solids

1. PROPERTIES OF
PARTICULATE SOLIDS

2. PROPERTIES OF SOLIDS
In general, solids are more difficult to handle than
liquids, vapors and gases because they appear in
many forms. They can be large angular pieces, wide
continuous sheets, finely divided powders, and they
may be hard and abrasive, tough and rubbery, soft or
fragile, dusty, plastic sticky. Whatever their form,
means must be found to manipulate these solids as
they occur and if possible to improve their handling
characteristics.

3. PROPERTIES OF SOLIDS
In chemical processes, solids are most commonly
found in the form of particles. The main concern of
this course includes the study of the properties,
methods of formation, modification, separation and
handling of particulates solids.

4. PROPERTIES OF SOLIDS
1. Density – defined as the mass per unit volume and usually expressed by
the symbol 𝜌. Usual units are lbs/ft3 or g/cm3
𝜌 =
𝑚
𝑣
2. Specific Gravity – is the ratio of the density of the material to the density of
some reference substance.
𝑆. 𝐺. =
𝜌𝑠𝑢𝑏𝑠𝑡𝑎𝑛𝑐𝑒
𝜌𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒
(dimensionless ratio)
3. Bulk density(Apparent Density) – the total mass per unit total volume.
Ex. The true density of quartz sand is 2.65 g/cm3 but a 2.65 grams mass of
quartz sand may occupy a total or bulk volume of 2 cm3 and have a bulk density
of 𝜌𝑏 = 1.33 g/𝑐𝑚3
.
𝜌𝑏 =
𝑚𝑡
𝑣𝑡
Bulk density varies with the size distribution of the particles and their
environment hence it is not an intensive property. The porosity of the solids
itself and the material with which the pores or voids are filled influence bulk
density. For a single nonporous particle, the true density 𝜌 equals the bulk
density 𝜌𝑏.

5. PROPERTIES OF SOLIDS
4. Hardness – usually defined as resistance to scratching. For
certain metals and plastics it may be defined as resistance to
indentation. This is usually expressed in terms of Mohs’ scale,
which is based on a series of minerals of increasing hardness
numbers as follows:
1-TALC 6-FELDSPAR
2-GYPSUM 7-QUARTZ
3-CALCITE 8-TOPAZ
4-FLUORITE 9-CORUNDUM, SAPPHIRE
5-APATITE 10-DIAMOND

6. PROPERTIES OF SOLIDS
5. Brittleness – refers to the ease with which a substance may
be broken by impact. The hardness of mineral is not a sure
criterion of its brittleness.
~Friability – the inverse quality to toughness
6. Friction – the resistance to sliding of one material against
another material. The coefficient of friction is the ratio of the
force parallel to the surface of friction in the direction of
motion required to maintain a constant velocity, to the force
perpendicular to the surface of friction and normal to the
direction of motion.

7. CHARACTERIZATION OF SOLID
PARTICLES
Individual solid particles are characterized by their
size, shape and density.
Size and shape are easily specified for regular
particles, such as spheres and cubes, but for irregular
particles ?

8. WHY MEASURE PARTICLE
PROPERTIES?
 Better control of quality of product (cement, urea,
cosmetics etc)
 Better understanding of products, ingredients.
 Designing of equipment for different operations
such as crushing, grinding, conveying, separation,
storage etc.

9. In addition to chemical composition, the behavior of particulate materials is often
dominated by the physical properties of the constituent particles.
These can influence a wide range of material properties including, for example,
reaction and dissolution rates, how easily ingredients flow and mix, or
compressibility and abrasivity.
From a manufacturing and development perspective, some of the most important
physical properties to measure are:
 Particle size
 Particle shape
 Surface properties
 Mechanical properties
 Charge properties
 microstructure

