Particle Size Analysis

UNIT-IV 10 Hrs.
Micromeritics:
Particle size and distribution, mean particle size, number and weight distribution,
particle number, methods for determining particle size by different methods,
counting and separation method, particle shape, specific surface, methods for
determining surface area, permeability, adsorption, derived properties of
powders, porosity, packing arrangement, densities, bulkiness & flow properties.
By; Khalifa M. Asif Y. Asst. Professor Ali-Allana College of Pharmacy, Akkalkuwa

MICROMERITICS

https://youtu.be/ExvzdUA6Ed0
Micromeritics introduction

Definition: It is the science and technology of small particles.
* Given by Dalla Valle
 The unit of particle size used, micrometer (µm), micron (µ).
Micron (µm) [ 1 µm = 10–6m = 10–4 cm = 10–3 mm]
* As particle size decreases , area increases 
Micromeritics

1. Release and dissolution
 Particle size and surface area influence the release of a drug from a
dosage form.
 Higher surface area allows intimate contact of the drug with the
dissolution fluids in-vivo and increases the drug solubility and
dissolution.
2. Absorption and drug action
 Particle size and surface area influence the drug absorption and
subsequently the therapeutic action.
 Higher the dissolution, faster the absorption and hence quicker and
greater the drug action.
Importance of micromeritics in pharmacy
Size and size range of particles are very important in pharmacy.

3. Physical stability
 The particle size in a formulation influences the physical
stability of the suspensions and emulsions.
 Smaller the size of the particle, better the physical stability of
the dosage form.
4. Dose uniformity
 Good flow properties of granules and powders are important in
the manufacturing of tablets and capsules.

5. Determination of pore size of filters
 For accurate determination of pore size of filters the size of
particles are required.
4. Coating of Antigens
 Antigens are coated on adsorbent particles where the particle
size is important for uniform dose calculation.

A powder sample is characterized by three things:
a) Shape of the particles,
b) Size of the particles and
c) Particle Size distribution
Fundamental properties

https://youtu.be/307cVsjR2_k
Shape of the Particles

https://youtu.be/_BHE1ma7e78
Particle size and
Equivalent diameter

https://youtu.be/8lmWaz7CygU
Average Particle Size
and Particle Size
Distribution

Particle Size
The size of a sphere is readily expressed in terms of its diameter.
 Diameter of sphere = 2r
 The surface area of sphere is = 4πr2
 Volume of sphere = 4/3πr3
 Generally pharmaceutical powders are non-spherical in nature and
their surface area and volume change with dimension. Therefore it is
difficult to express the size as a meaningful diameter.
 In such case it is expressed in terms of equivalent spherical diameters.

 The Surface diameter, ds, is the diameter of a sphere with the same
surface area as the particle.
 The Volume diameter, dv, is the diameter of a sphere with the same
volume as the particle.
 The Projected diameter, dp, is the diameter of a sphere with the same
projected area observed under microscope.
 The Stokes diameter, dst, is the diameter which describes an equivalent
sphere undergoing sedimentation at the same rate as the particle.
 The Sieve diameter, dsieve, is the diameter of a sphere that will just pass
through the same aperture size as the particle.
 The volume surface diameter, dvs, is the diameter of a sphere that has
the same ratio of surface area to volume as for the particle.

Average Particle Size
 We can conduct a microscopic examination of a sample of a powder
and record the number of particles.
 Particles lying within various size ranges can be obtained and data
can be plotted shown in Table.

 Edmundson derived a general equation for the average particle size,
whether it be an arithmetic, geometric or a harmonic mean diameter
𝒅𝒎𝒆𝒂𝒏 =
𝜮𝒏𝒅 𝒑+𝒇
𝜮𝒏𝒅 𝒇
𝟏/𝒑
n = the number of particles.
d = equivalent diameters.
p = an index related to the size of an individual particle ( because d
raised to the power p =1, p =2, or p =3 is an expression of the particle
length, surface, or volume, respectively.)
The value of the index p also decides whether the mean is;
arithmetic (if p is positive),
geometric (if p is zero), or
harmonic (p is negative).

 For a collection of particles, the frequency with which a particle in a
certain size range occurs is expressed by nd f.
 When the frequency index, f,
has values of 0, 1, 2, or 3, then
the size frequency distribution
is expressed in terms of the
total number, length, surface,
or volume of the particles,
respectively.
Statistical diameters

If all the particles have same diameter then the powder sample is
called a monodisperse system, but if all the particles are not of
equal sizes then that powder sample is called polydisperse system.
 Most of the pharmaceutical powders and dispersion are
polydisperse systems.

 Any collection of particles is usually polydisperse. It is
therefore necessary to know not only the size of a certain
particle, but also how many particles of the same size exist in the
sample.
 Thus, we need an estimate of the size range present and the
number of each particle size.
 This is the particle-size distribution and from it we can calculate
an average particle size for the sample.
Particle Size Distribution

 When the number of particles lying within a certain size range is
plotted against the size range or mean particle size, a graph is
obtained, that is called as frequency distribution curve.
 The width of histogram represent the size range, and the height
represent the frequency of occurrence in each size range.
 This is important because it is possible to have two samples with
the same average diameter but different distributions.

Number and Weight Distributions
 The data in Table are shown as a number distribution, as they were
collected by a counting technique such as microscopy.
 We can get data based on a weight, rather than a number,
distribution.

 It is possible to convert the number distribution to a weight distribution and
vice versa.
 As the general shape and density of the particles are independent of the size
range present in the sample, an estimate of the weight distribution of the data
in Table can be obtained by calculating the values shown in columns 9 and
10.

 The significant differences in the two distributions is apparent, even
though they relate to the same sample.
 For this reason, it is important to distinguish carefully between size
distributions on a weight and a number basis.

Particle Number
 A significant expression in particle technology is the number of
particles per unit weight, N, which is expressed in terms of dvn·
The number of particles per unit weight is obtained as follows.
Assume that the particles are spheres,
The volume of single particle is = 𝝅𝒅𝟑
𝟔
The mass is = 𝝅𝒅𝟑𝝆
𝟔
 The number of particles per gram is then obtained from the equation
𝑵 =
𝟔
𝝅𝒅𝟑

Methods for determining particle size
Many methods available for determining particle size such as;
1. Separation methods
A. Sieving.
B. Sedimentation.
2. Counting methods
A. Optical microscopy.
B. Conductivity method.
3. Surface area determination
A. Air permeability
B. Adsorption

https://youtu.be/MtbfJy3LIsQ
Methods for
determination of Particle
size & Particle size
distribution.

A guide to range of particle sizes applicable to each method is;
Particle size Method
< 1 m Electron microscope,
Ultracentrifuge,
Adsorption
1 – 100 m Optical microscope,
Sedimentation,
Coulter counter,
Air permeability
50 m Sieving

https://youtu.be/E4WoS5Vth6o
Sieve Analysis

Sieving
(range: 50-1200 µm)
 Standard size sieves are available to cover a
wide range of size.
 Powder is placed on the previously arranged
set of sieves in which the sieves are
arranged in decreasing order of their mesh
size.
 The set of sieve is shaken for a fixed period
(1 to 5 min), using mechanical shaker.
 The material which is retained on each sieve
is collected & weigh separately to obtain
frequency distribution curve.

Advantages
 Easy to perform, simple
 Wide size range
 Inexpensive
Disadvantages
 Known problems of reproducibility.
 Wear/damage of sieve in use or cleaning.
 Irregular/agglomerated particles cause misinterpretation.
 Rod-like particles : overestimate of under-size.
 Duration of shaking may alter the result.

Sedimentation
(range: 0.08-300 µm)
 Methods depend on the fact that the terminal velocity of a
particle in a fluid increases with size.
 Stokes’ equation or Stokes’s law
𝒗 =
𝒉
𝒕
=
𝒅𝒔𝒕
𝟐
𝝆𝟏 − 𝝆𝟐 𝐠
𝟏𝟖𝜼

𝒅𝒔𝒕 =
𝟏𝟖𝜼
𝝆𝟏 − 𝝆𝟐 𝐠
𝒉
𝒕
𝒅𝒔𝒕 = Stokes’s diameter
𝒉 = distance of fall in time t
𝝆𝟏 = density of particles
𝝆𝟐 = density of dispersion medium
𝜼 = viscosity of medium
𝐠 = gravitational acceleration.

Andreasen Pipette
 A 1% or 2% suspension of the particles in a medium
containing a suitable deflocculating agent is
introduced into the vessel and brought to the 550-ml
mark.
 The stoppered vessel is shaken to distribute the
particles uniformly throughout the suspension, and
the apparatus, with pipette in place, is clamped
securely in a constant-temperature bath.
 At various time intervals, 10 ml samples are
withdrawn and discharged by means of the two-way
stopcock.

 The samples are evaporated and weighed or analyzed by other
appropriate means.
 The particle diameter corresponding to the various time periods is
calculated from Stokes's law.
 h in equation being the height of the liquid above the lower end of the
pipette at the time each sample is removed.
 The residue or dried sample obtained at a particular time is the weight
fraction.
 The cumulative percentage by weight undersize can then be plotted
on a probability scale against the particle diameter

Disadvantages
 Sedimentation analyses must be carried out at concentrations
which are sufficiently low for interactive effects between particles
to be negligible.
 Large particles create turbulence.
 Careful temperature control is necessary.
 Particle re-aggregation during extended measurements.
 Particles have to be completely insoluble in the suspending liquid.
Advantages
 Equipment required can be relatively simple and inexpensive.
 Can measure a wide range of sizes with considerable accuracy
and reproducibility.

Conductivity method / Coulter counter
 Particle size ranging from 0.5 to 500 μm is measured by this
method.
 In this method particle volume is measured and converted in to
particle diameter.
 Size is expressed as volume diameter, dv.
 This is quick & accurate method.

 Particles are suspended in a conducting electrolyte and placed in beaker.
 The electrolyte solution is filled In sample cell, that has an orifice and
maintain contact with the external medium.
 Electrodes are placed in
the solution (in side the
cell) and suspension
outside.
 A known volume of a
dilute suspension is
pumped through the
orifice.

 A constant voltage is applied across the electrodes to produce a
current.
 As the particle travels through the orifice, it displaces its own volume
of electrolyte, and this results in an increased resistance between the
two electrodes.
 The change in resistance, which is related to the particle volume,
causes a voltage pulse that is amplified and fed to a pulse-height
analyzer calibrated in terms of particle size.
 The instrument records electronically all those particles producing
pulses that are within two threshold values of the analyzer.
 By systematically varying the threshold settings and counting the
number of particles in a constant sample size, it is possible to obtain a
particle-size distribution.

Advantages
 4000 particles per second can be counted. Therefore size
distribution analysis can be completed in relatively short time.
 It gives accurate results.
Disadvantages
 Unsuitable for polar and highly water soluble materials due to
solvation.
 Instrument is expensive.
Applications
In study of;
 Particle growth in suspension and solution.
 Dissolution of drugs in desired medium
 Effect of antibacterial agent on the growth of micro-organism.
 Size distributions of the mineral part of human kidney stones.

https://youtu.be/bzcc_DqHvqM
Optical Microscopy

 The microscope eyepiece is fitted with a micrometer by which
the size of the particles may be estimated.
Optical microscopy
(range: 0.2-100 µm)

 According to the optical microscopic method, powder is directly
sprinkled on glass slide (or an emulsion or suspension drop is
mounted on ruled slide on a mechanical stage.)
 The microscope eyepiece is fitted with a micrometer (ocular
micrometer or eye piece scale) which is calibrated by using stage
micrometer.
 By matching the particle against the eye piece scale, the size of the
particles can be estimated.
 The ordinary microscope used for measurement the particle-size in the
range of 0.2 to about 100 µm.
 For reproducible result atleast 300-500 particles must be observed.

 The particles are measured along an arbitrarily chosen fixed line,
generally made horizontally across the center of the particle.
 Popular measurements are the
1. Feret diameter
2. Martin diameter
3. projected area diameter.
Martin's diameter is the length of a
line that bisects the particle image.
Feret's diameter is the distance between two tangents on opposite sides of
the particle parallel to some fixed direction, the y direction.
Projected area diameter is the diameter of a circle with the same area as
that of the particle observed perpendicular to the surface on which the
particle rests.

Disadvantages
1. The diameter is obtained from only two dimensions of the particle.
2. The number of particles that must be counted (300-500) to obtain a
good estimation of the distribution makes the method somewhat slow
and tedious.
3. Not suitable for extremely small particles.
4. Unknowingly same particle may be observed repeatedly.
Advantages
1. Simple method.
2. Particles are easily observed.
3. Agglomeration and contamination of particles can be detected.

 The geometric shape and surface condition of particles refers to shape
of particles.
 Particles may be spherical, rounded, elongated, acicular, angular etc.
 If the shape of a particle is perfectly spherical it is easy to express it
by its diameter; but if it is not spherical then it becomes very difficult
to express. Hence, equivalent diameters are taken in to consideration.
 Most of the pharmaceutical particles are not perfectly spherical.
 Particle shape affects the physicochemical, biopharmaceutical
properties of formulation.
Particle Shape

Particle shape and surface area
 The shape affects the flow and packing properties of a powder, as
well as having some influence on the surface area.
 The surface area per unit weight or volume is an important
characteristic of a powder in adsorption and dissolution rate
studies.
 A sphere has minimum surface area per unit volume.
 The more asymmetric a particle, the greater is the surface area per
unit volume.

 The surface area or volume of a sphere can be calculated simply by
𝐒𝐮𝐫𝐟𝐚𝐜𝐞 𝐚𝐫𝐞𝐚 = 𝝅𝒅𝟐
𝐕𝐨𝐥𝐮𝐦𝐞 =
𝝅𝒅𝟑
𝟔
 The surface area and volume of a spherical particle are therefore
proportional to the square and cube, respectively, of the diameter.
 To obtain the surface or volume of a particles whose shape is not
spherical one must choose an equivalent diameter through correction
factor (e.g. for microscopic method, projected diameter, dp)

 By means of proportionality constants, we can then write
𝐒𝐮𝐫𝐟𝐚𝐜𝐞 𝐚𝐫𝐞𝐚 = 𝜶𝒔𝒅𝒑
𝟐 = 𝝅𝒅𝒔
𝟐
where 𝜶𝒔 is the surface area factor and ds is the equivalent surface
diameter.
 For volume we write
𝐕𝐨𝐥𝐮𝐦𝐞 = 𝜶𝒗𝒅𝒑
𝟑 =
𝝅𝒅𝒗
𝟑
𝟔
Where 𝜶𝒗, is the volume factor and dv, is the equivalent volume
diameter.

 The surface area and volume factor “shape factors” are, in reality,
the ratio of one diameter to another.
 Thus, for a sphere,
𝜶𝒔 =
𝝅𝒅𝒔
𝟐
𝒅𝒑
𝟐
= 𝟑. 𝟏𝟒
and
𝜶𝒗 =
𝝅𝒅𝒗
𝟑
𝟔𝒅𝒑
𝟑
= 𝟎. 𝟓𝟐𝟒
 There are as many of these volume and shape factors as there are
pairs of equivalent diameters.
 The ratio 𝜶𝒔/𝜶𝒗, is also used to characterize particle shape.
 When the particle is spherical, 𝜶𝒔/𝜶𝒗= 6.0
 The more asymmetric the particle, the more this ratio exceeds the
minimum value of 6.

Specific surface
Specific surface area is defined as the surface per unit weight (Sw) or unit
volume (Sv) of the material.
 It can be derived from equations given above.
 Taking the general case, for asymmetric particles where the
characteristic dimension is not yet defined,
Sv =
Surface area of particles
volume of particles
Sv =
𝜶𝒔𝒅𝟐
𝜶𝒗𝒅𝟑 =
𝜶𝒔
𝜶𝒗𝒅
=
𝟔
𝒅

𝑺𝒘 =
𝟔
𝒅𝒗𝒔 𝝆
𝑺𝒘 =
𝒔𝒗
𝝆
 The surface area per unit weight therefore,
Or
Sw =
𝜶𝒔
𝜶𝒗𝒅𝒗𝒔𝝆
Where the dimension is now defined as 𝒅𝒗𝒔 the volume-surface
diameter.
 For spherical particles

 The above method of estimation is based on particle diameter
data. It can be used to estimate the specific surface area for non
porous solids.
 For porous materials following methods are used;
1. Adsorption method
2. Air permeability method
Powder surface area-Methods

Adsorption method
 Particles having large specific surface area are good adsorbent
of gases and solute form solution.
 Amount of gas or solute that is adsorbed to form
monomolecular layer on the adsorbent is a function of surface
area of the powder.
Principle

 In this method solute from solution is adsorbed on the surface of test
material whose surface area is to be determined.
 A known quantity of material (adsorbent) is added to solution and stirred
for sufficient period to attain adsorption equilibrium.
 The mixture is the filtered and filtrate is analyzed to find unadsorbed
amount of solute. The difference in amount added and that of amount
unadsorbed gives amount of solute adsorbed.
 From the knowledge of cross-sectional area of a molecule and total number
of solute molecules adsorbed, it is possible to calculate the surface area of
test material.
 A practical example of this type is determination of surface area of
activated charcoal by adsorption method using aqueous acetic acid solution.
Monolayer solution adsorption

 Determination of surface area is carried out by gas adsorption method using
an instrument called Quantsorb.
 A powder material whose surface area is to be determined is placed into a
cell of the instrument. The nitrogen gas is used as adsorbate.
 Helium, an inert gas, which is not adsorbed, is also passed through the
powder in a cell.
 A thermal conductivity detector measures the amount of nitrogen adsorbed
at every equilibrium pressure.
 A bell-shaped curve is obtained on a strip-chart recording system.
 The height of signal gives the rate of adsorption of nitrogen and the area
under the curve is calculated to obtain the amount of gas adsorbed on
powder sample.
Adsorption of gas on powders

Air permeability method
 Powder is packed in the sample holder as a compact plug. In this
packing, surface-surface contact between particles appear as a series of
capillaries. The surface of this capillaries is a function of the surface
area of powder.
 When air is allowed to pass through the powder bed at a constant
pressure, the bed resist the flow of air. This results in the pressure drop.
 The greater the surface area per gram of powder, Sw, the greater the
resistance to flow.
 The permeability of air for a given pressure drop is inversely
proportional to specific surface.
Principle

It consist of sample tube containing the packed powder sample with one end
connected to an air pump through a constant pressure regulator. The other end
is attached to a calibrated manometer.
Fisher subsieve sizer
Pressure
Varies
with
particle
size

Working
 The air pump buildup air pressure and is connected to a
constant pressure regulator.
 Air is passed through the air dryer to remove moisture.
 Air is then allowed to flow through the packed powder in the
sample tube.
 The flow of air is measured by manometer.
 The level of the fluid in manometer indicate the average
diameter of the particles.

The Koezeny-carman equation is used to estimate the surface area by
this method
𝑽 =
𝑨
𝜼 𝒔𝒘
𝟐
∆𝑷𝒕
𝑲𝒍
𝜺
(𝟏 − 𝜺)𝟐
Where,
A = cross sectional area of bed (pack), cm2
∆𝑷 = pressure difference of plug
t = time of flow, seconds
l = length of the sample holder
𝜺 = porosity of powder
Sw = surface area per gram of powder, cm2
/g
𝜼 = viscosity of air
K = a constant of irregular capillaries
V = volume of air flowing through the bed, cm3

Derived properties of powders

1. True density: The true density of a sample excludes the volume
of the pores and voids within the powder sample.
𝑻𝒓𝒖𝒆 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 =
𝑾𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒑𝒐𝒘𝒅𝒆𝒓
𝒕𝒓𝒖𝒆 𝒗𝒐𝒍𝒖𝒎𝒆 𝒐𝒇 𝒑𝒐𝒘𝒅𝒆𝒓
2. Bulk density: The bulk density value includes the volume of all
of the pores within the powder sample.
𝑩𝒖𝒍𝒌 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 (𝝆) =
𝑴𝒂𝒔𝒔 𝒐𝒇 𝒑𝒐𝒘𝒅𝒆𝒓 (𝒘)
𝑩𝒖𝒍𝒌 𝒗𝒐𝒍𝒖𝒎𝒆 (𝑽𝒃)
Density of powders
True volume (VP) = volume of powder itself.
Bulk volume (Vb) = true volume + volume of spaces between particles
Density is defined as weight per unit volume (W/V).

 Bulk density is used to check the uniformity of bulk chemical
(Q.C. measures).
 The size of capsule is mainly determined by bulk volume for a
given dose of material. The higher the bulk volume, lower will be
bulk density & bigger the size of capsule.
 It helps in selecting the proper size of container, packing material,
mixing apparatus in the production of tablet and capsule.
Applications of Bulk density

Porosity
 Porosity or void fraction is a measure of the void (i.e. "empty")
spaces in a material, and is a fraction of the volume of voids over
the total volume,
 Values between 0 and 1, or as a percentage between 0% and 100%.
 Suppose a powder, such as zinc oxide, is placed in a graduated
cylinder and the total volume is noted. The volume occupied is
known as the bulk volume, Vb.

Void volume = Bulk volume – True volume
𝑽 = 𝑽𝒃 − 𝑽𝒑
 If the powder is nonporous, that is, has no internal pores or
capillary spaces, the bulk volume of the powder consists of the
true volume of the solid particles plus the volume of the spaces
between the particles.
 The volume of the spaces, known as the void volume, V, is given
by the equation

The porosity, or voids, ε, of powder is defined as; the ratio of the
void volume to the bulk volume of the packing.
𝑷𝒐𝒓𝒐𝒔𝒊𝒕𝒚(𝜺) =
𝒗𝒐𝒊𝒅 𝒗𝒐𝒍𝒖𝒎𝒆
𝒃𝒖𝒍𝒌 𝒗𝒐𝒍𝒖𝒎𝒆
𝑷𝒐𝒓𝒐𝒔𝒊𝒕𝒚(𝜺) =
𝒃𝒖𝒍𝒌 𝒗𝒐𝒍𝒖𝒎𝒆 − 𝒕𝒓𝒖𝒆 𝒗𝒐𝒍𝒖𝒎𝒆
𝒃𝒖𝒍𝒌 𝒗𝒐𝒍𝒖𝒎𝒆
𝜺 =
𝑽𝒃 − 𝑽𝒑
𝑽𝒃
Porosity is frequently expressed in percent
% 𝜺 = 𝟏 −
𝑽𝒑
𝑽𝒃
× 𝟏𝟎𝟎

Porosity measurement
Porosity of powders can be measured by;
1. Direct method/Taping method
2. Water saturation method
3. Water evaporation method
4. Computed tomography method /industrial CT scanning
5. Mercury intrusion porosimetry
6. Gas expansion method
Applications of Porosity
 Porosity influences the rate of disintegration and dissolution. The
higher the porosity, the faster the rate of dissolution.
 Porosity is applied in the studies of adsorption & diffusion of drug
materials.

Packing Arrangements
 Powder beds of uniform-sized spheres can assume either two ideal
packing arrangements:
(a) closest or rhombohedral and
(b) open, loosest, or cubic packing.
(a) (b)
 The theoretic porosity of a powder consisting of uniform spheres
in close packing is 26% and for loosest packing is 48%.

 The particles in real powders, it is to be expected that the particle of
ordinary powders may have any arrangement intermediate between the
two ideal packings of Figure, an most powders in practice have
porosities between 30% and 50%.
 If the particles are of greatly different sizes, the smaller ones may sift
between the larger ones to give porosities below the theoretical
minimum of 26%.
 If powders containing flocculates or aggregates, which lead to the
formation of bridges and arches in the packing, the porosity may be
above the theoretical maximum of 48%.
 In real powder systems, almost any degree of porosity is possible.
 Crystalline materials compressed under a force of 100,000 lb/in.2 can
have porosities of less than 1%.

Bulkiness
Specific bulk volume, the reciprocal of bulk density, is often called
bulkiness or bulk.
 It is an important consideration in the packaging of powders.
 The bulk density of calcium carbonate can vary from 0.1 to 1.3, and
the lightest or bulkiest type would require a container about 13
times larger than that needed for the heaviest variety.
 Bulkiness increases with a decrease in particle size.
 In a mixture of materials of different sizes, however, the smaller
particles sift between the larger ones and tend to reduce the
bulkiness.

Flow properties
 It depends on particle size, shape, porosity , moisture content and
density.
 Powders may be free-flowing or cohesive (“sticky”).
 Powder transfer through large equipment such as hopper.
Uneven powder flow may results in…
 excess entrapped air within powders → capping or lamination.
 increase particle’s friction with die wall causing lubrication
problems, and increase dust contamination risks during powder
transfer.

Tests to evaluate the flowability of a powder:
1. Carr’s compressibility index
 A volume of powder is filled into a graduated glass cylinder and
repeatedly tapped for a known duration. The volume of powder
after tapping is measured.
𝑪𝒂𝒓𝒓’𝒔 𝒊𝒏𝒅𝒆𝒙 % =
𝑻𝒂𝒑𝒑𝒆𝒅 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 – 𝑷𝒐𝒖𝒓𝒆𝒅 𝒐𝒓 𝒃𝒖𝒍𝒌 𝒅𝒆𝒏𝒔𝒊𝒕𝒚
𝑻𝒂𝒑𝒑𝒆𝒅 𝒅𝒆𝒏𝒔𝒊𝒕𝒚
× 𝟏𝟎𝟎
Flow description % Compressibility
Excellent flow 5-15
Good 16-18
Fair 19-21
Poor 22-35
Very poor 36-40
Extremely poor >40

2. Hausner's ratio
Hausner's ratio=Tapped density /Poured or bulk density
 Hausner's ratio is related to interparticle friction
 Value less than 1.25 indicates good flow.
 Value greater than 1.5 indicates poor flow.

3. The angle of repose 𝜽
 The frictional forces in a loose powder can be measured by the
angle of repose 𝜽.
𝐭𝐚𝒏𝜽 =
𝒉
𝒓
𝜽 = the maximum angle possible between the surface of a pile of
powder and horizontal plane

 The sample is poured onto a horizontal surface and the angle of the
resulting pyramid is measured.
 The user normally selects the funnel orifice through which the
powder flows slowly and reasonably constantly.
Significance
 Angle of repose less than 20 (excellent flow)
 Angle of repose between 20-30 (good flow)
 Angle of repose between 30-34 (Pass flow)
 Angle of repose greater than 40 (poor flow)

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