This document summarizes key concepts in particle technology and characterization. It discusses:
1. Methods for characterizing solid particles including size, shape, density, and specific surface area. Common metrics like sphericity and equivalent diameter are defined.
2. Factors that influence particle motion through fluids, including drag, terminal velocity, and settling regimes defined by particle Reynolds number. Equations for motion under gravity and centrifugal forces are provided.
3. Size reduction techniques like crushing and grinding. Empirical laws relating energy to size reduction are described. Common size reduction equipment is also outlined.
This document summarizes a student project analyzing sediment transport in turbulent flows. It constructs a differential equation to model the vertical distribution of suspended sediment concentration. The turbulent fluctuations are expressed as a diffusive flux, with sediment diffusivity determined empirically. Steady state solutions are found for constant, linear, and parabolic (Vanoni) distributions of diffusivity. The accuracy and time scale of the steady state solutions are shown to depend strongly on the dimensionless Rouse number, which measures a flow's ability to suspend particles. Figures and diagrams support the analysis and conclusions.
1) The physical properties of liquids can be studied without causing chemical changes and depend on intermolecular forces. Examples include surface tension, viscosity, and refractive index.
2) Viscosity is a measure of a liquid's resistance to flow and is determined by the attraction between layers of a liquid. It can be measured using an Ostwald viscometer.
3) Refractive index is the ratio of the speed of light in a vacuum to that in the liquid and can be used to study molecular structure based on molar refractivity. Abbe's refractometer can precisely measure refractive index.
Here are the answers to 4 questions from the list:
1. Methods to determine interfacial tension:
- Drop weight method: In this method, a drop of liquid is formed at the end of a capillary tube immersed in another liquid medium. The weight of the drop is measured which is directly proportional to the interfacial tension.
- Du Nouy ring method: In this method, a platinum ring is immersed in the liquid and then pulled out. The force required to detach the ring from the liquid surface is measured which is directly proportional to the interfacial tension.
2. Factors influencing rate of reaction: The factors that influence the rate of a chemical reaction include concentration, temperature, pressure
This document discusses molecular diffusion in gases through three parts. Part I introduces concepts like mass transfer, diffusion, convection and Fick's laws of diffusion. It also defines terms like mass concentration, molar concentration, mass fraction and mole fraction. Part II discusses different types of diffusion like equimolar counter diffusion and diffusion with convection. It also covers diffusion through varying cross-sectional areas. Part III describes experimental methods to determine diffusion coefficients for gases through experiments using two vessels connected by a capillary tube. It also briefly discusses multicomponent diffusion and mass transfer coefficients.
Measuring the Surface Tension of Water by Light Diffraction on Capillary WavesSEENET-MTP
Â
The SEENET-MTP Seminar: Trends in Modern Physics
19â21 August 2011, NiĆĄ, Serbia
Talk by Ljubisa Nesic (Faculty of Science and Mathetamtics, Univ. of Nis)
This document defines and provides examples of key properties of fluids, including:
1) Density, which is the mass per unit volume, and includes mass density, specific weight, and relative density. Common values are provided for fluids like water, mercury, air and oil.
2) Viscosity, which is a fluid's resistance to shear forces, including dynamic viscosity and kinematic viscosity. Viscosity is higher for fluids like syrup than water.
3) Units and dimensions are defined for each property in the MLT system. Typical values shown include densities of common fluids like water and air, along with viscosities of water, air, mercury and oil.
1. Mass transfer is the movement of a component from one location to another where the concentration is different. It occurs through molecular diffusion and eddy diffusion.
2. Molecular diffusion is the random movement of molecules due to thermal motion. Eddy diffusion is the random macroscopic fluid motion in turbulent flows.
3. Fick's first law states that the rate of molecular diffusion is proportional to the concentration gradient. The rate of mass transfer stops when concentrations are uniform.
This document summarizes a student project analyzing sediment transport in turbulent flows. It constructs a differential equation to model the vertical distribution of suspended sediment concentration. The turbulent fluctuations are expressed as a diffusive flux, with sediment diffusivity determined empirically. Steady state solutions are found for constant, linear, and parabolic (Vanoni) distributions of diffusivity. The accuracy and time scale of the steady state solutions are shown to depend strongly on the dimensionless Rouse number, which measures a flow's ability to suspend particles. Figures and diagrams support the analysis and conclusions.
1) The physical properties of liquids can be studied without causing chemical changes and depend on intermolecular forces. Examples include surface tension, viscosity, and refractive index.
2) Viscosity is a measure of a liquid's resistance to flow and is determined by the attraction between layers of a liquid. It can be measured using an Ostwald viscometer.
3) Refractive index is the ratio of the speed of light in a vacuum to that in the liquid and can be used to study molecular structure based on molar refractivity. Abbe's refractometer can precisely measure refractive index.
Here are the answers to 4 questions from the list:
1. Methods to determine interfacial tension:
- Drop weight method: In this method, a drop of liquid is formed at the end of a capillary tube immersed in another liquid medium. The weight of the drop is measured which is directly proportional to the interfacial tension.
- Du Nouy ring method: In this method, a platinum ring is immersed in the liquid and then pulled out. The force required to detach the ring from the liquid surface is measured which is directly proportional to the interfacial tension.
2. Factors influencing rate of reaction: The factors that influence the rate of a chemical reaction include concentration, temperature, pressure
This document discusses molecular diffusion in gases through three parts. Part I introduces concepts like mass transfer, diffusion, convection and Fick's laws of diffusion. It also defines terms like mass concentration, molar concentration, mass fraction and mole fraction. Part II discusses different types of diffusion like equimolar counter diffusion and diffusion with convection. It also covers diffusion through varying cross-sectional areas. Part III describes experimental methods to determine diffusion coefficients for gases through experiments using two vessels connected by a capillary tube. It also briefly discusses multicomponent diffusion and mass transfer coefficients.
Measuring the Surface Tension of Water by Light Diffraction on Capillary WavesSEENET-MTP
Â
The SEENET-MTP Seminar: Trends in Modern Physics
19â21 August 2011, NiĆĄ, Serbia
Talk by Ljubisa Nesic (Faculty of Science and Mathetamtics, Univ. of Nis)
This document defines and provides examples of key properties of fluids, including:
1) Density, which is the mass per unit volume, and includes mass density, specific weight, and relative density. Common values are provided for fluids like water, mercury, air and oil.
2) Viscosity, which is a fluid's resistance to shear forces, including dynamic viscosity and kinematic viscosity. Viscosity is higher for fluids like syrup than water.
3) Units and dimensions are defined for each property in the MLT system. Typical values shown include densities of common fluids like water and air, along with viscosities of water, air, mercury and oil.
1. Mass transfer is the movement of a component from one location to another where the concentration is different. It occurs through molecular diffusion and eddy diffusion.
2. Molecular diffusion is the random movement of molecules due to thermal motion. Eddy diffusion is the random macroscopic fluid motion in turbulent flows.
3. Fick's first law states that the rate of molecular diffusion is proportional to the concentration gradient. The rate of mass transfer stops when concentrations are uniform.
Sediment is any particulate matter that can be transported by fluid flow and eventually deposited. There are four main categories of sediments based on size: gravel, sand, silt, and clay. Incipient motion, or the initial movement of sediment particles, is important to studying sediment transport and channel design. Two main approaches to modeling incipient motion are the shear stress approach and velocity approach. Shields developed a widely used diagram relating the critical shear stress needed to initiate motion to other dimensionless parameters like particle size, fluid properties, and sediment density. White's analysis also models critical shear stress as proportional to particle size. The velocity approach uses field surveys of permissible flow velocities before sediment starts moving in different channel materials.
This document discusses the aerodynamic properties of food materials, specifically terminal velocity and drag coefficient. Terminal velocity is the constant velocity attained by a falling object in air as gravitational force equals drag force. It depends on properties of the object like size, shape, density as well as fluid density and drag coefficient. Methods to measure terminal velocity and drag coefficient include free fall and photographic techniques. Equations are provided relating these properties to calculate terminal velocity for different shapes like spheres, disks and cylinders.
Mass transfer is the movement of mass from one location to another, such as between phases or components. It occurs through various processes like absorption, evaporation, drying, and distillation. Mass transfer involves both diffusive and convective transport mechanisms. Diffusion is the movement of molecules from a region of higher concentration to lower concentration down a concentration gradient via random molecular motion. Convection involves the bulk flow of a fluid carrying dissolved or suspended materials. Fick's first law describes the rate of diffusion, while Fick's second law describes how concentration changes over time at a given point for diffusion.
This document summarizes various models and theories of drug dissolution. It discusses diffusion layer theory, which involves drug dissolving from the solid into a saturated film and then diffusing into the bulk solution. The Noyes-Whitney and Nerst-Brunner equations are presented to model this. Other models covered include zero-order and first-order release kinetics, the Hixson-Crowell cube root model accounting for changing surface area, Danckwert's surface renewal theory, and the interfacial barrier/limited solvation theory involving an energy barrier to dissolution. Theories of dissolution aim to quantitatively understand and interpret in vitro dissolution results.
This document summarizes a microfluidics experiment studying diffusion using a microfluidic device. It includes sections on the introduction, theoretical background, description of equipment, general experimental instructions, and development of two experiments. The first experiment varied the inlet velocity of dye from 10-20 ÎŒm/min while holding water velocity constant to study how diffusion coefficient and Peclet number change with velocity. Results showed diffusion coefficient decreased and Peclet number increased with higher dye velocity. The second experiment was initially intended to study electrophoresis but was changed to use pressure control instead due to equipment limitations.
WATS 9 (1-50) Fluid Mechanics and ThermodynamicsMark Russell
Â
The WATS approach to assessment was developed as part of an LTSN Engineering Mini-Project, funded at the University of Hertfordshire which aimed to develop a set of 'student unique' tutorial sheets to actively encourage and improve student participation within a first year first âfluid mechanics and thermodynamicsâ module. Please see the accompanying Mini-Project Report âImproving student success and retention through greater participation and tackling student-unique tutorial sheetsâ for more information.
The WATS cover core Fluid Mechanics and Thermodynamics topics at first year undergraduate level. 11 tutorial sheets and their worked solutions are provided here for you to utilise in your teaching. The variables within each question can be altered so that each student answers the same question but will need to produce a unique solution.
What follows is a set of STUDENT UNIQUE SHEETS for WATS 9.
Molecular weight determination of polymers by viscometrymisha minaal
Â
This document discusses methods for determining the molecular weight of polymers using viscometry. It explains that viscosity is related to molecular weight through equations like the Mark-Houwink and Flory-Fox equations. An Ubbelohde viscometer is commonly used to measure the viscosity of polymer solutions and calculate values like intrinsic viscosity. These viscosity values can then be used in the equations to determine the average molecular weight of the polymer. The document also discusses how melt viscosity relates to molecular weight for linear polymers.
The document discusses transport phenomena and provides definitions and examples of key concepts in vector and tensor analysis used to describe transport phenomena. It defines transport phenomena as dealing with the movement of physical quantities in chemical or mechanical processes. There are three main types of transport: momentum, energy, and mass transport. Vector and tensor quantities like velocity, stress, and strain gradient are used to describe transport phenomena. Tensors have a magnitude and direction(s) and transform under coordinate system rotations. The document provides examples of scalar, vector, and tensor notation and the Kronecker delta, alternating unit tensor, and mathematical operations on vectors like addition, dot product, and cross product.
FMM- UNIT I FLUID PROPERTIES AND FLOW CHARACTERISTICSKarthik R
Â
Units and dimensions- Properties of fluids- mass density, specific weight, specific volume, specific gravity, viscosity, compressibility, vapor pressure, surface tension and capillarity. Flow characteristics â concept of control volume - application of continuity equation, energy equation and momentum equation.
Solution:
(a) Pressure at point Q = Height of mercury column x Density of mercury x Gravitational acceleration
= (75 cm) x (1.36 x 104 kg mâ3) x (10 m sâ2)
= 1.02 x 105 Pa
The rate of gas diffusion into a liquid is directly proportional to the partial pressures of the gas, the surface area available for gas exchange, and the solubility coefficient of the gas. It is inversely proportional to the gram molecular weight of the gas molecules and the thickness of the membrane through which diffusion occurs.
This document contains solutions to physics problems involving unit conversions and vector calculations.
1) It provides step-by-step workings and calculations for various conversion problems between units like inches, centimeters, liters, gallons, etc.
2) It also shows the decomposition of vectors into x and y components and calculations of resultant vectors and displacements by summing the x and y components.
3) The problems cover a wide range of physics concepts involving kinematics, forces, densities, areas, volumes, and conversions between different units of length, volume, speed and other physical quantities.
This document discusses surface tension of liquids. It begins by providing examples of surface tension phenomena like water spiders walking on water. It then defines surface tension as the property of liquid surfaces that allows them to resist an external force. The document explains surface tension using molecular theory - molecules in the surface film experience an unbalanced inward force due to stronger cohesive forces within the liquid. This inward force minimizes the surface area and leads to the stretched membrane-like behavior of the surface. The document also defines related terms like surface energy, range of molecular forces, sphere of influence, and provides an example calculation for the force of surface tension.
Determination of molecular weight of polymers by visometryudhay roopavath
Â
This document discusses methods for determining the molecular weight of polymers using viscometry. It defines various types of average molecular weights and explains how intrinsic viscosity is measured through polymer solution viscosity. Viscosity measurements are used to calculate intrinsic viscosity and relate it to molecular weight through the Mark-Houwink-Sakurada equation. Double extrapolation plots of reduced viscosity and inherent viscosity versus concentration are used to determine intrinsic viscosity.
This document discusses methods for characterizing polymer molecular weight. It describes average molecular weights like number-average (Mn) and weight-average (Mw), and how they are calculated. Absolute methods like endgroup analysis directly relate measurable properties to molecular weight, while relative methods like solution viscosity instead relate measurements to molecular weight when calibrated with an absolute technique. Solution viscosity measurements utilize equations like Huggins' to correlate intrinsic viscosity and molecular weight. Size exclusion chromatography can rapidly determine molecular weight distribution and averages.
1) The height of a geotextile tube increases as the required tensile force in the circumferential direction or pumping pressure increases. However, beyond a certain pressure, height increases only marginally while required tensile force rises exponentially.
2) A higher initial water content in soil slurry leads to thinner filter cakes forming above geotextiles, making it easier for soil particles to pass through.
3) Both the number and size of air bubbles trapped in soil filter cakes increases from the bottom to the top of the cake and adversely impacts dewatering rates and permeability.
Physical properties of sediments and water sediment mixtureJyoti Khatiwada
Â
This document discusses various physical properties of sediments and water-sediment mixtures. It defines key concepts like particle density, bulk density, porosity, void ratio, viscosity, and kinematic viscosity. It explains that particle density refers to the density of solid sediment particles, while bulk density includes pore spaces. Porosity and void ratio quantify the pore space. Viscosity and kinematic viscosity describe the resistance of fluids to flow, with kinematic viscosity being the ratio of dynamic viscosity to density. Newtonian mixtures have viscosities that do not depend on shear rate.
multiphase flow modeling and simulation ,Pouriya Niknam , UNIFIPouriya Niknam
Â
This document discusses modeling and simulation of multiphase flows using computational fluid dynamics (CFD). It begins with definitions of multiphase flow and discusses important types including bubbly, droplet, particle-laden, and annular flows. The document then provides tips on multiphase simulation including choosing appropriate modeling approaches such as Lagrangian, Eulerian, or volume of fluid methods depending on the problem. It concludes with discussions of challenges such as convergence difficulties and appropriate solver settings and techniques to address these challenges.
This document contains 19 multiple choice questions regarding mechanical properties of fluids. The questions cover topics such as pressure, density, buoyancy, and their relationships. Key details assessed include the definitions of fluid, gauge pressure, factors that influence pressure in liquids, and applications of fluid properties such as hydraulic jacks.
1. The dynamics of fine particles are important for understanding dust control in mines. Small particles have a high surface area, which leads to greater viscous resistance in air compared to larger particles.
2. When a small particle falls due to gravity, viscous resistance from air increases with velocity until the particle reaches a constant terminal settling velocity. Terminal velocities of fine particles are very small, causing them to remain suspended for long periods.
3. Newton derived the drag force equation for spherical particles moving through a fluid. For small particles, Stokes derived an equation showing drag force is directly proportional to velocity. Understanding drag forces and terminal settling velocities is key to modeling aerosol particle behavior.
What happens when the digital tools and platforms we make and use for communication and entertainment are hijacked for terrorism, violence against the vulnerable and nefarious transactions? What role do designers and developers play? Are we complicit as creators of these technologies and products? Should we police them or fight back? As Portfolio Lead for Northern Lab, Northern Trust's internal innovation startup focused on client and partner experience, Antonio will share a mix of provocative scenarios torn from today's headlines and compelling stories where activism and technology facilitated peaceâand war.
As a call-to-action for designers and developers to engage in projects capable of transformational change, he'll explore the question: How might technology foster new experiences to better accelerate social activism and make the world a smarter, safer place?
This document summarizes upcoming CSS features like Box Alignment Level 3, CSS Grid Layout, CSS Shapes, CSS Feature Queries, and CSS Custom Properties. It explains what each feature does at a high level and provides example code snippets. The document also encourages developers to get involved by filing issues on browser bug trackers, requesting new features, and creating blog posts/demos to help drive adoption of these new CSS specifications.
Sediment is any particulate matter that can be transported by fluid flow and eventually deposited. There are four main categories of sediments based on size: gravel, sand, silt, and clay. Incipient motion, or the initial movement of sediment particles, is important to studying sediment transport and channel design. Two main approaches to modeling incipient motion are the shear stress approach and velocity approach. Shields developed a widely used diagram relating the critical shear stress needed to initiate motion to other dimensionless parameters like particle size, fluid properties, and sediment density. White's analysis also models critical shear stress as proportional to particle size. The velocity approach uses field surveys of permissible flow velocities before sediment starts moving in different channel materials.
This document discusses the aerodynamic properties of food materials, specifically terminal velocity and drag coefficient. Terminal velocity is the constant velocity attained by a falling object in air as gravitational force equals drag force. It depends on properties of the object like size, shape, density as well as fluid density and drag coefficient. Methods to measure terminal velocity and drag coefficient include free fall and photographic techniques. Equations are provided relating these properties to calculate terminal velocity for different shapes like spheres, disks and cylinders.
Mass transfer is the movement of mass from one location to another, such as between phases or components. It occurs through various processes like absorption, evaporation, drying, and distillation. Mass transfer involves both diffusive and convective transport mechanisms. Diffusion is the movement of molecules from a region of higher concentration to lower concentration down a concentration gradient via random molecular motion. Convection involves the bulk flow of a fluid carrying dissolved or suspended materials. Fick's first law describes the rate of diffusion, while Fick's second law describes how concentration changes over time at a given point for diffusion.
This document summarizes various models and theories of drug dissolution. It discusses diffusion layer theory, which involves drug dissolving from the solid into a saturated film and then diffusing into the bulk solution. The Noyes-Whitney and Nerst-Brunner equations are presented to model this. Other models covered include zero-order and first-order release kinetics, the Hixson-Crowell cube root model accounting for changing surface area, Danckwert's surface renewal theory, and the interfacial barrier/limited solvation theory involving an energy barrier to dissolution. Theories of dissolution aim to quantitatively understand and interpret in vitro dissolution results.
This document summarizes a microfluidics experiment studying diffusion using a microfluidic device. It includes sections on the introduction, theoretical background, description of equipment, general experimental instructions, and development of two experiments. The first experiment varied the inlet velocity of dye from 10-20 ÎŒm/min while holding water velocity constant to study how diffusion coefficient and Peclet number change with velocity. Results showed diffusion coefficient decreased and Peclet number increased with higher dye velocity. The second experiment was initially intended to study electrophoresis but was changed to use pressure control instead due to equipment limitations.
WATS 9 (1-50) Fluid Mechanics and ThermodynamicsMark Russell
Â
The WATS approach to assessment was developed as part of an LTSN Engineering Mini-Project, funded at the University of Hertfordshire which aimed to develop a set of 'student unique' tutorial sheets to actively encourage and improve student participation within a first year first âfluid mechanics and thermodynamicsâ module. Please see the accompanying Mini-Project Report âImproving student success and retention through greater participation and tackling student-unique tutorial sheetsâ for more information.
The WATS cover core Fluid Mechanics and Thermodynamics topics at first year undergraduate level. 11 tutorial sheets and their worked solutions are provided here for you to utilise in your teaching. The variables within each question can be altered so that each student answers the same question but will need to produce a unique solution.
What follows is a set of STUDENT UNIQUE SHEETS for WATS 9.
Molecular weight determination of polymers by viscometrymisha minaal
Â
This document discusses methods for determining the molecular weight of polymers using viscometry. It explains that viscosity is related to molecular weight through equations like the Mark-Houwink and Flory-Fox equations. An Ubbelohde viscometer is commonly used to measure the viscosity of polymer solutions and calculate values like intrinsic viscosity. These viscosity values can then be used in the equations to determine the average molecular weight of the polymer. The document also discusses how melt viscosity relates to molecular weight for linear polymers.
The document discusses transport phenomena and provides definitions and examples of key concepts in vector and tensor analysis used to describe transport phenomena. It defines transport phenomena as dealing with the movement of physical quantities in chemical or mechanical processes. There are three main types of transport: momentum, energy, and mass transport. Vector and tensor quantities like velocity, stress, and strain gradient are used to describe transport phenomena. Tensors have a magnitude and direction(s) and transform under coordinate system rotations. The document provides examples of scalar, vector, and tensor notation and the Kronecker delta, alternating unit tensor, and mathematical operations on vectors like addition, dot product, and cross product.
FMM- UNIT I FLUID PROPERTIES AND FLOW CHARACTERISTICSKarthik R
Â
Units and dimensions- Properties of fluids- mass density, specific weight, specific volume, specific gravity, viscosity, compressibility, vapor pressure, surface tension and capillarity. Flow characteristics â concept of control volume - application of continuity equation, energy equation and momentum equation.
Solution:
(a) Pressure at point Q = Height of mercury column x Density of mercury x Gravitational acceleration
= (75 cm) x (1.36 x 104 kg mâ3) x (10 m sâ2)
= 1.02 x 105 Pa
The rate of gas diffusion into a liquid is directly proportional to the partial pressures of the gas, the surface area available for gas exchange, and the solubility coefficient of the gas. It is inversely proportional to the gram molecular weight of the gas molecules and the thickness of the membrane through which diffusion occurs.
This document contains solutions to physics problems involving unit conversions and vector calculations.
1) It provides step-by-step workings and calculations for various conversion problems between units like inches, centimeters, liters, gallons, etc.
2) It also shows the decomposition of vectors into x and y components and calculations of resultant vectors and displacements by summing the x and y components.
3) The problems cover a wide range of physics concepts involving kinematics, forces, densities, areas, volumes, and conversions between different units of length, volume, speed and other physical quantities.
This document discusses surface tension of liquids. It begins by providing examples of surface tension phenomena like water spiders walking on water. It then defines surface tension as the property of liquid surfaces that allows them to resist an external force. The document explains surface tension using molecular theory - molecules in the surface film experience an unbalanced inward force due to stronger cohesive forces within the liquid. This inward force minimizes the surface area and leads to the stretched membrane-like behavior of the surface. The document also defines related terms like surface energy, range of molecular forces, sphere of influence, and provides an example calculation for the force of surface tension.
Determination of molecular weight of polymers by visometryudhay roopavath
Â
This document discusses methods for determining the molecular weight of polymers using viscometry. It defines various types of average molecular weights and explains how intrinsic viscosity is measured through polymer solution viscosity. Viscosity measurements are used to calculate intrinsic viscosity and relate it to molecular weight through the Mark-Houwink-Sakurada equation. Double extrapolation plots of reduced viscosity and inherent viscosity versus concentration are used to determine intrinsic viscosity.
This document discusses methods for characterizing polymer molecular weight. It describes average molecular weights like number-average (Mn) and weight-average (Mw), and how they are calculated. Absolute methods like endgroup analysis directly relate measurable properties to molecular weight, while relative methods like solution viscosity instead relate measurements to molecular weight when calibrated with an absolute technique. Solution viscosity measurements utilize equations like Huggins' to correlate intrinsic viscosity and molecular weight. Size exclusion chromatography can rapidly determine molecular weight distribution and averages.
1) The height of a geotextile tube increases as the required tensile force in the circumferential direction or pumping pressure increases. However, beyond a certain pressure, height increases only marginally while required tensile force rises exponentially.
2) A higher initial water content in soil slurry leads to thinner filter cakes forming above geotextiles, making it easier for soil particles to pass through.
3) Both the number and size of air bubbles trapped in soil filter cakes increases from the bottom to the top of the cake and adversely impacts dewatering rates and permeability.
Physical properties of sediments and water sediment mixtureJyoti Khatiwada
Â
This document discusses various physical properties of sediments and water-sediment mixtures. It defines key concepts like particle density, bulk density, porosity, void ratio, viscosity, and kinematic viscosity. It explains that particle density refers to the density of solid sediment particles, while bulk density includes pore spaces. Porosity and void ratio quantify the pore space. Viscosity and kinematic viscosity describe the resistance of fluids to flow, with kinematic viscosity being the ratio of dynamic viscosity to density. Newtonian mixtures have viscosities that do not depend on shear rate.
multiphase flow modeling and simulation ,Pouriya Niknam , UNIFIPouriya Niknam
Â
This document discusses modeling and simulation of multiphase flows using computational fluid dynamics (CFD). It begins with definitions of multiphase flow and discusses important types including bubbly, droplet, particle-laden, and annular flows. The document then provides tips on multiphase simulation including choosing appropriate modeling approaches such as Lagrangian, Eulerian, or volume of fluid methods depending on the problem. It concludes with discussions of challenges such as convergence difficulties and appropriate solver settings and techniques to address these challenges.
This document contains 19 multiple choice questions regarding mechanical properties of fluids. The questions cover topics such as pressure, density, buoyancy, and their relationships. Key details assessed include the definitions of fluid, gauge pressure, factors that influence pressure in liquids, and applications of fluid properties such as hydraulic jacks.
1. The dynamics of fine particles are important for understanding dust control in mines. Small particles have a high surface area, which leads to greater viscous resistance in air compared to larger particles.
2. When a small particle falls due to gravity, viscous resistance from air increases with velocity until the particle reaches a constant terminal settling velocity. Terminal velocities of fine particles are very small, causing them to remain suspended for long periods.
3. Newton derived the drag force equation for spherical particles moving through a fluid. For small particles, Stokes derived an equation showing drag force is directly proportional to velocity. Understanding drag forces and terminal settling velocities is key to modeling aerosol particle behavior.
What happens when the digital tools and platforms we make and use for communication and entertainment are hijacked for terrorism, violence against the vulnerable and nefarious transactions? What role do designers and developers play? Are we complicit as creators of these technologies and products? Should we police them or fight back? As Portfolio Lead for Northern Lab, Northern Trust's internal innovation startup focused on client and partner experience, Antonio will share a mix of provocative scenarios torn from today's headlines and compelling stories where activism and technology facilitated peaceâand war.
As a call-to-action for designers and developers to engage in projects capable of transformational change, he'll explore the question: How might technology foster new experiences to better accelerate social activism and make the world a smarter, safer place?
This document summarizes upcoming CSS features like Box Alignment Level 3, CSS Grid Layout, CSS Shapes, CSS Feature Queries, and CSS Custom Properties. It explains what each feature does at a high level and provides example code snippets. The document also encourages developers to get involved by filing issues on browser bug trackers, requesting new features, and creating blog posts/demos to help drive adoption of these new CSS specifications.
My books- Hacking Digital Learning Strategies http://hackingdls.com & Learning to Go https://gum.co/learn2go
Resources at http://shellyterrell.com/classmanagement
The reality for companies that are trying to figure out their blogging or content strategy is that there's a lot of content to write beyond just the "buy now" page.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
The document discusses differentiation and its applications. It provides a brief history of differentiation and introduces concepts such as the derivative and reverse process of integration. Some key applications of differentiation discussed include using it to determine maximum/minimum values, in subjects like physics, chemistry, and economics, and in devices like odometers, speedometers, and radar guns. Two surveys were conducted on the awareness and uses of differentiation. In conclusion, differentiation can help improve devices and make tomorrow better by finding how one variable changes with respect to another.
This document provides an itinerary and overview for a 3-day sharing session on characterization of powders and porous solids. The itinerary outlines topics to be covered each day, including gas sorption, mercury porosimetry, chemisorption, microporosity, and more. The document also provides brief histories of sorption science and techniques for measuring properties like particle size, porosity, and specific surface area. Methods discussed include gas adsorption, mercury porosimetry, microscopy, and light scattering.
Micromeritics is the study of the properties of small particles. It involves characterizing individual particles and particle size distributions in powders. Particle size is important for properties like dissolution, flowability, and stability. Smaller particle sizes increase surface area and dissolution rate. Different techniques measure different particle size parameters like length, surface area, or volume. Understanding the particle size distribution provides essential information about the range of particle sizes present in a sample.
This document introduces key terminology used in multiphase flow modeling. It defines a continuous phase/primary phase as the bulk carrier fluid and dispersed phase/secondary phase as the discrete particles, droplets, or bubbles suspended in the continuous phase. Volume fraction and densities are also defined for both phases. Velocities include superficial velocities based on mass flow rates and phase velocities relating the actual velocity to volume fraction. Other terms introduced are mass concentration, quality, phase loading, and Stokes number which indicates particle independence from the continuous phase flow.
Physical Characterization of a Method for Production of High Stability Suspen...Editor IJCATR
Â
Suspensions/Dispersions are encountered in a wide range of
applications, e.g., liquid abrasive cleaners, ceramics, medicines,
inks, paintsâŠ.etc. In most cases it is necessary to keep the
suspension stable for the product lifetime. A new modified
differential sedimentation measuring system is suggested and used
to identify physical parameters affecting the sedimentation in
suspensions. The technique is discussed in details. It is found that
particle sizes as well as viscosity of continuous phase are the most
important factors governing the stability of a suspension. Empirical
relations are extracted to quantitatively describe the weight effect of
each factor. The modified measuring system shows good accuracy
enough to detect fluctuations in concentration of suspended
particles due to their Brownian diffusion, as well as the particles
concentrations in the stable suspension. This study confirmed the
fact that particles diameters measured by Zetasizer are much
greater than those measured by the transmission electron
microscope. This study presents a proposal for new technique for
particle size separation based on the differential sedimentation in
viscose fluids. This new method is a differential viscosity column.
The proposed size separation technique may help to separate
engineered nano-particles with higher resolution
Mate 280 characterization of powders and porous materialsSami Ali
Â
Particle size, surface area, and porosity are important characteristics that control many properties of materials. Particle size can be measured using techniques like sieving, sedimentation, light scattering, and gas adsorption which measure different parameters like size, surface area, or settling rate depending on the technique. Gas adsorption is commonly used to measure specific surface area and porosity by adsorbing gas molecules on the internal surface of porous materials.
Dynamic light scattering measures the fluctuation changes in the intensity of scattered light to determine particle size and properties. It works by measuring the rate at which the intensity of scattered light fluctuates due to Brownian motion of particles. Larger particles diffuse more slowly than smaller particles, so intensity fluctuations are slower for large particles. The correlation function contains information about particle diffusion, with steeper curves indicating more monodisperse samples and more extended decay indicating greater polydispersity. Dynamic light scattering can determine particle size distribution, hydrodynamic radius, and diffusion coefficient.
Dynamic light scattering measures the fluctuation changes in the intensity of scattered light to determine particle size and properties. It works by measuring the rate at which the intensity of scattered light fluctuates due to Brownian motion of particles. Larger particles diffuse more slowly than smaller particles, so intensity fluctuations are slower for large particles. The correlation function contains information about particle diffusion, with steeper curves indicating more monodisperse samples and more extended decay indicating greater polydispersity. Dynamic light scattering can determine particle size distribution, hydrodynamic radius, and diffusion coefficient.
The document provides information about the evaluation scheme, course outcomes, history, and concepts of chemical engineering and mechanical operations for a course. It discusses particle characterization, average particle sizes including Sauter mean diameter, and provides an example calculation for determining Sauter mean diameter from size analysis data.
Simple Harmonic Oscillator Equipment ï· No special safet.docxjennifer822
Â
Simple Harmonic Oscillator
Equipment:
ï· No special safety equipment is required for this lab.
ï· Computer with PASCO 850 Universal Interface and PASCO Capstone
ï· PASCO Motion Sensor
ï· Vertical Stand with horizontal cross bar.
ï· Spring kit.
ï· Mass hanger.
ï· Set of masses.
Introduction
Imagine a spring that is suspended from a support. When no mass is attached at the end of the
spring, it has a length L (called its rest length). If a mass is added to the spring, its length increases by
âL. The equilibrium position of the mass is now a distance L + âL from the springâs support
What happens if the mass is pulled down a small distance A from the equilibrium position? The
spring exerts a restoring force, F = -kx, where x is the distance the spring is pulled down and k is the
force constant of the spring. The negative sign indicates that the force points opposite of the
direction of the displacement of the mass. The restoring force causes the mass to oscillate or move
up and down within a range of A from the equilibrium. The distance A or maximum displacement
from the equilibrium is called an amplitude of oscillation. The period of oscillation for simple
harmonic motion depends on the mass and the force constant of the spring.
We expect that the frequency of the oscillations will be found from:
đ =
1
2đ
â
đ
đ
Here, đ is the frequency in hertz (Hz), đ is the spring constant in N/m, and đ is the mass attached to
the spring, in kg.
Another measure of the oscillations is the period. This is the time for one oscillation. It is:
đ =
1
đ
= 2đâ
đ
đ
Note that the amplitude of oscillation is not present in the formulas above and, therefore, it has no
effect on the period and frequency of oscillation.
Objective
ï· To verify the dependence of a period of a spring-mass system acting as a simple harmonic
oscillator on mass, spring constant, and amplitude.
Part #1. Measuring the Spring-Mass System
1. Suspend a green spring from a horizontal support rod and add enough mass to the other end
to stretch the spring so the coils do not touch.
2. Open âMotion Sensor Set Upâ file located online next to the lab instructions.
3. Place the Motion Sensor directly under the spring and orient it at 90°.
4. Lightly tap the mass. Let it oscillate a few times so the mass hanger will move up-and-down
without much side-to-side motion. Make sure the coils donât touch when the mass is at its
highest point. If they do, try to create a more gentle oscillation.
5. While the mass is oscillating, press Record to monitor the position of the mass relative to the
sensor over a period of several oscillations.
6. Rescale the data to fit the Graph window if necessary.
7. Using the Coordinate Tool, measure the time of five consecutive peaks.
8. Use the measured time to calculate the experimental value of the period of oscillations by
calculating the difference between two sequ
1) The dynamics and physical properties of fine particles are important for understanding dust control in mines. Small particles have a high surface area to mass ratio.
2) As particle size decreases, viscous resistance from air increases due to the larger surface area. A small particle falling in air is opposed by viscous resistance until it reaches a constant terminal settling velocity.
3) The terminal settling velocity of fine particles is very small, on the order of centimeters or millimeters per hour, which is why airborne fine dust particles can remain suspended for a long time.
This document discusses applications of integral calculus to physics and engineering problems involving force, pressure, and centers of mass. It provides examples of using integrals to calculate the hydrostatic force on structures like dams and cylinders submerged in water. It also explains how to find the center of mass of an object or system of point masses by taking moments about axes and dividing by total mass. Formulas are given for calculating hydrostatic pressure, moments, and centers of mass in one and two dimensions.
Packed beds and fluidized beds are devices that provide a large surface area for contact between gases/liquids and solids/gases to enable rapid mass and heat transfer. In packed beds, a packing material is placed in a column through which a liquid flows downward and a gas flows upward in countercurrent fashion. The pressure drop through the bed can be calculated using the Ergun equation. A fluidized bed is a packed bed where the upward fluid velocity is high enough to loosen the particles, allowing them to behave like a fluid mixture. The minimum fluidization velocity is the velocity where the upward fluid force balances the particle weight.
This document discusses the effect of mass and partial slip on boundary layer flow of a nanofluid over a porous plate embedded in a porous medium. The governing equations for momentum, energy, and nanoparticle concentration are presented. Similarity transformations are applied to reduce the governing partial differential equations to a system of ordinary differential equations. The equations are then solved numerically using the fourth-order Runge-Kutta method. Results for shear stress, temperature distribution, nanoparticle volume fraction, skin friction coefficient, Nusselt number, and Sherwood number are obtained to illustrate the effects of various parameters including mass slip, partial slip, permeability, thermophoresis, and Brownian motion.
This document provides an introduction to fluid mechanics. It discusses the key topics in fluid mechanics including fluid statics, kinematics, and fluid dynamics. It also defines important fluid properties such as density, viscosity, compressibility, and surface tension. Density measures the mass per unit volume of a substance and can vary with temperature and pressure. Viscosity represents the internal friction within fluids. Compressibility measures how a fluid's volume changes with pressure. Surface tension is responsible for capillary action in small tubes.
This document summarizes a numerical study on free-surface flow conducted using a computational fluid dynamics (CFD) solver. The study examines the wave profile generated by a submerged hydrofoil through several test cases varying parameters like the turbulence model, grid resolution, and hydrofoil depth. The document provides background on the governing equations solved by the CFD solver and the interface capturing technique used to model the free surface. Five test cases are described that investigate grid convergence, the impact of laminar vs turbulent models, the relationship between hydrofoil depth and wave height, and the effect of discretization schemes.
Fluid properties such as density, specific volume, specific weight, specific gravity, compressibility, viscosity, and surface tension are discussed. Density is defined as the mass of a substance per unit volume. Specific volume is defined as the volume of substance per unit mass. Specific weight is the weight of substance per unit volume. Specific gravity is the ratio of density of a substance to the density of water. Compressibility refers to the change in volume of a fluid with changes in pressure. Viscosity is a measure of a fluid's resistance to shear forces and depends on factors like cohesion and molecular momentum. The falling sphere viscometer is used to measure viscosity and involves dropping a sphere in a fluid and measuring its velocity over
The current study examines the generation and propagation of a Third order solitary water wave along
the channel. Surface displacement and wave profi le prediction challenges are interesting subjects in the
fi eld of marine engineering and many researchers have tried to investigate these parameters. To study the
wave propagation problem, here, fi rstly the meshless Incompressible Smoothed Particle Hydrodynamics
(ISPH) numerical method is described. Secondly,
Main Java[All of the Base Concepts}.docxadhitya5119
Â
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
This presentation was provided by Steph Pollock of The American Psychological Associationâs Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Â
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
How to Fix the Import Error in the Odoo 17Celine George
Â
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Â
Letâs explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Â
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
Advantages and Disadvantages of CMS from an SEO Perspective
Â
Partical technology
1. Chapter 1. Characterisation of solid particles
What is particle technology?
Techniques for processing and handling particulate solids. It plays a
major role in the production of materials in industry.
Chapter 1. Characterisation of solid particles
Individual solid particles are characterised by their size, shape, and
density.
1.1 Particle shape
The shape of an individual particle is expressed in terms of the
sphericity F s, which is independent of particle size. The sphericity of a
particle is the ratio of the surface-volume ratio of a sphere with equal
volume as the particle and the surface-volume ratio of the particle. For a
spherical particle of diameter D p, F s =1; for a non-spherical particle,
the sphericity is defined as
Dp: equivalent diameter of particle
Sp: surface area of one particle
vp: volume of one particle
The equivalent diameter is sometimes defined as the diameter of a
sphere of equal volume. For fine particles, Dp is usually taken to be the
nominal size based on screen analysis or microscopic analysis. The
surface area is found from adsorption measurements or from the
pressure drop in a bed of particles. For many crushed materials, F s is
between 0.6 and 0.8. For particles rounded by abrasion, F smay be as
high as 0.95.
1.2 Particle size
In general "diameter" may be specified for any equidimensional
particles. Particles that are not equidimensional, i.e. that are longer in
one direction than in others, are often characterised by the second
2. longest major dimension. For needle like particles, Dp would refer to the
thickness of the particle, not their length. Units used for particle size
depend on the size of particles.
Coarse particles: inches or millimetres
Fine particles: screen size
Very fine particles: micrometers or nanometers
Ultra fine particles: surface area per unit mass, m2/g
1.3 Mixed particle sizes and size analysis
In a sample of uniform particles of diameter Dp, the total volume of the
particles is m/r p, where m = mass of the sample, r p = density. Since the
volume of one particle is vp, the total number of particle in the sample is
The total surface area of the particles is
To apply the above two equations to mixtures of particles having various
size and densities, the mixture is sorted into fractions, each of constant
density and approximately constant size.
1.4 Specific surface of mixture
If the particle density r p and spericity F s are known, the surface area of
particles in each fraction can be calculated and added to give the specific
surface, Aw.
where xi = mass fraction in a given increment,
= average diameter,
taken as arithmetic average of the smallest and largest particle diameters
3. in increment.
1.5 Average particle size
(1). Volume-surface mean diameter,
, defined by
If the number of particles in each fraction Ni is known, then
(2). Arithmetic mean diameter
NT = number of particles in the entire sample
(3). Mass mean diameter
(4). Volume mean diameter
1.6 Number of particles in mixture
4. The volume of any particle is proportional to its "diameter" cubed.
a = volume shape factor
Assuming that a is independent of size
1.7 Screen analysis
Standard screens are used to measure the size (and size distribution) of
particles in the size range between about 3 and 0.0015in (76mm and
38m m).
Screen is identified by meshes per inch, e.g. 10mesh, Dp = 1/10 = 0.1in.
The area of the openings in any one screen in the series is exactly twice
that of the openings in the next smaller screen. The ratio of the actual
mesh dimension of any screen to that of the next smaller screen is
=1.41.
Analysis using standard screen: Screens are arranged serially in a stack,
with the smallest mesh at the bottom and the largest at the top. Materials
are loaded at top and then shacked for a period of time (e.g. 20 minutes).
14/20: through 14 mesh and on 20 mesh
Screen analysis gives: xi and
.
Chapter 2. Motion of Particles through Fluids
2.1 Motion of particles through fluids
2.1.1 Mechanics of particle motion
Three forces acting on a particle moving through a fluid:
1). The external force, gravitational or centrifugal;
2). The buoyant force, which acts parallel with the external force but in
5. the opposite direction;
3). The drag force, which appears whenever there is relative motion
between the particle and the fluid
Drag: the force in the direction of flow exerted by the fluid on the solid is
called drag.
2.1.2 Equations for one-dimensional motion of particle through fluid
Consider a particle of mass m moving through a fluid under the action of
an external force Fe. Let the velocity of the particle relative to the fluid
be u, let the buoyant force on the particle be Fb and let the drag be FD,
then
(1)
The external force can be expressed as a product of the mass and the
acceleration ae of the particle from this force,
(2)
The buoyant force is, be Archimedesâ law, the product of the mass of the
fluid displaced by the particle and the acceleration from the external
force. The volume of the particle is m/r p, the mass of fluid displaced is
(m/r p)r , where r is the density of the fluid. The buoyant force is then
Fb = mr ae/r p (3)
The drag force is
FD = CDu2r Ap/2 (4)
where CD is the drag coefficient, Ap is the projected area of the particle
in the plane perpendicular to the flow direction.
By substituting the forces into Eq(1), we have
6. (5)
Motion from gravitational force:
In this case, ae = g
(6)
Motion in a centrifugal field:
ae = rw 2
(7)
In this equation, u is the velocity of the particle relative to the fluid and is
directed outwardly along a radius.
2.2 Terminal velocity
In gravitational settling, g is constant. Also, the drag always increases
with velocity. The acceleration decreases with time and approaches zero.
The particle quickly reaches a constant velocity which is the maximum
attainable under the circumstances. This maximum settling velocity is
called terminal velocity.
(8)
(9)
In motion from a centrifugal force, the velocity depends on the radius
and the acceleration is not constant if the particle is in motion with
respect to the fluid. In many practical use of centrifugal force, du/dt is
small. If du/dt is neglected, then
7. (10)
Motion of spherical particles:
If the particles are spheres of diameter Dp, then
m = p Dp3r p/6
Ap = p Dp2/4
Substitution of m and Ap into the equation for ut gives the equation for
gravity settling of spheres:
(11)
2.3 Drag coefficient
Drag coefficient is a function of Reynolds number. The drag curve
applies only under restricted conditions:
i). The particle must be a solid sphere;
ii). The particle must be far from other particles and the vessel wall so
that the flow pattern around the particle is not distorted;
iii). It must be moving at its terminal velocity with respect to the fluid.
Particle Reynolds number:
(12)
u: velocity of approaching stream
Dp: diameter of the particle
r : density of fluid
8. m : viscosity of fluid
Stokesâ law applies for particle Reynolds number less than 1.0
CD = 24/NRe,p (13)
From Eq(4)
FD = 3p m ut Dp (14)
From Eq(11)
ut = g Dp2(r p - r )/(18m ) (15)
At NRe,p =1, CD =26.5 instead of 24 from the above equation.
Centrifugal: rw 2 Âź g.
For 1000 < NRe,p <200,000, use Newtonâs law
CD = 0.44 (16)
FD= 0.055p Dp2 ut2r (17)
(18)
Newtonâs law applies to fairly large particles falling in gases or low
viscosity fluids.
Terminal velocity can be found by trial and error after
9. guessing NRe,p to get an initial estimate of CD.
2.4 Criterion for settling regime
To identify the range in which the motion of the particle lies, the velocity
term is eliminated from the Reynolds number by substituting utfrom
Stokesâ law
(19)
If Stokesâ law is to apply, NRe,p <1.0. Let us introduce a convenient
criterion K
(20)
Then NRe,p = K3/18. Setting NRe,p = 1 and solving for K gives K=2.6.
If K is less than 2.6 then Stokesâ law applies.
Substitution for ut using Newtonâs law
NRe,p = 1.75K1.5
Setting NRe,p = 1000 and solving for K gives K = 68.9. Setting NRe,p =
200,000 and solving for K gives K = 2,360.
· Stokesâ law range: K < 2.6
· Newtonâs law range: 68.9 < K < 2,360
· when K > 2,360 or 2.6 < K < 68.9, ut is found
from
using a value of CD found by trial from the
curve.
2.5 Hindered settling
In hindered settling, the velocity gradients around each particle are
affected by the presence of nearby particles. So the normal drag
10. correlations do not apply. Also, the particles in settling displace liquid,
which flows upward and make the particle velocity relative to the fluid
greater than the absolute settling velocity. For uniform suspension, the
settling velocity us can be estimated from the terminal velocity for an
isolated particle using the empirical equation of Maude and Whitmore
us = ut(e )n
Exponent n changes from about 4.6 in the Stokesâ law range to about 2.5
in the Newtonâs law region. For very small particles, the calculated
ratio us/ut is 0.62 for e =0.9 and 0.095 for e =0.6. With large particles, the
corresponding ratios are us/ut = 0.77 and 0.28; the hindered settling
effect is not as profound because the boundary layer thickness is a
smaller fraction of the particle size.
If particles of a given size are falling through a suspension of much finer
solids, the terminal velocity of the larger particles should be calculated
using the density and viscosity of the fine suspension. The MaudeWhitmore equation may then be used to estimate the settling velocity
with e taken as the volume fraction of the fine suspension, not the total
void fraction.
Suspensions of very fine sand in water is used in separating coal from
heavy minerals and the density of the suspension is adjusted to a value
slightly greater than that of coal to make the coal particles rise to the
surface, while the mineral particles sink to the bottom.
Chapter 3. Size Reduction
Four commonly used methods for size reduction: 1). Compression; 2). Impact; 3).
Attrition; 4). Cutting.
3.1 Principle of size reduction
Criteria for size reduction
An ideal crusher would (1) have a large capacity; (2) require a small power input per
unit of product; and (3) yield a product of the single size distribution desired.
Energy and power requirements in size reduction
The cost of power is a major expense in crushing and grinding, so the factors that
control this cost are important.
11. 3.2 Crushing efficiency
3.2.1 Empirical relationships: Rittingerâs and Kickâs law
The work required in crushing is proportional to the new surface created. This is
equivalent to the statement that the crushing efficiency is constant and, for a giving
machine and material, is independent of the sizes of feed and product. If the
sphericities a (before size reduction) and b (after size reduction) are equal and the
machine efficiency is constant, the Rittingerâs law can be written as
where P is the power required,
particle diameter before crushing,
and Kr is Rittingerâs coefficient.
is the feed rate to crusher,
is the average
is the average particle diameter after crushing,
Kickâs law: the work required for crushing a given mass of material is constant for the
same reduction ratio, that is the ratio of the initial particle size to the finial particle size
where Kk is Kickâs coefficient.
3.2.2 Bond crushing law and work index
The work required to form particles of size Dp from very large feed is proportional to
the square root of the surface-to-volume ratio of the product, sp/vp. Since s = 6/Dp, it
follows that
where Kb is a constant that depends on the type of machine and on the material being
crushed.
The work index, wi, is defined as the gross energy required in KWH per ton of feed to
reduce a very large feed to such a size that 80% of the product passes a 100 m screen.
If Dp is in millimetres, P in KW, and
in tons per hour, then
12. If 80% of the feed passes a mesh size of Dpa millimetres and 80% of the product a
mesh of Dpb millimetres, it follows that
Example: What is the power required to crush 100 ton/h of limestone if 80% of the
feed pass a 2-in screen and 80% of the product a 1/8 in screen? The work index for
limestone is 12.74.
Solution:
=100 ton/h, wi =12.74, Dpa =2 25.4=50.8 mm, Dpb =25.4/8=3.175 mm
3.3 Size reduction equipment
Size reduction equipment is divided into crushers, grinders, ultrafine grinders, and
cutting machines. Crusher do the heavy work of breaking large pieces of solid material
into small lumps. A primary crusher operates on run-of -mine material accepting
anything that comes from mine face and breaking it into 150 to 250 mm lumps.
A secondary crusher reduces these lumps into particles perhaps 6mm in
size. Grinders reduce crushed feed to powder. The product from an intermediate
grinder might pass a 40-mesh screen; most of the product from a fine grinder would
pass a 200-mesh screen with a 74 m opening. An ultrafine grinder accepts feed
particles no larger than 6mm and the product size is typically 1 to 5 m. Cutters give
particles of definite size and shape, 2 to 10mm in length.
The principal types of size-reduction machines are as follows:
A. Crushers (coarse and fine)
1. Jaw crushers
2. Gyratory crushers
3. Crushing rolls
B. Grinders (intermediate and fine)
1.
2.
3.
4.
Hammer mills; impactors
Rolling-compression mills
Attrition mills
Tumbling mills
C. Ultrafine grinders
13. 1. Hammer mills with internal classification
2. Fluid-energy mills
3. Agitated mills
D. Cutting machines
1. Knife cutters; dicers; slitters
Chapter 4. Mechanical Separations
Mechanical separations are performed based on the physical difference between
particles such as size, shape, or density. Mechanical separations are applicable to
heterogeneous mixtures, not to homogeneous solutions.
4.1 Screening
Screening is a method of separating particles according to size alone.
Undersize: fines, pass through the screen openings
Oversize: tails, do not pass
A single screen can make but a single separation into two fractions. These are called
unsized fractions, because although either the upper or lower limit of the particle sizes
they contain is known, the other limit is unknown. Material passed through a series of
screens of different sizes is separated into sized fractions, i.e. fractions in which both
the maximum and minimum particle sizes are known.
4.1.1 Screening equipment
Stationary screens and grizzlies; Gyrating screens; Vibrating screens; Centrifugal sitter.
Cutting diameter Dpc: marks the point of separation, usually Dpc is chosen to be the
mesh opening of the screen.
Actual screens do not give a perfect separation about the cutting diameter. The
undersize can contain certain amount of material coarser than Dpc, and the oversize can
contain certain amount of material that is smaller than Dpc.
4.1.2 Material balances over a screen
Let F, D, and B be the mass flow rates of feed, overflow, and underflow, respectively,
and xF, xD, and xB be the mass fractions of material A in the streams. The mass
14. fractions of material B in the feed, overflow, and underflow are 1- xF, 1- xD, and 1- xB.
F=D+B
FxF = DxD + BxB
Elimination of B from the above equations gives
Elimination of D gives
4.1.3 Screen effectiveness
A common measure of screen effectiveness is the ratio of oversize material A that is
actually in the overflow to the amount of A entering with the feed. These quantities
are DxD and FxF respectively. Thus
where EA is the screen effectiveness based on the oversize. Similarly, an
effectiveness EB based on the undersize materials is given by
A combined overall effectiveness can be defined as the product of the two individual
ratios.
Example: A quartz mixture is screened through a 10-mesh screen. The cumulative
screen analysis of feed, overflow and underfolw are given in the table. Calculate the
mass ratios of the overflow and underflow to feed and the overall effectiveness of the
screen.
Mesh
Dp (mm)
Feed
Overflow
Underflow
16. or gas, the valuable stream from the filter may be fluid, or the solid, or both.
Sometimes it is neither, as when waste solid must be separated from waste liquid prior
to disposal.
Filters are divided into three main groups: cake filters, clarifying filters, and crossflow
filters. Cake filters separate relatively large amount of solids as a cake of crystals or
sludge. Often they include provisions for washing the cake and for removing some of
the liquid from the solids before discharge. At the start of filtration in a cake filter,
some solid particles enter the pores of the medium and are immobilised, but soon
others begin to collect on the septum surface. After this brief period the cake of solids
does the filtration, not the septum; a visible cake of appreciable thickness builds up on
the surface and must be periodically removed. Clarifying filters remove small amount
of solids to produce a clean gas or a sparkling clear liquid such as beverage. The solid
particles are trapped inside the filter medium or on its external surfaces. Clarifying
filters differ from screens in that the pores of the filter medium are much larger in
diameter than the particles to be removed. In a crossflow filter, the feed suspension
flows under pressure at a fairly high velocity across the filter medium. A thin layer of
solids may form on the surface of the medium, but the high liquid velocity keeps the
layer from building up. The filter medium is a ceramic, metal, or polymer membrane
with pores small enough to exclude most of suspended particles. Some of the liquid
passes through the medium as clear filtrate, leaving a more concentrated suspension
behind.
4.3 The theory of filtration
In cake filters, the particles forming the cake are small and the flow through the bed is
slow. Streamline conditions are invariably obtained. From Kozeny equation,
(1)
where u is the velocity of the filtrate, L is the cake thickness, S is the specific surface of
the particles, is the porosity of cake, is the viscosity of the filtrate, and P is the
applied pressure difference. The filtrate velocity can also be written as
(2)
where V is the volume of filtrate which has passed in time t and A is the total crosssectional area of the filter cake.
For incompressible cakes can be taken as constant and the quantity 3/[5(1- )2S2] is
then a property of the particles forming the cake and should be constant for a given
material. Therefore
17. (3)
where
(4)
Eq(3) is the basic filtration equation and r is termed the specific resistance. It is seen to
depend on and S. For incompressible cakes it is taken as constant, but it will depend
on the rate of deposition, nature of particles, and on forces between the particles.
In Eq(3), the variables V and L are connected, and the relation between them can be
obtained by making a material balance between the solids in the slurry and in the cake.
Mass in the filter cake is (1- )AL
s,
where
s
is the density of the solids.
Mass of liquid retained in the filter cake is AL , where
is the density of the filtrate.
If J is the mass fractions of solids in the original suspension
(5)
That is
(6)
Therefore
(7)
and
(8)
If v is the volume of cake deposited by unit volume of filtrate then:
or
(9)
18. and from Eq(8):
(10)
Substituting for L in Eq(3)
or
(11)
Eq(11) can be regarded as the basic relation between P, V, and t. Two important
types of operation will be considered: 1). where the pressure difference is maintained
constant and, 2). where the rate of filtration is maintained constant.
Constant pressure difference
Eq(11) can be re-written as
(12)
Integrating Eq(12) gives
or
(13)
Thus for a constant pressure filtration, there is a linear relation between V2 and t.
Filtration at constant pressure is more frequently adopted in practical conditions.
Constant rate filtration
constant (14)
19. Therefore
or
In this case,
(15)
P is directly proportional to V.
Flow of filtrate through the septum and cake combined
Suppose that the filter septum to be equivalent to a thickness Ls of cake, then if P is
the pressure drop across the cake and septum combined Eq(3) can be written as:
(16)
i.e.
(17)
For constant rate filtration we have
(18)
For constant pressure filtration we have
(19)
4.4 Separations based on the motion of particles through fluids
Devices that separate particles of differing densities are known as sorting classifiers.
They use one of the two principal separation methods: sink-and-float and differential
settling.
4.4.1. Sink-and-float methods
A sink-and-float method uses a liquid sorting medium, the density of which is
intermediate between that of the light material and that of the heavy material. Then the
heavy particles settle through the medium, and the lighter ones float, and a separation
20. is thus obtained. This method has the advantage that, in principle, the separation
depends only on the difference in the densities of the two substances and is
independent of the particle size. This method is also known as the heavy-fluid
separation.
Heavy fluid processes are used to treat relatively coarse particles, usually greater than
10-mesh. A comment choice of medium is a pseudoliquid consisting of a suspension in
water of fine particles
4.4.2. Differential settling methods
Differential settling methods utilise the difference in terminal velocities that exist
between substances of different density. The density of the medium is less than that of
either substance.
Consider particles of two materials A and B settling through a medium of density .
Let A be the heavier. If the smallest particle of A settles faster than the largest particle
of B, then complete separation of A and B can be achieved.
For settling in the Stokesâ law region, the terminal velocity can be calculated as
For equal-settling particles, utA = utB, therefore
For settling in the Newtonâs law range
If the ratio of diameters of the smallest particle of A and the largest particle of B is
larger than the equal-settling ratio, then perfect separation of A and B can be achieved.