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Size reduction - particle
characterization
Content
• Particulate solids
• Particle characterisation
• Mean particle size
• Particle size distribution
• Efficiency of screening
These are generally more complicated systems than
the fluids, because of their complex geometrical
arrangements and also because of the basic problem of
defining completely the physical state of the material.
Characteristics of an individual particle:
1. Composition: affects density and conductivity
Particle is completely uniform/porous or it may consist of a
continuous matrix in which small particle of second material
are distributed.
2. Size: affects properties such as the surface per unit volume
and the rate at which particle will settle in the fluid.
Particulate solids
• Shape: Regular or irregular, basically used in
development of mathematical models.
Bulk solids :
• Particle size- distribution of particle size in the
mixture and to define the mean size which represents
the behavior of particulate mass as whole.
• It is frequently necessary to reduce the size of
particles, or
• Alternatively to form them into aggregates
• It may be necessary to mix two or more solids, and
• There may be a requirement to separate a mixture into
its components or according to the sizes of the
particles.
• Interaction b/w the particles and the surrounding fluid.
• Single particle: the simplest shape- is the sphere,
because of its symmetry, no orientation factor.
• The size of irregular shape particle is defined in terms of
an equivalent sphere.
• Some of the important sizes of equivalent spheres are:
• The sphere of the same – volume as the particle, surface
area as the particle, surface area per unit volume as the
particle, projected area of the particle on to a plane
perpendicular to its direction of motion; which will just
pass through the same size of square aperture as the
particle, settling velocity as the particle in a specific
fluid.
Particle characterisation
Equivalent dia. Type Symbol Equivalent behavior
Sieve Diameter dA Passing through the same sieve
diameter
Surface Diameter dS Having the same surface area
Volume Diameter dV Having same volume
Surface/Volume
diameter
(Sauter diameter)
dSV Having same surface/volume ratio
Laser Diameter dL Having the same interaction with
laser beam
Stock Diameter dST Of equal density, falling at the
same stock terminal velocity in a
given fluid
Particle size
• Considering all articles are of same size, unit mass of
particles consisting of n1 particles of characteristic
dimension d1, constituting a mass fraction x1, n2 particle
size of d2 and so on……
• If the size distribution can be represented by a continuous
function then:
• Where = density of particle
• K1 is constant whose value depends on the shape of particle.
Mean particle size
• VOLUME MEAN Dia.-
• Expressing this relation in finite difference form
• In terms of particle numbers, rather than mass
fraction
• MEAN VOLUME Dia:
• If instead of fraction of total mass, the surface in each
fraction is plotted against size, than a similar curve is
obtained although the means abscissa ds is then the
surface mean dia.
• Where
• K1 is constant, value depend upon particle shape
• Ds is also known as SAUTER MEAN DIAMETER and is the
dia of particle with the same specific surface as the
powder.
• Substituting for n1 from eqn.
Mean size based on surface
• The size of particle ds’ which is such that if all the particle
are of this size, the total surface will be same as in the
mixture:
• Substituting n1
• LENGTH MEAN Dia:
Mean surface diameter
• A mean length dia or arithmetic mean dia may
also be defined as
• Food material often consist of particle of different size to
characterize such particles materials, it is necessary to determine
their particle size distribution (PSD) to define a mean diameter
size.
• Methods for determining of particle size distribution include
sifting, microscopic examination, laser diffraction techniques etc.
• Sieve analysis is simple technique, commonly used for
determination of PSD and for the quantitative evaluation of the
fineness of powder.
• A weighed amount of material is placed on the top of a stack of
nested mesh sieve with opening sizes decreasing from top to
bottom. The assembly of sieves is mechanically shaken or vibrated
for a period of time.
• The amount of powder retained on each sieve is then weighted and
recorded.
Particle size distribution
• A frequency distribution curve is a plot of the frequency
with which a given particle size occurs (the % of total
particles either on a no. or mass basis) against size.
• Alternatively the data can be plotted as a cumulative
distribution in which either the cumulative % undersize or
the cumulative % oversize is plotted against size.
Mean particle size
• The efficiency of screening is defined as the ratio
of mass of material which passes the screen to the
which is capable of passing.
• Efficiency is based on- the size of particle.
• It may be assumed that the rate of passage of
particles of a given size through screen is
proportional to the number or mass of the
particles of that size on the screen at any instant.
Efficiency of screening
• If w is the mass of particles of a particular size on the screen at a time
t, then:
• Particle and for a given screen-
• Thus mass of particles (w1-w2) passing the screen in time t is given
by:
• A quantitative indication of mean size
The results of size analysis can most
conveniently be represented by mean of
cumulative mass fraction curve, in which
the proportion of particles (x) smaller than
a certain size (d) is plotted against size (d)
Fineness modulus:
• The fineness modulus (FM) is a empirical figure
obtained by adding the total % of the sample of an
aggregate retained on each of a specified series of
sieves and dividing the sum by 100.
• The fineness modulus indicates the uniformity of
grind n resultant product.
• The avg. particle size Dp in mm represented in
terms of fineness modulus:

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Size reduction particle charactrisation

  • 1. Size reduction - particle characterization
  • 2. Content • Particulate solids • Particle characterisation • Mean particle size • Particle size distribution • Efficiency of screening
  • 3. These are generally more complicated systems than the fluids, because of their complex geometrical arrangements and also because of the basic problem of defining completely the physical state of the material. Characteristics of an individual particle: 1. Composition: affects density and conductivity Particle is completely uniform/porous or it may consist of a continuous matrix in which small particle of second material are distributed. 2. Size: affects properties such as the surface per unit volume and the rate at which particle will settle in the fluid. Particulate solids
  • 4. • Shape: Regular or irregular, basically used in development of mathematical models. Bulk solids : • Particle size- distribution of particle size in the mixture and to define the mean size which represents the behavior of particulate mass as whole. • It is frequently necessary to reduce the size of particles, or • Alternatively to form them into aggregates • It may be necessary to mix two or more solids, and • There may be a requirement to separate a mixture into its components or according to the sizes of the particles. • Interaction b/w the particles and the surrounding fluid.
  • 5. • Single particle: the simplest shape- is the sphere, because of its symmetry, no orientation factor. • The size of irregular shape particle is defined in terms of an equivalent sphere. • Some of the important sizes of equivalent spheres are: • The sphere of the same – volume as the particle, surface area as the particle, surface area per unit volume as the particle, projected area of the particle on to a plane perpendicular to its direction of motion; which will just pass through the same size of square aperture as the particle, settling velocity as the particle in a specific fluid. Particle characterisation
  • 6. Equivalent dia. Type Symbol Equivalent behavior Sieve Diameter dA Passing through the same sieve diameter Surface Diameter dS Having the same surface area Volume Diameter dV Having same volume Surface/Volume diameter (Sauter diameter) dSV Having same surface/volume ratio Laser Diameter dL Having the same interaction with laser beam Stock Diameter dST Of equal density, falling at the same stock terminal velocity in a given fluid Particle size
  • 7. • Considering all articles are of same size, unit mass of particles consisting of n1 particles of characteristic dimension d1, constituting a mass fraction x1, n2 particle size of d2 and so on…… • If the size distribution can be represented by a continuous function then: • Where = density of particle • K1 is constant whose value depends on the shape of particle. Mean particle size
  • 8. • VOLUME MEAN Dia.- • Expressing this relation in finite difference form • In terms of particle numbers, rather than mass fraction • MEAN VOLUME Dia:
  • 9. • If instead of fraction of total mass, the surface in each fraction is plotted against size, than a similar curve is obtained although the means abscissa ds is then the surface mean dia. • Where • K1 is constant, value depend upon particle shape • Ds is also known as SAUTER MEAN DIAMETER and is the dia of particle with the same specific surface as the powder. • Substituting for n1 from eqn. Mean size based on surface
  • 10. • The size of particle ds’ which is such that if all the particle are of this size, the total surface will be same as in the mixture: • Substituting n1 • LENGTH MEAN Dia: Mean surface diameter
  • 11. • A mean length dia or arithmetic mean dia may also be defined as
  • 12. • Food material often consist of particle of different size to characterize such particles materials, it is necessary to determine their particle size distribution (PSD) to define a mean diameter size. • Methods for determining of particle size distribution include sifting, microscopic examination, laser diffraction techniques etc. • Sieve analysis is simple technique, commonly used for determination of PSD and for the quantitative evaluation of the fineness of powder. • A weighed amount of material is placed on the top of a stack of nested mesh sieve with opening sizes decreasing from top to bottom. The assembly of sieves is mechanically shaken or vibrated for a period of time. • The amount of powder retained on each sieve is then weighted and recorded. Particle size distribution
  • 13. • A frequency distribution curve is a plot of the frequency with which a given particle size occurs (the % of total particles either on a no. or mass basis) against size. • Alternatively the data can be plotted as a cumulative distribution in which either the cumulative % undersize or the cumulative % oversize is plotted against size. Mean particle size
  • 14. • The efficiency of screening is defined as the ratio of mass of material which passes the screen to the which is capable of passing. • Efficiency is based on- the size of particle. • It may be assumed that the rate of passage of particles of a given size through screen is proportional to the number or mass of the particles of that size on the screen at any instant. Efficiency of screening
  • 15. • If w is the mass of particles of a particular size on the screen at a time t, then: • Particle and for a given screen- • Thus mass of particles (w1-w2) passing the screen in time t is given by: • A quantitative indication of mean size The results of size analysis can most conveniently be represented by mean of cumulative mass fraction curve, in which the proportion of particles (x) smaller than a certain size (d) is plotted against size (d)
  • 16. Fineness modulus: • The fineness modulus (FM) is a empirical figure obtained by adding the total % of the sample of an aggregate retained on each of a specified series of sieves and dividing the sum by 100. • The fineness modulus indicates the uniformity of grind n resultant product. • The avg. particle size Dp in mm represented in terms of fineness modulus: