y g, p of the product.  • A linear relationship was found between oil uptake during  frying and porosity prior to frying (Pinthus,Weinberg, & Saguy,  f i d it i t f i (Pi th W i b &S 1995).  • Porosity increased during frying of restructured potato  y g y g p product and after a short initial period, it was found to be  linearly correlated with oil uptake. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 75. DETERMINATION OF VOLUME OF  DETERMINATION OF VOLUME OF DIFFERENT KINDS OF PORES • Total specific pore volume within the material  can be  calculated if the specific volume of all kinds of pores—closed  pores          , blind pores,  pores blind pores ,and flow‐through pores  and flow through pores are known: • Total specific pore volume within the material can be  calculated by measuring specific bulk  and the specific  solid volume determined after compacting the sample to  solid volume determined after compacting the sample to exclude all the pores       : SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 76. DETERMINATION OF VOLUME OF  DETERMINATION OF VOLUME OF DIFFERENT KINDS OF PORES • The difference between the specific solid volume determined  by gas pycnometer and specific solid volume after  compacting the sample        , gives the volume of closed pores  compacting the sample gives the volume of closed pores since in a gas pycnometer, gas enters into the open and blind  pores but not the closed ones. From these results, the specific  volume of closed pores can be calculated: • Volume of flow through or open pores of the sample Volume of flow through or open pores of the sample,   ,  can be measured directly using liquid extrusion porosimetry. From Eq. (1.51), the specific volume of the blind pores is: SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 77. DETERMINATION OF VOLUME OF  DETERMINATION OF VOLUME OF DIFFERENT KINDS OF PORES • Substituting Eqs. (1.52) and (1.53) into Eq. (1.54): • The fraction of open, closed, or blind pores can be calculated  by dividing the specified pore volume by total pore volume. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 78. SHRINKAGE • Shrinkage is the decrease in volume of the food S age s t e dec ease o u e o t e ood during processing such as drying. g • When moisture is removed from food during drying, there is a pressure imbalance between inside and outside of the food. • This generates contracting stresses leading to material shrinkage or collapse (Mayor & Sereno, 2004). 2004) • Shrinkage affects the diffusion coefficient of the material and therefore has an effect on the drying rate. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 79. SHRINKAGE SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 80. SHRINKAGE • Apparent shrinkage is defined as the ratio of Apparent shrinkage is defined as the ratio of  the apparent volume at a given moisture  content to the initial apparent volume of  content to the initial apparent volume of materials before processing: when SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 81. SHRINKAGE • Shrinkage is also defined as the percent change from the initial apparent volume. • Two types of shrinkage are usually observed in food materials. If there is a uniform shrinkage in all dimensions of the material it is called material, isotropic shrinkage. • Th The nonuniform shrinkage i if hi k in diff different dimensions, on the other hand, is called anisotropic shrinkage. i i hi k SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 82. REFERENCES 1. 2. 3. 4. 5. 6. Bayram, M. (2005). Determination of the sphericity of granular food  materials. Journal of Food Engineering, 68, 385–390. Karathanos,V.T.,&Saravacos, G.D. (1993). Porosity and pore size  distribution of starch materials. Journal of Food Engineering, 18, 259 distribution of starch materials Journal of Food Engineering 18 259– 280. McCabe, W.L, Smith, J.C., & Harriot, P. (1993). Unit Operations of  Chemical Engineering, 5th ed. Singapore: McGraw‐Hill. Mohsenin, N.N. (1970). Physical Properties of Plant and Animal  h ( ) h l f l d l Materials. New York: Gordon and Breach. Maduako, J.N.,&Faborode, M.O. (1990). Some physical properties of  p p yp g f f gy, , cocoa pods in relation to primary processing. Ife Journal of Technology, 2,  1–7. Sabliov, C.M., Boldor, D.,Keener, K.M.,&Farkas, B.E. (2002). Image  processing method to determine surface area and volume of axi‐ symmetric agricultural products. International Journal of Food  symmetric agricultural products International Journal of Food Properties, 5, 641–653. SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 83. THANK YOU SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES
  • 84. MASS AND DENSITY
  • 85. MASS • Mass is a measure for inertia and heaviness of a body. Heaviness i caused b the E h’ gravitational attraction f H i is d by h Earth’s i i l i for a body. The force between the body of interest and the planet Earth is called the weight force of the body. Mathematically, this force can be expressed as the product of the body’s mass and the Earth’s acceleration due to gravity, as shown by equation (3 1) (3.1). (3.1) • where MASS & DENSITY
  • 86. MASS • The density of planet Earth varies with location and the planet is slightly pear shaped and not in the shape of a perfect pear‐shaped sphere, the value of gravitational acceleration differs slightly with location on the Earth’s surface. Considering the rotation of the planet a body resting at the equator will have a greater planet, tangential speed and centrifugal force than in regions far north or south of the equator. • The value of Earth’s gravitational acceleration in Zurich, h l f h’ l l h Switzerland is used as a standard for calculations, and is called standard gravitational acceleration having the value g = 2 9.80665m∙ s−2.When a balance which was adjusted in Zurich, is taken to another place on the Earth, but is not corrected for the local gravitational acceleration, the displayed weight may be in error. MASS & DENSITY
  • 87. MASS • Table 3.1 illustrates this concept for a body having a mass of  1kg. To avoid erroneous weight measurements of this type, a  1k T id i h f hi balance has to be recalibrated at the location in which it will  be used. For this purpose, commercial mass standards are  produced with the help of national standards organizations  around the world.  Table 3.1  Weighing a 1 kg mass in different place MASS & DENSITY
  • 88. WEIGHING AND ATMOSPHERIC BUOYANCY • A balance is an instrument measuring the weighing force of a g g g body. However, it usually does not display a force signal (e.g. newtons), but a mass signal (e.g. kilograms).This is due to the principle of calibration used for balances: A mass standard is placed on the balance that causes a deformation, which can be read as an angle, a distance or an electric voltage, depending on the type of balance. • A calibration has to be performed for every type of sensing/measuring instrument For this purpose appropriate instrument. purpose, respective standard materials and procedures are needed, that make it possible to perform calibration of an instrument in i any l b t laboratory. MASS & DENSITY
  • 89. WEIGHING AND ATMOSPHERIC BUOYANCY • From a scientific point of view the calibration procedure described for a balance is basically to use the instrument as a “force meter,” then divide the force G measured by the value of the local gravitational acceleration g, and display the result (equation volume of h d f hydrometer i m3) t in ). (3.2) • Since the middle ages the weight of a body has been a manifold of a reference weight. So weighing is simply a comparison to a given mass standard. From this point of view weighing is dividing the weight force of the given body and weight force of a mass standard and the result is a dimensionless number. That is the principle of all mechanical and electronic balances up to today, and a consequence of lacking an expression for mass with fundamental natural constants. MASS & DENSITY
  • 90. WEIGHING AND ATMOSPHERIC BUOYANCY (3.3) • where MASS & DENSITY
  • 91. WEIGHING AND ATMOSPHERIC BUOYANCY • Most weight measurements are carried out with body and balance surrounded by atmospheric air, which is a gaseous fluid possessing density. Only bodies of material with density greater than atmospheric air at the Earth’s surface can impart a force when p p placed upon a balance. • For example a rubber balloon filled with helium gas (less dense than air) possesses mass but it will not rest on a balance It will rise mass, balance. upward into the atmosphere in search of an altitude at which the density of the atmosphere is in equilibrium with itself. His upward force caused the density of the Earth’s atmosphere is known as Earth s buoyancy. This atmospheric buoyancy causes a body resting on a balance when surrounded by atmospheric air to exhibit a slightly smaller weight measurement than if it were in a vacuum (Figure 3.1). MASS & DENSITY
  • 92. WEIGHING AND ATMOSPHERIC BUOYANCY Figure 3.1  A balance is adjusted to zero weight (picture I). A mass of 1 kg is weight  in atmosphere (picture II) and in vacuum (picture III) MASS & DENSITY
  • 93. WEIGHING AND ATMOSPHERIC BUOYANCY • The calculation needed to correct for this buoyancy effect in y y order to yield the true mass of a body is called atmospheric buoyancy correction. The true mass of a body mK is the product of the displayed mass m*K and a correctional factor K m K. The value of the correctional factor K depends on the density of the air surrounding the balance. Because weight measurement is a comparison of a body of interest and a mass standard, the densities of both materials also influence ( q ( ) ( ) the correctional factor (equations (3.4) to (3.6): (3.4) MASS & DENSITY
  • 94. WEIGHING AND ATMOSPHERIC BUOYANCY (3.5) (3.6) • Wh Where MASS & DENSITY
  • 95. WEIGHING AND ATMOSPHERIC BUOYANCY • The density of air depends on its pressure, temperature, y p p , p , humidity and its concentration of CO2. • For practical purposes, the density of atmospheric air at normal room t l temperature and sea l l ( t d d conditions) t d level (standard diti ) can be taken to be approximately 1.2 kg ∙ m−3. A simple approach to calculate the density of air more precisely is given by equation (3.7): (3.7) • where MASS & DENSITY
  • 96. WEIGHING AND ATMOSPHERIC BUOYANCY • In contrast to air, the density of water is 1000 times greater , y g (1000 kg ∙ m−3). Therefore, the density range of most food, agricultural and biological materials is in the same order of 3 magnitude as that of water about 1200 ± 300 kg ∙ m−3. The water, densities of materials with high water content are in a range more closely to that of water (between 1000 and 1100 kg ∙ 3 m−3) while dry materials like agricultural grains, seeds and dry beans consisting of proteins, carbohydrates, starch or g g cellulose are often in the range 1400–1600 kg ∙ m−3. MASS & DENSITY
  • 97. DENSITY • The density of a substance is the quotient of mass over y q volume. The standard international (SI) units for expressing density are kg ∙ m−3.The same definition is valid for solid, liquid, liquid gaseous and disperse systems like foams bulk goods or foams, powders. • The reciprocal of density is called specific volume and the units are m3 ∙ kg−1 (equations (3.8) and (3.9). (3.8) (3.9) MASS & DENSITY
  • 98. DENSITY • where MASS & DENSITY
  • 99. DENSITY TEMPERATURE DEPENDENCY OF DENSITY • Many materials undergo thermal expansion when heated, meaning they increase in volume without any change in mass. For this reason, the density of a given material often depends on temperature. Since the volume of a material normally increases with temperature, the density usually decreases with t ith temperature. Thi effect i much l t This ff t is h larger i gaseous in systems than in liquid or solid systems. MASS & DENSITY
  • 100. DENSITY TEMPERATURE DEPENDENCY OF DENSITY – IDEAL GAS • For many engineering applications air can be assumed to For many engineering applications air can be assumed to  behave as an ideal gas, meaning that the ideal gas law can be  used for calculating the density of air as a function of  temperature and pressure (equations (3.10) and (3.11). (3.10) (3.11) • where MASS & DENSITY
  • 101. DENSITY TEMPERATURE DEPENDENCY OF DENSITY – IDEAL GAS  • In case of low temperatures and humid air the ideal gas law loses accuracy, and will lead to error. To calculate the density of air more precisely as a function of water vapor partial pressure and atmospheric pressure, equation (3.7) can be used. MASS & DENSITY
  • 102. DENSITY TEMPERATURE DEPENDENCY OF DENSITY – SOLID AND LIQUIDS • The density of liquids and solids is a function of temperature. Small changes in volume caused by temperature change can be calculated with the aid of the thermal expansion coefficient: (3.12) • where MASS & DENSITY
  • 103. DENSITY TEMPERATURE DEPENDENCY OF DENSITY – SOLID AND LIQUIDS • Water shows abnormal behavior in a narrow range of temperature near its freezing point at atmospheric pressure. When lowering the temperature of water from 4 ◦C and 0◦C, C 0 C, the density of water actually decreases rather than increases. This abnormal behavior of water (see Figure 3.2 and Figure 3.3 is taken into 3 3 i t k i t account within th polynomial f ti of t ithi the l i l function f Bertsch (1983) for calculation of the density of liquid water (equation (3.13): (3.13) MASS & DENSITY
  • 104. DENSITY TEMPERATURE DEPENDENCY OF DENSITY – SOLID AND LIQUIDS Fig. 3.2 Normal (N) and abnormal (H O)  Fig 3 2 Normal (N) and abnormal (H2O) thermal expansion (schematic) Fig. 3.3 Abnormality of water (H2O): g y ( ) Temperature dependency of density compared to normal behavior (N) MASS & DENSITY
  • 105. DENSITY TEMPERATURE DEPENDENCY OF DENSITY – SOLID AND LIQUIDS • A further abnormality of water is that the solid phase (ice) has a lower density than the liquid phase at the same temperature. This behavior has important consequences for the biosphere. Because of this temperature dependency of density, control or measurement and recording of temperature i necessary when d it i measured f t t is h density is d for process control and quality control purposes. MASS & DENSITY
  • 106. DENSITY PRESSURE DEPENDENCY OF DENSITY • Materials are compressible. On application of pressure their volume decreases, causing the density to be a function of pressure as well as temperature. Gases are far more compressible than liquids and solids. Over a normal temperature range many gases can be assumed to behave like ideal id l gases. MASS & DENSITY
  • 107. DENSITY PRESSURE DEPENDENCY OF DENSITY – IDEAL GAS • For ideal gases the density is directly proportional to the pressure: ( (3.14) ) (3.15) (3.16) • so the density of the ideal gas is (3.17) MASS & DENSITY
  • 108. DENSITY PRESSURE DEPENDENCY OF DENSITY – IDEAL GAS • The negative slope of the volume–pressure curve divided by the initial volume is called the compressibility . It is the inverse compression modulus K of a material. (3.18) (3.19) MASS & DENSITY
  • 109. DENSITY PRESSURE DEPENDENCY OF DENSITY – LIQUIDS AND SOLIDS • Ideal liquids and solids show an elastic behavior. That means their volume can decrease by a certain amount when a pressure is applied, but that it will fully recover to the initial volume when the pressure is restored. For this type of material the change in volume on increasing the pressure can be l l t d based b calculated b d on equation (3 20) ti (3.20): (3.20) • with (2.8) and because of m = const the relative density is: (3.21) MASS & DENSITY
  • 110. DENSITY PRESSURE DEPENDENCY OF DENSITY – LIQUIDS AND SOLIDS • where MASS & DENSITY
  • 111. DENSITY PRESSURE DEPENDENCY OF DENSITY – LIQUIDS AND SOLIDS • Liquids and solids with very low compressibility show a very small volume reduction and often are treated in practice as incompressible materials. Water has very low compressibility with a value of ≈ 5x10−10 Pa−1. So, up to pressures in the order of 10 MPa (100 bar), the reduction of the volume in water is so small th t it can b neglected. Alth ll that be l t d Although i hi h pressure h in high processing of food, where the pressure will range to some 100MPa, the compressibility of water cannot be neglected. MASS & DENSITY
  • 112. DENSITY SPECIFIC GRAVITY (RELATIVE DENSITY) • The ratio of the absolute density of a material to the density of a reference material is called relative density d. Water at 4 °C or 20°C is most often used as the reference material for C 20 C this purpose. In the USA and Canada, when water is used as the reference standard, the term“ relative density” is not used, and i replaced b th t d d is l d by the term“ specific gravity.” Si “ ifi it ” Since water is nearly always chosen as the reference standard world‐wide, for practical purposes the terms “relative density” and “specific gravity” may be considered as synonymous. (3.22) (3 22) MASS & DENSITY
  • 113. DENSITY SPECIFIC GRAVITY (RELATIVE DENSITY) • Where • It is important to note that both density and specific gravity (relative density) relate to the same physical property. However, density d i must b reported i di be d in dimensional units of mass per unit i l i f i volume (e.g. g ∙ cm−3 or kg ∙ m−3), while specific gravity (relative density) is a ratio of densities, and is always a dimensionless number. In the case where density is being reported in dimensional units of g ∙cm−3 and with the density of the reference material being 1 g ∙ cm−3 or nearly 1 g ∙ cm−3 it is interesting to note that numerical values of both density and specific gravity (relative density)will be the same, respectively. MASS & DENSITY
  • 114. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY • Table 3.2 shows examples of different methods used for density measurement. MASS & DENSITY
  • 115. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY PYCNOMETRIC MEASUREMENT • By weighing a known volume of a liquid, the density of that liquid can be measured in a simple way Glass bulbs with way. precisely known volume that are used for this purpose are called pycnometers. A pycnometer can also be any other instrument d i d f the same purpose that may h i designed for h h have sample chambers of precisely known volume, but made of other materials (not glass bulbs). The glass bulb or sample chamber will have a marker to which the liquid sample must be carefully filled. Then the density of the fluid can be calculated by: (3.23) MASS & DENSITY
  • 116. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY PYCNOMETRIC MEASUREMENT • Because of thermal expansion of the glass, the pycnometer volume is known for the temperature at which it was calibrated, only. So, for measurement of the absolute density, pycnometers should be used at the same temperature at which they were calibrated. hi h h lib d • Another way is to measure the relative density (specific gravity) rather than the absolute density. For this purpose, the pycnometer is weighed with the sample liquid and again weighed with the reference liquid (often water).The ratio of both weights gives the relative density d or specific gravity of d, the sample. MASS & DENSITY
  • 117. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY PYCNOMETRIC MEASUREMENT (3.24) (3 24) where MASS & DENSITY
  • 118. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY PYCNOMETRIC MEASUREMENT • Once the relative density d, or specific gravity, of the sample is known, known and the density of the reference material is known from the literature, the absolute density of the sample can be calculated: (3.25) MASS & DENSITY
  • 119. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY PYCNOMETRIC MEASUREMENT • Fig. 3.4 and 3.5 show different designs of glass pycnometers Fig. 3.4  Pycnometer designs: (a) Reischauer, (b) Bingham, (c) Gay‐Lussac,  (d) Sprengel,(e) Lipkin, (f) Hubbard MASS & DENSITY
  • 120. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY PYCNOMETRIC MEASUREMENT Fig. 3.5  Examples of pycnometers . The right one is for viscous samples  and powders MASS & DENSITY
  • 121. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROSTATIC BALANCES (BUOYANCY WEIGHING) • The principle of a hydrostatic balance is based on Archimedes law of buoyancy If a body is submersed in a fluid its weight buoyancy. will be lowered because of the buoyancy force. The buoyancy force is directly proportional to the volume of the submersed body d the density f the fluid. By b d and th d it of th fl id B measurement of th t f the buoyancy force with the balance, the volume of the body can be determined quite accurately, and together with the measured mass of the body, the density is obtained. MASS & DENSITY
  • 122. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROSTATIC BALANCES (BUOYANCY WEIGHING) • A simple technique for making this type of measurement is to place a beaker partially filled with water on top of a top‐ top loading balance, with the weight of beaker and water tared‐ out to read zero on the display. Then, fully submerge the solid body beneath th water surface, t ki care th t it neither b d b th the t f taking that ith touches the bottom nor the sides of the beaker. The weight reading shown on the display of the balance will be the weight of the volume of water displaced by the solid body. Since density of water is known, the precise volume of the solid body is determined. MASS & DENSITY
  • 123. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROSTATIC BALANCES (BUOYANCY WEIGHING) (3.8) (3.26) • with ∆m as the difference in weight (in kg) of the body before and after submersion: (3.27) (3.28) (3 28) (3.29) (3.30) MASS & DENSITY
  • 124. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROSTATIC BALANCES (BUOYANCY WEIGHING) • where • S th d it f b d So the density of a body can be obtained by taking first the  b bt i d b t ki fi t th weight prior to submersion (that means weighing in air) and  its weight when submersed in a fluid with a known density F  using equation (3.30). MASS & DENSITY
  • 125. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROSTATIC BALANCES (BUOYANCY WEIGHING) • With the ratio (3.31) (3 31) • the relative density d (specific gravity) of the body is (3.32) (3.33) • That means d can be calculated very quickly after two  readings from the balance. MASS & DENSITY
  • 126. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROSTATIC BALANCES (BUOYANCY WEIGHING) • If the weight in air mL is not corrected for atmospheric buoyancy, buoyancy the density obtained by hydrostatic weighing can be called apparent density of the body. If that correction made, then mL and K will be slightly higher, and can be called true mass and t t d true d it density. • On the other hand when a body of known volume is submersed in a fluid, the difference in weight of the body in , g y air and the weight of fluid displaced by the body can be used to determine the density of the fluid, and can be calculated with equation (3 34): (3.34): (3.34) MASS & DENSITY
  • 127. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROSTATIC BALANCES (BUOYANCY WEIGHING) • Figure 3.6 shows a special design of hydrostatic balance that is  suitable for measuring the density of a solid or the density of  suitable for measuring the density of a solid or the density of the liquid in the reservoir when used with a solid body of  precisely known volume. Fig. 3.6 Hydrostatic balance design. 1: balance, 2: platform, 3: small beaker, beaker 4: large beaker 5: support beaker, bracket, 6: pan, 7: thermometer MASS & DENSITY
  • 128. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROSTATIC BALANCES (BUOYANCY WEIGHING) • To obtain the density of a solid, the sample is weighed first in air, and then it is submersed and the weight is taken again. As can be seen in Figure 3.6 there is a small pan mounted on the weighing plate of the balance. A small beaker on a cable is suspended within a larger beaker containing the fluid of interest. The large beaker is resting on a raised platform so its weight is not transmitted to the balance. • To obtain the fluid density in the large beaker, a test body with known p p g volume is first placed on the pan and its weight in air is measured. Then the test body is placed into the small beaker, submersed in the fluid and weighed once again. Then the density of the liquid is g q ( ) calculated using equation (3.34). It should be remembered that the density of the fluid is dependent on temperature so the temperature must be controlled and recorded. MASS & DENSITY
  • 129. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY MOHR‐WESTPHAL BALANCE • The Mohr–Westphal balance (see Figure 3.7) is another type  of hydrostatic balance. It is designed as a nonsymmetric beam  of hydrostatic balance It is designed as a nonsymmetric beam balance for measuring the density of liquids. Fig. 3.7  Mohr‐Westphal balance 1:  beam, 2: weights, 3: buoyancy body, 4:  beam 2: weights 3: buoyancy body 4: liquid sample MASS & DENSITY
  • 130. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY MOHR‐WESTPHAL BALANCE • At the free end of the arm of the balance a “buoyancy body” is suspended in air The buoyancy body is normally made of air. glass and can have a built‐in thermometer. Then the buoyancy body is submersed into the liquid of interest. • Because of the effect of buoyancy, the weight of the submersed glass body will appear lower than it was in air, and will bring the balance out of zero. g • The buoyancy force can be measured by successively adding small weights to the arm until the balance is restored to zero. The Th measurement i th repeated with water as a reference t is then t d ith t f liquid. MASS & DENSITY
  • 131. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY MOHR‐WESTPHAL BALANCE • The ratio of both readings provides the relative density or  specific gravity of the liquid as can be shown below. With the  specific gravity of the liquid as can be shown below With the buoyancy force (3.40) (3.41) • With the fluid of interest (3.42) • With water as reference material (3.43) (3 43) MASS & DENSITY
  • 132. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY MOHR‐WESTPHAL BALANCE • So the ratio is (3.44) • Because the volume of the glass body is the same for both readings, then (3.45) • So the specific gravity is simply (3.46) (3 46) MASS & DENSITY
  • 133. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY MOHR‐WESTPHAL BALANCE • where MASS & DENSITY
  • 134. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY MOHR‐WESTPHAL BALANCE • The result should be recorded along with the temperature of  the measurement. Often both readings are taken at 20  C and  the measurement Often both readings are taken at 20 ◦C and the result is written as d20/20. The quantity d20/4 would mean  that the density of the liquid was compared to the density of  water at 4°C: t t 4°C MASS & DENSITY
  • 135. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY MOHR‐WESTPHAL BALANCE • The Mohr–Westphal balance can also be used to measure the density of a solid sample which is submersed in a fluid with known density. For this purpose, equation (3.37) would be used to calculate the volume of the sample. MASS & DENSITY
  • 136. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROMETER • Hydrometers (Fig 3.8) are hollow glass bodies with the shape of a buoy buoy. • Hydrometers are designed with a volume to mass ratio in such a way that the glass body will float at a certain depth in the liquid under investigation. • Depending upon the density of that liquid the hydrometer will float at a higher or lower position The upper part of the position. hydrometer has a scale for reading the nonsubmersed part h of the floating glass body. MASS & DENSITY
  • 137. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROMETER • The nonsubmersed length of the hydrometer can be read with the aid of a scale on the upper part of the hydrometer hydrometer. • A weight at the bottom of the hydrometer acts like the keel of a sailboat to ensure that it will float in the liquid in a vertical orientation. • The scale can be calibrated directly in units of density or, e.g. in concentration units (Fig 3 9) 3.9). MASS & DENSITY
  • 138. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROMETER Fig. 3.8 Hydrometer. 1:scale, 2: body  (with and without thermometer), 3: keel Fig. 3.9 Reading of a hydrometer scale at the liquid surface (example) MASS & DENSITY
  • 139. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROMETER • The floating depth position of the hydrometer depends on  weight force and interfacial force (force due to surface  weight force and interfacial force (force due to surface tension). It is (3.47) • Which means: (3.48) • so (3.49) MASS & DENSITY
  • 140. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROMETER • The nonsubmersed part of the hydrometer has the length (3.50) • Which means (3.51) • Sometimes the combination of two physical properties will give the information needed about a process or a product. For example, by knowing both the density and refractive index of beer wort, the alcohol content can be calculated, and by this, the progress of fermentation MASS & DENSITY
  • 141. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROMETER MASS & DENSITY
  • 142. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROMETER • Without consideration of interfacial tension effects the  hydrometer equation simplifies to hydrometer equation simplifies to (3.52) • There are hydrometers available which are corrected for  interfacial tension offered in different range categories called – L (l L (low, 15–35mN ∙m−1), 15 35 N 1) – M(medium, 35–65 mN ∙ m−1) and  – H (high, for higher values). MASS & DENSITY
  • 143. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY SUBMERSION TECHNIQUE • Pycnometers and hydrometers do not work very well with liquids of high viscosity viscosity. • For highly viscous liquids, measurement of density can be performed with the submersion technique (see Fig 3.10). • A beaker with the viscous liquid sample is put on a balance. The display value is recorded, or the display may be set to zero (tare) (tare). • Then a test body with known volume is pressed into the sample. MASS & DENSITY
  • 144. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY SUBMERSION TECHNIQUE Fig. 3.10 Submersion technique  for density measurement. 1:  depth mark, 2: liquid sample, 3:  buoyancy body of known volume MASS & DENSITY
  • 145. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY SUBMERSION TECHNIQUE • The buoyancy force caused by the submerged test body is transferred to the balance and appears on the display as an apparent increased weight m. • This increased weight force is the buoyancy force, and is the weight of the displaced liquid, which is equal in volume to the volume of the submersed solid body: (3.53) • and (3.54) MASS & DENSITY
  • 146. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY SUBMERSION TECHNIQUE • So (3.55) • where MASS & DENSITY
  • 147. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY SUBMERSION TECHNIQUE • For precision measurement, the buoyancy body can be a hollow metal sphere with calibrated volume To avoid errors volume. from buoyancy of the mounting rod there is normally a depth mark on the rod which indicates the right depth position for immersion so th t th submerged section of rod i accounted i i that the b d ti f d is t d for in the calibrated volume. MASS & DENSITY
  • 148. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS • Many agricultural materials and food and feed ingredients are in the form of granular materials (grains meals and powders) (grains, powders), which are bulk solids made up of small particles. • The weight or size of the individual particles within any of these types of materials may vary over a large range e.g. from frozen diced vegetables to corn cornels to fine powder p particles. • The term “solid density” means the density of the solid material of which a particle is made, no matter what type of fluid fl id or other material may exist b t th t i l i t between th particles. the ti l MASS & DENSITY
  • 149. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS • Solid particles contain pores or hollow cavities filled with gases or liquids this contributes to the density of the solid liquids, solid. • When pores or cavities occur, it is important to state whether they are closed or open. If they are closed, meaning they are located completely within the solid particle, they belong to the solid. If they are open to the surroundings at the particle surface, e.g. the atmosphere, they do not belong to the solid , g p , y g body. • To avoid communication errors the density of solids should be given with a note lik “i l di pore volume” or “ ith t i ith t like “including l ” “without pore volume.” MASS & DENSITY
  • 150. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS • This can be accomplished by how the system boundaries are  defined, and can be calculated as follows: defined and can be calculated as follows: (3.8) • where MASS & DENSITY
  • 151. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS • To measure the density of a solid particle often simply means  to measure its volume, because its mass is known upon  to measure its volume because its mass is known upon weighing. • To get the volume of the solid sample without its open pores,  a pycnometer technique with an appropriate liquid can be  used.  • The liquid must not alter or dissolve the sample For this The liquid must not alter or dissolve the sample. For this  purpose, a sequence of weighings is conducted as indicated in  Figure 3.11.  MASS & DENSITY
  • 152. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS • After weighing the empty pycnometer m0 the pycnometer is  weighed with the sample m weighed with the sample mP.  • Then the pycnometer is filled up to a designated mark with an  appropriate reference liquid of known density and weighed  again mP,F.  • Finally,  the pycnometer is weighed when filled to the same  mark with only the reference liquid m mark with only the reference liquid mF: MASS & DENSITY
  • 153. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS Fig. 3.11  Pycnometer measurement of the density of a solid granular material, e.g. a  powder MASS & DENSITY
  • 154. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS • The density of the solid material then is  (3.8) (3.56) (3.57) (3.58) (3 58) MASS & DENSITY
  • 155. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS (3.59) (3.60) (3.61) MASS & DENSITY
  • 156. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS (3.62) (3.63) • where MASS & DENSITY
  • 157. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY BULK DENSITY • Powders and bulk goods contain hollow spaces or voids filled with gas normally air The density of that type of bulk gas, air. material, including the void spaces, is called bulk density. • Using equation (3.8) the bulk density can be calculated by weighing a sample of the bulk material and measurement of its volume. • The volume of the whole bulk material must be taken “as is ” as is. To measure this volume, the sample material can be poured into a beaker or cylinder up to a known volumetric mark. MASS & DENSITY
  • 158. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY BULK DENSITY • Different technique in filling the beaker or cylinder may lead to different distributions of solid particles and hollow spaces spaces. So, to get repeatable results the technique of filling has to be standardized. • To overcome problems with repeatable filling technique, the bulk material can be tapped before reading of the volume. By tapping the material, the solid particles will “settle” into the pp g , p most stable situation they can reach. The void spaces will get smaller as the solid particles settle step by step into a spatial situation where the bulk density will reach a maximum The maximum. time needed to reach this maximum depends on tapping MASS & DENSITY speed and tapping amplitude.
  • 159. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY BULK DENSITY Figure 3.12. Device for tapping of bulK goods:  1: rotating cam, 2: housing, 3: powder sample,  y g 4: cylinder, 5: overring MASS & DENSITY
  • 160. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY BULK DENSITY • Figure 3.12 shows an example of a device which can be used to measure bulk density and tapped bulk density subsequently. • First the bulk material is filled into a 1000 cm3 cylinder until it is overflowing under repeatable technique conditions. Then with aid of a flat spatula, the excess overflow of sample material is scraped away from the top of the cylinder to leave p y p y the sample perfectly level at the top, and the 1000 cm3 sample is weighed to get the bulk density. MASS & DENSITY
  • 161. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY BULK DENSITY • Now a cylindrical extension overring is slipped onto the 1000 cm3 cylinder and more sample material is filled in The in. cylinder is mounted on the tapping device and moved for a fixed number of tappings. In German testing standards a number of 2500 with a f b f ith frequency of 250 s−1 i specified. f 1 is ifi d • After this the sample material is adjusted to 1000 cm3 again and weighed. The tapped bulk density should be recorded g pp y with the parameters of its measurement. MASS & DENSITY
  • 162. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY BULK DENSITY • The difference between bulk density and maximum tapped bulk density provides information about the ability of the bulk material to be compressed by gravity or pressure. Powders can be characterized for this property by the Hausner ratio, which i th quotient of t hi h is the ti t f tapped b lk d it over untapped d bulk density t d bulk density (see Table 3.3). Table 2.7.  Characterization of  Characterization of powder flowability by Hausner ratio  MASS & DENSITY
  • 163. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY POROSITY • Also the volume of the hollow void space (pores) can be calculated. calculated The ratio of the volume of the void space (pores) and the total volume of the bulk is called porosity ɛ: (3.64) (3 64) (3.65) • because mB ≈ mS = m (3.66) MASS & DENSITY
  • 164. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY POROSITY • So ( (3.67) ) • With ɛ as the relative volume of the hollow pore space, and α as the relative volume of the solid particle space it is evident  that: (3.68) MASS & DENSITY
  • 165. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY POROSITY • where MASS & DENSITY
  • 166. THE END THE END RHEOLOGICAL PROPERTIES OF FOODS
  • 167. MASS AND DENSITY
  • 168. MASS • Mass is a measure for inertia and heaviness of a body. Heaviness i caused b the E h’ gravitational attraction f H i is d by h Earth’s i i l i for a body. The force between the body of interest and the planet Earth is called the weight force of the body. Mathematically, this force can be expressed as the product of the body’s mass and the Earth’s acceleration due to gravity, as shown by equation (3 1) (3.1). (3.1) • where MASS & DENSITY
  • 169. MASS • The density of planet Earth varies with location and the planet is slightly pear shaped and not in the shape of a perfect pear‐shaped sphere, the value of gravitational acceleration differs slightly with location on the Earth’s surface. Considering the rotation of the planet a body resting at the equator will have a greater planet, tangential speed and centrifugal force than in regions far north or south of the equator. • The value of Earth’s gravitational acceleration in Zurich, h l f h’ l l h Switzerland is used as a standard for calculations, and is called standard gravitational acceleration having the value g = 2 9.80665m∙ s−2.When a balance which was adjusted in Zurich, is taken to another place on the Earth, but is not corrected for the local gravitational acceleration, the displayed weight may be in error. MASS & DENSITY
  • 170. MASS • Table 3.1 illustrates this concept for a body having a mass of  1kg. To avoid erroneous weight measurements of this type, a  1k T id i h f hi balance has to be recalibrated at the location in which it will  be used. For this purpose, commercial mass standards are  produced with the help of national standards organizations  around the world.  Table 3.1  Weighing a 1 kg mass in different place MASS & DENSITY
  • 171. WEIGHING AND ATMOSPHERIC BUOYANCY • A balance is an instrument measuring the weighing force of a g g g body. However, it usually does not display a force signal (e.g. newtons), but a mass signal (e.g. kilograms).This is due to the principle of calibration used for balances: A mass standard is placed on the balance that causes a deformation, which can be read as an angle, a distance or an electric voltage, depending on the type of balance. • A calibration has to be performed for every type of sensing/measuring instrument For this purpose appropriate instrument. purpose, respective standard materials and procedures are needed, that make it possible to perform calibration of an instrument in i any l b t laboratory. MASS & DENSITY
  • 172. WEIGHING AND ATMOSPHERIC BUOYANCY • From a scientific point of view the calibration procedure described for a balance is basically to use the instrument as a “force meter,” then divide the force G measured by the value of the local gravitational acceleration g, and display the result (equation volume of h d f hydrometer i m3) t in ). (3.2) • Since the middle ages the weight of a body has been a manifold of a reference weight. So weighing is simply a comparison to a given mass standard. From this point of view weighing is dividing the weight force of the given body and weight force of a mass standard and the result is a dimensionless number. That is the principle of all mechanical and electronic balances up to today, and a consequence of lacking an expression for mass with fundamental natural constants. MASS & DENSITY
  • 173. WEIGHING AND ATMOSPHERIC BUOYANCY (3.3) • where MASS & DENSITY
  • 174. WEIGHING AND ATMOSPHERIC BUOYANCY • Most weight measurements are carried out with body and balance surrounded by atmospheric air, which is a gaseous fluid possessing density. Only bodies of material with density greater than atmospheric air at the Earth’s surface can impart a force when p p placed upon a balance. • For example a rubber balloon filled with helium gas (less dense than air) possesses mass but it will not rest on a balance It will rise mass, balance. upward into the atmosphere in search of an altitude at which the density of the atmosphere is in equilibrium with itself. His upward force caused the density of the Earth’s atmosphere is known as Earth s buoyancy. This atmospheric buoyancy causes a body resting on a balance when surrounded by atmospheric air to exhibit a slightly smaller weight measurement than if it were in a vacuum (Figure 3.1). MASS & DENSITY
  • 175. WEIGHING AND ATMOSPHERIC BUOYANCY Figure 3.1  A balance is adjusted to zero weight (picture I). A mass of 1 kg is weight  in atmosphere (picture II) and in vacuum (picture III) MASS & DENSITY
  • 176. WEIGHING AND ATMOSPHERIC BUOYANCY • The calculation needed to correct for this buoyancy effect in y y order to yield the true mass of a body is called atmospheric buoyancy correction. The true mass of a body mK is the product of the displayed mass m*K and a correctional factor K m K. The value of the correctional factor K depends on the density of the air surrounding the balance. Because weight measurement is a comparison of a body of interest and a mass standard, the densities of both materials also influence ( q ( ) ( ) the correctional factor (equations (3.4) to (3.6): (3.4) MASS & DENSITY
  • 177. WEIGHING AND ATMOSPHERIC BUOYANCY (3.5) (3.6) • Wh Where MASS & DENSITY
  • 178. WEIGHING AND ATMOSPHERIC BUOYANCY • The density of air depends on its pressure, temperature, y p p , p , humidity and its concentration of CO2. • For practical purposes, the density of atmospheric air at normal room t l temperature and sea l l ( t d d conditions) t d level (standard diti ) can be taken to be approximately 1.2 kg ∙ m−3. A simple approach to calculate the density of air more precisely is given by equation (3.7): (3.7) • where MASS & DENSITY
  • 179. WEIGHING AND ATMOSPHERIC BUOYANCY • In contrast to air, the density of water is 1000 times greater , y g (1000 kg ∙ m−3). Therefore, the density range of most food, agricultural and biological materials is in the same order of 3 magnitude as that of water about 1200 ± 300 kg ∙ m−3. The water, densities of materials with high water content are in a range more closely to that of water (between 1000 and 1100 kg ∙ 3 m−3) while dry materials like agricultural grains, seeds and dry beans consisting of proteins, carbohydrates, starch or g g cellulose are often in the range 1400–1600 kg ∙ m−3. MASS & DENSITY
  • 180. DENSITY • The density of a substance is the quotient of mass over y q volume. The standard international (SI) units for expressing density are kg ∙ m−3.The same definition is valid for solid, liquid, liquid gaseous and disperse systems like foams bulk goods or foams, powders. • The reciprocal of density is called specific volume and the units are m3 ∙ kg−1 (equations (3.8) and (3.9). (3.8) (3.9) MASS & DENSITY
  • 181. DENSITY • where MASS & DENSITY
  • 182. DENSITY TEMPERATURE DEPENDENCY OF DENSITY • Many materials undergo thermal expansion when heated, meaning they increase in volume without any change in mass. For this reason, the density of a given material often depends on temperature. Since the volume of a material normally increases with temperature, the density usually decreases with t ith temperature. Thi effect i much l t This ff t is h larger i gaseous in systems than in liquid or solid systems. MASS & DENSITY
  • 183. DENSITY TEMPERATURE DEPENDENCY OF DENSITY – IDEAL GAS • For many engineering applications air can be assumed to For many engineering applications air can be assumed to  behave as an ideal gas, meaning that the ideal gas law can be  used for calculating the density of air as a function of  temperature and pressure (equations (3.10) and (3.11). (3.10) (3.11) • where MASS & DENSITY
  • 184. DENSITY TEMPERATURE DEPENDENCY OF DENSITY – IDEAL GAS  • In case of low temperatures and humid air the ideal gas law loses accuracy, and will lead to error. To calculate the density of air more precisely as a function of water vapor partial pressure and atmospheric pressure, equation (3.7) can be used. MASS & DENSITY
  • 185. DENSITY TEMPERATURE DEPENDENCY OF DENSITY – SOLID AND LIQUIDS • The density of liquids and solids is a function of temperature. Small changes in volume caused by temperature change can be calculated with the aid of the thermal expansion coefficient: (3.12) • where MASS & DENSITY
  • 186. DENSITY TEMPERATURE DEPENDENCY OF DENSITY – SOLID AND LIQUIDS • Water shows abnormal behavior in a narrow range of temperature near its freezing point at atmospheric pressure. When lowering the temperature of water from 4 ◦C and 0◦C, C 0 C, the density of water actually decreases rather than increases. This abnormal behavior of water (see Figure 3.2 and Figure 3.3 is taken into 3 3 i t k i t account within th polynomial f ti of t ithi the l i l function f Bertsch (1983) for calculation of the density of liquid water (equation (3.13): (3.13) MASS & DENSITY
  • 187. DENSITY TEMPERATURE DEPENDENCY OF DENSITY – SOLID AND LIQUIDS Fig. 3.2 Normal (N) and abnormal (H O)  Fig 3 2 Normal (N) and abnormal (H2O) thermal expansion (schematic) Fig. 3.3 Abnormality of water (H2O): g y ( ) Temperature dependency of density compared to normal behavior (N) MASS & DENSITY
  • 188. DENSITY TEMPERATURE DEPENDENCY OF DENSITY – SOLID AND LIQUIDS • A further abnormality of water is that the solid phase (ice) has a lower density than the liquid phase at the same temperature. This behavior has important consequences for the biosphere. Because of this temperature dependency of density, control or measurement and recording of temperature i necessary when d it i measured f t t is h density is d for process control and quality control purposes. MASS & DENSITY
  • 189. DENSITY PRESSURE DEPENDENCY OF DENSITY • Materials are compressible. On application of pressure their volume decreases, causing the density to be a function of pressure as well as temperature. Gases are far more compressible than liquids and solids. Over a normal temperature range many gases can be assumed to behave like ideal id l gases. MASS & DENSITY
  • 190. DENSITY PRESSURE DEPENDENCY OF DENSITY – IDEAL GAS • For ideal gases the density is directly proportional to the pressure: ( (3.14) ) (3.15) (3.16) • so the density of the ideal gas is (3.17) MASS & DENSITY
  • 191. DENSITY PRESSURE DEPENDENCY OF DENSITY – IDEAL GAS • The negative slope of the volume–pressure curve divided by the initial volume is called the compressibility . It is the inverse compression modulus K of a material. (3.18) (3.19) MASS & DENSITY
  • 192. DENSITY PRESSURE DEPENDENCY OF DENSITY – LIQUIDS AND SOLIDS • Ideal liquids and solids show an elastic behavior. That means their volume can decrease by a certain amount when a pressure is applied, but that it will fully recover to the initial volume when the pressure is restored. For this type of material the change in volume on increasing the pressure can be l l t d based b calculated b d on equation (3 20) ti (3.20): (3.20) • with (2.8) and because of m = const the relative density is: (3.21) MASS & DENSITY
  • 193. DENSITY PRESSURE DEPENDENCY OF DENSITY – LIQUIDS AND SOLIDS • where MASS & DENSITY
  • 194. DENSITY PRESSURE DEPENDENCY OF DENSITY – LIQUIDS AND SOLIDS • Liquids and solids with very low compressibility show a very small volume reduction and often are treated in practice as incompressible materials. Water has very low compressibility with a value of ≈ 5x10−10 Pa−1. So, up to pressures in the order of 10 MPa (100 bar), the reduction of the volume in water is so small th t it can b neglected. Alth ll that be l t d Although i hi h pressure h in high processing of food, where the pressure will range to some 100MPa, the compressibility of water cannot be neglected. MASS & DENSITY
  • 195. DENSITY SPECIFIC GRAVITY (RELATIVE DENSITY) • The ratio of the absolute density of a material to the density of a reference material is called relative density d. Water at 4 °C or 20°C is most often used as the reference material for C 20 C this purpose. In the USA and Canada, when water is used as the reference standard, the term“ relative density” is not used, and i replaced b th t d d is l d by the term“ specific gravity.” Si “ ifi it ” Since water is nearly always chosen as the reference standard world‐wide, for practical purposes the terms “relative density” and “specific gravity” may be considered as synonymous. (3.22) (3 22) MASS & DENSITY
  • 196. DENSITY SPECIFIC GRAVITY (RELATIVE DENSITY) • Where • It is important to note that both density and specific gravity (relative density) relate to the same physical property. However, density d i must b reported i di be d in dimensional units of mass per unit i l i f i volume (e.g. g ∙ cm−3 or kg ∙ m−3), while specific gravity (relative density) is a ratio of densities, and is always a dimensionless number. In the case where density is being reported in dimensional units of g ∙cm−3 and with the density of the reference material being 1 g ∙ cm−3 or nearly 1 g ∙ cm−3 it is interesting to note that numerical values of both density and specific gravity (relative density)will be the same, respectively. MASS & DENSITY
  • 197. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY • Table 3.2 shows examples of different methods used for density measurement. MASS & DENSITY
  • 198. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY PYCNOMETRIC MEASUREMENT • By weighing a known volume of a liquid, the density of that liquid can be measured in a simple way Glass bulbs with way. precisely known volume that are used for this purpose are called pycnometers. A pycnometer can also be any other instrument d i d f the same purpose that may h i designed for h h have sample chambers of precisely known volume, but made of other materials (not glass bulbs). The glass bulb or sample chamber will have a marker to which the liquid sample must be carefully filled. Then the density of the fluid can be calculated by: (3.23) MASS & DENSITY
  • 199. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY PYCNOMETRIC MEASUREMENT • Because of thermal expansion of the glass, the pycnometer volume is known for the temperature at which it was calibrated, only. So, for measurement of the absolute density, pycnometers should be used at the same temperature at which they were calibrated. hi h h lib d • Another way is to measure the relative density (specific gravity) rather than the absolute density. For this purpose, the pycnometer is weighed with the sample liquid and again weighed with the reference liquid (often water).The ratio of both weights gives the relative density d or specific gravity of d, the sample. MASS & DENSITY
  • 200. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY PYCNOMETRIC MEASUREMENT (3.24) (3 24) where MASS & DENSITY
  • 201. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY PYCNOMETRIC MEASUREMENT • Once the relative density d, or specific gravity, of the sample is known, known and the density of the reference material is known from the literature, the absolute density of the sample can be calculated: (3.25) MASS & DENSITY
  • 202. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY PYCNOMETRIC MEASUREMENT • Fig. 3.4 and 3.5 show different designs of glass pycnometers Fig. 3.4  Pycnometer designs: (a) Reischauer, (b) Bingham, (c) Gay‐Lussac,  (d) Sprengel,(e) Lipkin, (f) Hubbard MASS & DENSITY
  • 203. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY PYCNOMETRIC MEASUREMENT Fig. 3.5  Examples of pycnometers . The right one is for viscous samples  and powders MASS & DENSITY
  • 204. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROSTATIC BALANCES (BUOYANCY WEIGHING) • The principle of a hydrostatic balance is based on Archimedes law of buoyancy If a body is submersed in a fluid its weight buoyancy. will be lowered because of the buoyancy force. The buoyancy force is directly proportional to the volume of the submersed body d the density f the fluid. By b d and th d it of th fl id B measurement of th t f the buoyancy force with the balance, the volume of the body can be determined quite accurately, and together with the measured mass of the body, the density is obtained. MASS & DENSITY
  • 205. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROSTATIC BALANCES (BUOYANCY WEIGHING) • A simple technique for making this type of measurement is to place a beaker partially filled with water on top of a top‐ top loading balance, with the weight of beaker and water tared‐ out to read zero on the display. Then, fully submerge the solid body beneath th water surface, t ki care th t it neither b d b th the t f taking that ith touches the bottom nor the sides of the beaker. The weight reading shown on the display of the balance will be the weight of the volume of water displaced by the solid body. Since density of water is known, the precise volume of the solid body is determined. MASS & DENSITY
  • 206. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROSTATIC BALANCES (BUOYANCY WEIGHING) (3.8) (3.26) • with ∆m as the difference in weight (in kg) of the body before and after submersion: (3.27) (3.28) (3 28) (3.29) (3.30) MASS & DENSITY
  • 207. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROSTATIC BALANCES (BUOYANCY WEIGHING) • where • S th d it f b d So the density of a body can be obtained by taking first the  b bt i d b t ki fi t th weight prior to submersion (that means weighing in air) and  its weight when submersed in a fluid with a known density F  using equation (3.30). MASS & DENSITY
  • 208. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROSTATIC BALANCES (BUOYANCY WEIGHING) • With the ratio (3.31) (3 31) • the relative density d (specific gravity) of the body is (3.32) (3.33) • That means d can be calculated very quickly after two  readings from the balance. MASS & DENSITY
  • 209. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROSTATIC BALANCES (BUOYANCY WEIGHING) • If the weight in air mL is not corrected for atmospheric buoyancy, buoyancy the density obtained by hydrostatic weighing can be called apparent density of the body. If that correction made, then mL and K will be slightly higher, and can be called true mass and t t d true d it density. • On the other hand when a body of known volume is submersed in a fluid, the difference in weight of the body in , g y air and the weight of fluid displaced by the body can be used to determine the density of the fluid, and can be calculated with equation (3 34): (3.34): (3.34) MASS & DENSITY
  • 210. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROSTATIC BALANCES (BUOYANCY WEIGHING) • Figure 3.6 shows a special design of hydrostatic balance that is  suitable for measuring the density of a solid or the density of  suitable for measuring the density of a solid or the density of the liquid in the reservoir when used with a solid body of  precisely known volume. Fig. 3.6 Hydrostatic balance design. 1: balance, 2: platform, 3: small beaker, beaker 4: large beaker 5: support beaker, bracket, 6: pan, 7: thermometer MASS & DENSITY
  • 211. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROSTATIC BALANCES (BUOYANCY WEIGHING) • To obtain the density of a solid, the sample is weighed first in air, and then it is submersed and the weight is taken again. As can be seen in Figure 3.6 there is a small pan mounted on the weighing plate of the balance. A small beaker on a cable is suspended within a larger beaker containing the fluid of interest. The large beaker is resting on a raised platform so its weight is not transmitted to the balance. • To obtain the fluid density in the large beaker, a test body with known p p g volume is first placed on the pan and its weight in air is measured. Then the test body is placed into the small beaker, submersed in the fluid and weighed once again. Then the density of the liquid is g q ( ) calculated using equation (3.34). It should be remembered that the density of the fluid is dependent on temperature so the temperature must be controlled and recorded. MASS & DENSITY
  • 212. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY MOHR‐WESTPHAL BALANCE • The Mohr–Westphal balance (see Figure 3.7) is another type  of hydrostatic balance. It is designed as a nonsymmetric beam  of hydrostatic balance It is designed as a nonsymmetric beam balance for measuring the density of liquids. Fig. 3.7  Mohr‐Westphal balance 1:  beam, 2: weights, 3: buoyancy body, 4:  beam 2: weights 3: buoyancy body 4: liquid sample MASS & DENSITY
  • 213. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY MOHR‐WESTPHAL BALANCE • At the free end of the arm of the balance a “buoyancy body” is suspended in air The buoyancy body is normally made of air. glass and can have a built‐in thermometer. Then the buoyancy body is submersed into the liquid of interest. • Because of the effect of buoyancy, the weight of the submersed glass body will appear lower than it was in air, and will bring the balance out of zero. g • The buoyancy force can be measured by successively adding small weights to the arm until the balance is restored to zero. The Th measurement i th repeated with water as a reference t is then t d ith t f liquid. MASS & DENSITY
  • 214. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY MOHR‐WESTPHAL BALANCE • The ratio of both readings provides the relative density or  specific gravity of the liquid as can be shown below. With the  specific gravity of the liquid as can be shown below With the buoyancy force (3.40) (3.41) • With the fluid of interest (3.42) • With water as reference material (3.43) (3 43) MASS & DENSITY
  • 215. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY MOHR‐WESTPHAL BALANCE • So the ratio is (3.44) • Because the volume of the glass body is the same for both readings, then (3.45) • So the specific gravity is simply (3.46) (3 46) MASS & DENSITY
  • 216. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY MOHR‐WESTPHAL BALANCE • where MASS & DENSITY
  • 217. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY MOHR‐WESTPHAL BALANCE • The result should be recorded along with the temperature of  the measurement. Often both readings are taken at 20  C and  the measurement Often both readings are taken at 20 ◦C and the result is written as d20/20. The quantity d20/4 would mean  that the density of the liquid was compared to the density of  water at 4°C: t t 4°C MASS & DENSITY
  • 218. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY MOHR‐WESTPHAL BALANCE • The Mohr–Westphal balance can also be used to measure the density of a solid sample which is submersed in a fluid with known density. For this purpose, equation (3.37) would be used to calculate the volume of the sample. MASS & DENSITY
  • 219. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROMETER • Hydrometers (Fig 3.8) are hollow glass bodies with the shape of a buoy buoy. • Hydrometers are designed with a volume to mass ratio in such a way that the glass body will float at a certain depth in the liquid under investigation. • Depending upon the density of that liquid the hydrometer will float at a higher or lower position The upper part of the position. hydrometer has a scale for reading the nonsubmersed part h of the floating glass body. MASS & DENSITY
  • 220. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROMETER • The nonsubmersed length of the hydrometer can be read with the aid of a scale on the upper part of the hydrometer hydrometer. • A weight at the bottom of the hydrometer acts like the keel of a sailboat to ensure that it will float in the liquid in a vertical orientation. • The scale can be calibrated directly in units of density or, e.g. in concentration units (Fig 3 9) 3.9). MASS & DENSITY
  • 221. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROMETER Fig. 3.8 Hydrometer. 1:scale, 2: body  (with and without thermometer), 3: keel Fig. 3.9 Reading of a hydrometer scale at the liquid surface (example) MASS & DENSITY
  • 222. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROMETER • The floating depth position of the hydrometer depends on  weight force and interfacial force (force due to surface  weight force and interfacial force (force due to surface tension). It is (3.47) • Which means: (3.48) • so (3.49) MASS & DENSITY
  • 223. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROMETER • The nonsubmersed part of the hydrometer has the length (3.50) • Which means (3.51) • Sometimes the combination of two physical properties will give the information needed about a process or a product. For example, by knowing both the density and refractive index of beer wort, the alcohol content can be calculated, and by this, the progress of fermentation MASS & DENSITY
  • 224. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROMETER MASS & DENSITY
  • 225. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY HYDROMETER • Without consideration of interfacial tension effects the  hydrometer equation simplifies to hydrometer equation simplifies to (3.52) • There are hydrometers available which are corrected for  interfacial tension offered in different range categories called – L (l L (low, 15–35mN ∙m−1), 15 35 N 1) – M(medium, 35–65 mN ∙ m−1) and  – H (high, for higher values). MASS & DENSITY
  • 226. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY SUBMERSION TECHNIQUE • Pycnometers and hydrometers do not work very well with liquids of high viscosity viscosity. • For highly viscous liquids, measurement of density can be performed with the submersion technique (see Fig 3.10). • A beaker with the viscous liquid sample is put on a balance. The display value is recorded, or the display may be set to zero (tare) (tare). • Then a test body with known volume is pressed into the sample. MASS & DENSITY
  • 227. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY SUBMERSION TECHNIQUE Fig. 3.10 Submersion technique  for density measurement. 1:  depth mark, 2: liquid sample, 3:  buoyancy body of known volume MASS & DENSITY
  • 228. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY SUBMERSION TECHNIQUE • The buoyancy force caused by the submerged test body is transferred to the balance and appears on the display as an apparent increased weight m. • This increased weight force is the buoyancy force, and is the weight of the displaced liquid, which is equal in volume to the volume of the submersed solid body: (3.53) • and (3.54) MASS & DENSITY
  • 229. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY SUBMERSION TECHNIQUE • So (3.55) • where MASS & DENSITY
  • 230. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY SUBMERSION TECHNIQUE • For precision measurement, the buoyancy body can be a hollow metal sphere with calibrated volume To avoid errors volume. from buoyancy of the mounting rod there is normally a depth mark on the rod which indicates the right depth position for immersion so th t th submerged section of rod i accounted i i that the b d ti f d is t d for in the calibrated volume. MASS & DENSITY
  • 231. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS • Many agricultural materials and food and feed ingredients are in the form of granular materials (grains meals and powders) (grains, powders), which are bulk solids made up of small particles. • The weight or size of the individual particles within any of these types of materials may vary over a large range e.g. from frozen diced vegetables to corn cornels to fine powder p particles. • The term “solid density” means the density of the solid material of which a particle is made, no matter what type of fluid fl id or other material may exist b t th t i l i t between th particles. the ti l MASS & DENSITY
  • 232. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS • Solid particles contain pores or hollow cavities filled with gases or liquids this contributes to the density of the solid liquids, solid. • When pores or cavities occur, it is important to state whether they are closed or open. If they are closed, meaning they are located completely within the solid particle, they belong to the solid. If they are open to the surroundings at the particle surface, e.g. the atmosphere, they do not belong to the solid , g p , y g body. • To avoid communication errors the density of solids should be given with a note lik “i l di pore volume” or “ ith t i ith t like “including l ” “without pore volume.” MASS & DENSITY
  • 233. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS • This can be accomplished by how the system boundaries are  defined, and can be calculated as follows: defined and can be calculated as follows: (3.8) • where MASS & DENSITY
  • 234. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS • To measure the density of a solid particle often simply means  to measure its volume, because its mass is known upon  to measure its volume because its mass is known upon weighing. • To get the volume of the solid sample without its open pores,  a pycnometer technique with an appropriate liquid can be  used.  • The liquid must not alter or dissolve the sample For this The liquid must not alter or dissolve the sample. For this  purpose, a sequence of weighings is conducted as indicated in  Figure 3.11.  MASS & DENSITY
  • 235. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS • After weighing the empty pycnometer m0 the pycnometer is  weighed with the sample m weighed with the sample mP.  • Then the pycnometer is filled up to a designated mark with an  appropriate reference liquid of known density and weighed  again mP,F.  • Finally,  the pycnometer is weighed when filled to the same  mark with only the reference liquid m mark with only the reference liquid mF: MASS & DENSITY
  • 236. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS Fig. 3.11  Pycnometer measurement of the density of a solid granular material, e.g. a  powder MASS & DENSITY
  • 237. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS • The density of the solid material then is  (3.8) (3.56) (3.57) (3.58) (3 58) MASS & DENSITY
  • 238. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS (3.59) (3.60) (3.61) MASS & DENSITY
  • 239. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY DENSITY OF SOLIDS (3.62) (3.63) • where MASS & DENSITY
  • 240. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY BULK DENSITY • Powders and bulk goods contain hollow spaces or voids filled with gas normally air The density of that type of bulk gas, air. material, including the void spaces, is called bulk density. • Using equation (3.8) the bulk density can be calculated by weighing a sample of the bulk material and measurement of its volume. • The volume of the whole bulk material must be taken “as is ” as is. To measure this volume, the sample material can be poured into a beaker or cylinder up to a known volumetric mark. MASS & DENSITY
  • 241. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY BULK DENSITY • Different technique in filling the beaker or cylinder may lead to different distributions of solid particles and hollow spaces spaces. So, to get repeatable results the technique of filling has to be standardized. • To overcome problems with repeatable filling technique, the bulk material can be tapped before reading of the volume. By tapping the material, the solid particles will “settle” into the pp g , p most stable situation they can reach. The void spaces will get smaller as the solid particles settle step by step into a spatial situation where the bulk density will reach a maximum The maximum. time needed to reach this maximum depends on tapping MASS & DENSITY speed and tapping amplitude.
  • 242. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY BULK DENSITY Figure 3.12. Device for tapping of bulK goods:  1: rotating cam, 2: housing, 3: powder sample,  y g 4: cylinder, 5: overring MASS & DENSITY
  • 243. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY BULK DENSITY • Figure 3.12 shows an example of a device which can be used to measure bulk density and tapped bulk density subsequently. • First the bulk material is filled into a 1000 cm3 cylinder until it is overflowing under repeatable technique conditions. Then with aid of a flat spatula, the excess overflow of sample material is scraped away from the top of the cylinder to leave p y p y the sample perfectly level at the top, and the 1000 cm3 sample is weighed to get the bulk density. MASS & DENSITY
  • 244. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY BULK DENSITY • Now a cylindrical extension overring is slipped onto the 1000 cm3 cylinder and more sample material is filled in The in. cylinder is mounted on the tapping device and moved for a fixed number of tappings. In German testing standards a number of 2500 with a f b f ith frequency of 250 s−1 i specified. f 1 is ifi d • After this the sample material is adjusted to 1000 cm3 again and weighed. The tapped bulk density should be recorded g pp y with the parameters of its measurement. MASS & DENSITY
  • 245. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY BULK DENSITY • The difference between bulk density and maximum tapped bulk density provides information about the ability of the bulk material to be compressed by gravity or pressure. Powders can be characterized for this property by the Hausner ratio, which i th quotient of t hi h is the ti t f tapped b lk d it over untapped d bulk density t d bulk density (see Table 3.3). Table 2.7.  Characterization of  Characterization of powder flowability by Hausner ratio  MASS & DENSITY
  • 246. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY POROSITY • Also the volume of the hollow void space (pores) can be calculated. calculated The ratio of the volume of the void space (pores) and the total volume of the bulk is called porosity ɛ: (3.64) (3 64) (3.65) • because mB ≈ mS = m (3.66) MASS & DENSITY
  • 247. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY POROSITY • So ( (3.67) ) • With ɛ as the relative volume of the hollow pore space, and α as the relative volume of the solid particle space it is evident  that: (3.68) MASS & DENSITY
  • 248. DENSITY METHODS FOR LABORATORY MEASUREMENT OF DENSITY POROSITY • where MASS & DENSITY
  • 249. THE END THE END RHEOLOGICAL PROPERTIES OF FOODS