10. 1. PARTICLE SHAPE
The shape of an individual particle is expressed in terms of the sphericity, Φ𝑠
which is independent of particle size.
Sphericity is the ratio of surface area of sphere of same volume as particle to the
surface area of particle.
 For a spherical particle of a diameter Dp ; Φ𝑠=1
 For a non spherical particle; Φ𝑠 =
6𝑣𝑝
𝐷𝑝𝑆𝑝
where: Dp = equivalent diameter or nominal diameter of particle
Sp= surface area of one particle
vp=volume of one particle
Equivalent diameter – is sometimes defined as the diameter of a sphere of equal volume

11. For fine granular materials:
Nominal Size – based on screen analyses or
microscopic examination
Surface Area – found from adsorption
measurements or from pressure drop in a bed of
particles
For many crushed materials, Sphericity is between 0.6
and 0.8.
For particles rounded by abrasion, their sphericity may
be as high as 0.95.
For cubes and cylinders, for which length L equals the
diameter, the equivalent diameter is greater than L
and, Φ𝑠 found from the equivalent diameter would be
0.81 for cubes and 0.87 for cylinders
 it is more convenient to use nominal diameter L for
these shapes
 Surface area to volume ratio is 6/Dp
For column packings (rings and saddles), nominal size

12. 2. PARTICLE SIZE
By far the most important physical property of particulate samples is particle size.
Particle size has a direct influence on material properties such as:
 Reactivity or dissolution rate e.g. catalysts, tablets
 Stability in suspension e.g. sediments, paints
 Efficacy of delivery e.g. asthma inhalers
 Texture and feel e.g. food ingredients
 Appearance e.g. powder coatings and inks
 Flowability and handling e.g. granules
 Viscosity e.g. nasal sprays
 Packing density and porosity e.g. ceramics.
Particle size measurement is routinely carried out across a wide range of industries and is often a critical parameter in the
manufacturing of many products.
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

13. METHODS OF DETERMINING PARTICLE SIZE:
a) Microscope with movable cross hair – for very small particles
b) Screening – simplest method of laboratory sizing
c) Sedimentation – small particles of a given material fall in a fluid at a rate
proportional to their size.
d) Elutriation – dependent on the velocity of settling. Particles whose normal
falling velocity is less than the velocity of the fluid will be carried upward and
out of the vessel.
e) Centrifugation – centrifugal force is substituted for the normal force of
gravity when the size of very small particles is to be determined.
f) Magnetic methods – used if material is paramagnetic (such as magnetite)
Magnetic force is directly proportional to its specific surface.
g) Optical methods – the amount of light transmitted depends upon the
projected area of particles.

14. 2.1 MIXED PARTICLE SIZES AND
SIZE ANALYSIS
In a sample of uniform particles of diameter Dp, the total volume of
the particles is m/ρp, where m = mass of the sample, ρp = density.
Since the volume of one particle is vp, the total number of particle, N
in the sample is:
𝑁 =
𝑚
𝜌𝑝𝑣𝑝
The total surface area of particles, A:
𝐴 = 𝑁𝑠𝑝 =
6 𝑚
Φ𝑠𝜌𝑝𝐷𝑝
where: Dp = particle diameter
m = total mass of sample
𝜌𝑝 = particle density

15. 2.2 SPECIFIC SURFACE OF
MIXTURE
If the particle density ρp and sphericity Φs are known, the surface area
of particles in each fraction can be calculated and added to give the
specific surface, Aw (The total surface area of the unit mass of
particles):
Where xi = mass fraction in a given increment,
Dpi = average diameter (taken as arithmetic average of the
smallest and largest particle diameters in increment).

16. 2.3 AVERAGE PARTICLE SIZE
The average particle size for a mixture of particles is defined in
several different ways.
Volume surface mean diameter Ds:
If number of particle Ni in each fraction is known,
instead of mass fraction xi, then:

17. Arithmetic mean diameter:
NT = number of particles
in the entire sample
Mass mean diameter:
Volume mean diameter:
For sample consisting of uniform particles these
average diameters are, of course, all the same. For
mixture containing particle of various sizes,
however, the several average diameters may differ
widely from one another.

18. 2.4 NUMBER OF PARTICLES IN
MIXTURE
The volume of any particle is proportional to its "diameter" cubed.
a = volume shape factor
Assuming that a is independent of size, then: