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.

1. MICROMERITICS
Prepared by
Nabeela Moosakutty
Lecturer
Dept. of Pharmaceutics
KTN College of Pharmacy, Chalavara

2. Micromeritics
science and technology of small particles
 It is the study of the fundamental
and derived properties of individual
as well as a collection of particles
 Study involves characterization of
individual particles, particle size
distribution and powders
 The name micromeritics was given
by Dalla Valle
 Particle size is denoted in
micrometers µm (microns µ)
1 µm = 10-3 mm / 10-6 m
1nm = 10-9 m / 10-6 mm / 10-3 µm

3. Importance / Applications in pharmacy
 Dissolution and drug release Particle size of a drug affects the release from a
dosage form administered orally, parenterally, rectally and topically. A decrease
in the particle size of the drug increases the dissolution rate due to its high
specific surface area
 The necessary flow properties of solid powders in tablet and capsule
manufacture depends on the particle size, size distribution and particle shape
Asymmetric particles have poor flow characteristics and hence granulation
techniques are used to convert particles of uniform size having good flow
properties
 Bulk density, porosity and compressibility are also dependent on the particle
size and size distribution
Example bulk density of light and heavy magnesium carbonate differs because
of the difference in their particle size
 Rate of sedimentation in suspension and rate of creaming in emulsion is faster
with larger particles. Hence, to make a stable suspension or emulsion the
particle size must be controlled
 For accurate determination of pore size of filters the size of particles are
required
 Antigens are coated on adsorbent particles where the particle size is important
for uniform dose calculation

4.  Absorption and drug action
Particle size and surface area influences the drug absorption and subsequently
the therapeutic action
Higher the dissolution faster the absorption and hence greater the drug action
Physical stability
 Chemical properties of powder particles also depend on the particle size
Example smaller the particle size, more is the surface area exposed for surface
oxidation
 Particle size of the dispersed drug influences the spreadability and
performance of cosmetic preparations example dusting powders
 Particle size and size distribution has a profound influence on the uniform
mixing of the solids
 The stability of the systems (colloids, suspensions and emulsions) depends on
particle size. As the particle size increases the stability of these systems
decreases
 Texture, colour of certain drugs depends upon the particle size
Example difference in colour of yellow and red mercuric oxide is due to their
differences in their particle size
 Extraction and drying processes are accelerated following a reduction in the
particle size of the material
 The adsorption capacity of a material also increases by a decrease in its
particle size

5. Fundamental properties
 Particle size and size distribution
 Particle shape
 Particle volume
 Particle number
 Particle surface area
U.S standard Particle size µm
Very coarse >1000
Coarse 355-1000
Moderately coarse 180-355
Fine 125-180
Very fine 90-125

6. Particle size and size distribution
Particle size is a simple concept but it is a most critical process parameter in
preformulation and manufacturing
The reduction of particle size impacts directly on the bioavailability of drug
Size of a spherical particle expressed in terms of its diameter
For a perfect sphere, the surface area S = πd2
volume V = πd3 / 6
• Equivalent spherical diameter (ESD)
ESD of an irregularly shaped object is the diameter of a sphere of equivalent
volume

7. • Surface diameter ds
Diameter of a sphere having the same surface area as that of the asymmetric
particle in question
• Volume diameter dv
Diameter of a sphere having the same volume as the asymmetric particle in
question
• Projected area diameter dp
Diameter of a sphere having the same observed area as the asymmetric particle in
question, this diameter is usually determined by microscopic technique
• Stokes’ diameter dst
Diameter of an equivalent sphere sediments at the same rate as that of particle in
question, this diameter is usually determined by sedimentation method
According to the IUPAC definition
The equivalent diameter of a non-spherical particle is equal to a diameter of a
spherical particle that exhibits identical properties such as aerodynamic,
hydrodynamic, optical, electrical to that of the investigated non-spherical particle
For particles in non-turbulent motion, the equivalent diameter is identical to the
diameter encountered in the stoke’ s law
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

8. Average particle size
A powder sample is examined
under microscope and the
diameter of the particles are
measured individually. The
average diameter can be
expressed in various ways
Particle size = ∑nd / ∑n
n is the no. of particles in
each size range
d is the mean size range in
µm
Inorder to consider surface
and volume of particles
edmundson modified the
equation
Thus we need an estimate of the size range present and the number or weight
fraction of each particle size
This is the particle size distribution and from it we can calculate an average
particle size for the sample

9. Edmundson has derived a general equation for the average particle size
dmean = [ ∑ndp+f / ∑ndf ]1/p
Where,
n = number of particles in each size range
d = diameter of particles in a given size range
P= index related to the size of an individual particle
F = frequency index
d raised to the power p = 1 stands for length, p = 2 stands for surface area and p = 3
stands for volume of the particle
If p > 0 then dmean is arithmetic mean
If p = 0 then dmean is geometric mean
If p < 0 then dmean harmonic mean
f has values of 0, 1, 2, 3 then the frequency distribution is expressed in number (0),
length (1), surface (2) and volume or weight (3) of the particles, respectively
p f Type of mean
Size
Parameter
Frequency Comments
1 0 Arithmetic Length Number Useful if size range is small.
2 0 Arithmetic Surface Number Average Surface Area
3 0 Arithmetic Volume Number Average weight of particles
1 1 Arithmetic Length Length Of no use
1 2 Arithmetic Length Surface Important Pharmaceutically
1 3 Arithmetic Length Weight Sometimes useful

10. The size of spherical particle definitely and quantitatively explained through
diameter of particle. Particle of any material mostly to be asymmetrical in form and
non-spherical. When particle is hypothetically considered as spherical particle then
diameter of spherical particle can be categorized as ferret diameter; martin diameter;
projected area diameter
Diameter Definition
Feret The distance between tangents on opposite sides of the particle parallel to some
fixed direction that is Y direction
Martin The length of a line that bisects the particle image
Projected
area
The diameter of a circle with the same area as that of particle observed
perpendicular to the surface on which the particle rests

11. When the number or weight of particles lying within a certain size range is
plotted against the size range or mean particle size, a frequency distribution
curve is obtained
This is important because it is possible to have two samples with the same
average diameter but different distributions
Particle size distribution (PSD) is a primary factor referring to the list of values
which defines the range of particle sizes on the basis of their mass or volume of
particles
We cannot use the term average size because different sizes of particles cannot
describe the distribution pattern of the whole sample
The same sample can be measured through different techniques. It is important to
see that the particle size distribution (PSD) has numerous industrial applications
It is vital to define the stability, esthetic appearance, rate of absorption, catalyst
activity and bioavailability of drugs
In addition, regulatory agencies of different countries give special emphasis to
clearly establishing the PSD of excipients as well as pharmaceutical formulations
Types of Particle Size Distribution
 Number weighted distributions
Product quality research institute (PQRI) suggested that the use of image analysis
for particle size distribution will give a number-weighted distribution (number
average diameter)

12. Number weighted size is actually what one could see under a transmission electron
microscope
Volume weighted size means volume: It represents the population of particles, seen
by their volume. It also means that particles having a diameter twice the diameter of
another population of particles will be eight times more important than the smaller
ones (due to the equation of a sphere volume (r3) if the population number is the
same in each case.
Example, consider the fine particles.
Three particles are 1 μm, three are 2 μm,
and three are 3 μm in size (diameter).
Building a number distribution for these
particles will generate a homogeneous
distribution over the size, where each
particle size accounts for one-third of the
total. If this same result were converted to
a volume distribution, the result would
appear differently where 75% of the total
volume comes from the 3 μm particles,
and less than 3% comes from the 1 μm
particles. When presented as a volume
distribution it becomes more obvious that
the majority of the total particle mass or
volume comes from the 3 μm particles

13. Volume weighted distributions
Particle size distribution data are represented via the volume of the particle (volume
average diameter) equivalent to mass, if density is the same in each particle, i.e., the
relative contribution will be proportional to (size). Laser diffraction is the most
popular technique used for volume weighted distribution. From a commercial
perspective, this technique is extremely useful; it provides data for a sample in terms
of its volume/mass
With the number-average and weight-
average molecular masses of a polymer
sample, the number-average particle size
will tend to be more influenced by the
population of smaller particles, and vice
versa, the volume-average size will be
more sensitive to the presence of larger
particles. It is recommended that if one is
interested in a fraction of “extra-super-
nano” particles, the number-average size
should be used, and if the agglomerated or
microparticles admixture is to be followed,
the volume-average size is better option.
Also, the ratio of the volume-average and
number-average sizes will characterize the
width of the size distribution (i.e., size
dispersity)

14. When the log of the particle size is plotted against the cumulative percent
frequency on a probability scale, a linear relationship is obtained. This is known
as Log-probability plot
Has distinct advantage of two parameters- slope of the line and a reference point
• The reference point: logarithm of particle size equivalent to 50% on the
probability scale i.e 50% size (geometric mean diameter)
• The slope of the line: gives geometric standard deviation (σg )
σg = 84% undersize or 16% oversize / 50% size
Or
σg = 50% size / 16% undersize or 84% oversize
 Weight distributions
Data based on weight distributioon can be obtained by techniques such as sieve
analysis, Andreasen pipette etc
Number distribution can be convert into weight distribution and vice versa
Two approaches
• Using calculations based on the values of nd3
• Using Hatch-Choate Equations – log normal distribution curve
Log dln = log dg + 1.151 log2 σg (Number distribution)
Log dln = log dg - 5.757 log2 σg (Weight distribution)

15. Intensity weighted distributions
The intensity distribution is naturally weighted according to the scattering intensity
of each particle fraction or family. For biomaterials, the particle scattering intensity
is proportional to the square of the molecular mass. In itself, the intensity
distribution could be slightly misleading, in that a small amount of aggregation
agglomeration or the presence of a larger particle species can govern the
distribution. However, this distribution can be employed as a sensitive detector for
the presence of large material in the sample
Log - probability graph

16. Particle size determination methods
 Microscopic technique
Optical microscopy
Electron microscopy
 Sieving technique
Sieves
Air-jet sieving
 Sedimentation technique
Andreasen apparatus

17. Microscopic technique
 Most popular and accurate method
 One can look directly the shape of particle as well as check the dispersion and
agglomeration in the sample.
 Method is reasonably cheap and can provide image analysis that can be used for
examination of discrete particles.
 Limitation: the diameter of the particle is obtained from length and breadth i.e.,
it is two-dimensional and does not allow for estimation of thickness of particle
(depth)
Optical Microscopy
Size range 0.25 μm - 100 μm
It serves as a most suitable and favored method for the routine optimization of
some formulation variables
It is applied for the determination of particle size in suspension, aerosol, and
globule size of emulsions
The required sample size is less than 1 g
The particle size in optical microscopy is expressed by projected diameter (dp),
i.e., the diameter of a sphere having the same area as that of irregular particles
when observed under a microscope

18. A sample, dilute suspension of the powder particles
prepared in a liquid vehicle (in which it is insoluble)
and is mounted on a glass slide and placed on the
mechanical stage of microscope. The eyepiece of the
optical microscope is fitted with a micrometer which
is used for particle size determination. The radial field
can be projected on a screen for measurement and
photographs of the projected site can be taken from
the slide. The measurements are made horizontally
across the center of the particle (chosen fixed line)
Has to count 300-500 particles at least to get a good
size distribution analysis of data
As compared to an ultra microscope and electron
microscope, the resolving power is lower in an optical
microscope
Popular methods to express the particle diameter by
microscopic method-
1. Projected area diameter
2. Martin diameter
3. Feret diameter

19. Electron Microscopy
Ex: Scanning Electron Microscopy (SEM) Transmission Electron Microscopy
(TEM)
 An electron microscope is a dynamic instrument that uses highly energetic
electrons of beam for the determination of very fine scales of particles (up to 0.2
μm)
 It has a higher resolving power (0.3 nm) than an optical microscope that allows
the examination of very small objects
 The clear surface features of biological or any other materials can be observed
under electron microscopy e.g., histopathological studies, shape and size of an
organelles and useful in the investigation of clinical specimens like renal
diseases, tumor processes, storage disorders and infectious agents
 Method provides numerous advantages such as high magnification (310,000
and high resolution of 0.3 nm), individual particle examination and particle shape
measurement
However, this method is expensive and a trained operator is required
 SEM provides information related to the topography of particles but this
equipment is expensive and sample preparation for SEM is more complex and
time-consuming than optical microscopy. SEM is faster than TEM in producing
three-dimensional images of particles

20. Sieving technique
Most commonly used method
 Simpler and more cost-effective method for the particle size
analysis than microscopy
 Procedure for sieving analysis, a mass of sample is placed on
the stack of sieve in mechanical shaker. The mass of the sample
is shaken for definite period of time and the portion of sample
that passes from one sieve to be retained on the next finer sieve
is collected and weighed. Obtained data are analyzed for normal,
log-normal cumulative percentage frequency distribution, and
probability curve
 There is the requirement for a trained operator
 Precision is tough to achieve using this technique
 Not applicable for all dispersed systems
 Cohesive or non-spherical particle can clog the aperture due to
generation of electrostatic charge
 Attrition of particles during sieving may lead to size reduction
 Air-jet sieving overcomes the problem of the formation of
clumps on the sieve
In this method, a series of plates are fitted with a
reduced pressure stream of air which blows the particles that
creates the blockage during sieving process. This method is
suitable for particles having size below 40 μm. The sample is
introduced into the sieve and covered with a lid. Sieves fitted
with a powerful vacuum cleaner create a strong jet of air, which
helps to disperse the clogged particles present on the sieve
through the slotted nozzle rotating below the sieve mesh

21. Schematic diagram of air-jet sieving. The material on
the sieve is moved by a rotating jet of air: a vacuum
cleaner which is connected to the sieving machine
generates a vacuum inside the sieving chamber and
sucks in fresh air through a rotating slit nozzle

22. Sedimentation technique
 Sedimentation method is based on the principle of gravity that deals with the
measurement of the rate of settling of the particles of powders which are
uniformly dispersed in a fluid
 This method is used for the measurement of particle size in the range of 1200
μm
 In this method, the particle size is expressed via Stokes diameter (dst) which is
referred to as the diameter of an equivalent sphere having the same rate of
sedimentation of the irregular particles
 Sedimentation of particles can be studied by using Andreasen pipette, balance
method and hydrometer method
The formula of Stokes law
V = h/t = dst
2 (ρs – ρ0) g / 18 ղ0
where,
V is the rate of settling
h is the distance of fall in time t
g is the gravitational acceleration,
dst is the mean diameter of the particles based on the velocity of sedimentation
ρs is the mass density of the particles
ρ0 is the mass density of the medium
η0 is the viscosity of the medium

23. ANDREASEN PIPETTE METHOD
 Developed by Andreasen and Lundberg
 Employs the sedimentation principle - To
analyze the particle size distribution of a powder in
a wet sample
 Sedimentation method is based on the Stokes
law
 The Andreasen fixed pipette comprises of a 200
mm well-calibrated cylindrical vessel of about
5.5cm internal diameter with a vertical scale
graduated from 0 to 20 cm on it and of volume
capacity of 550 ml suspension
The stopper has an integral 10ml bulb
pipette fitted with a two-way stopcock at the
center of the cylinder and held in a position by
glass stopper so that its tip overlaps with the zero
level and a side tube for discharging the sample
The stem of the pipette is made up of
narrow bore tubing in order to minimize the
volume retained in the stem after each sampling.
When the pipette is fitted into its place in the
cylinder, its lower tip is 20cm below the surface of
the suspension

24. The two-way stopcock allows easy withdrawal of samples which can be centrifuged
and weighed. Thus, the weight of each residue taken out is termed as the weight of
undersize and the sum of all weight is called the cumulative weight of undersize
For analysis of particle size distribution
A 1 or 2% suspension of the powder is prepared in a medium containing a suitable
deflocculating agent to break any powder aggregates
The suspension is introduced into the vessel up to the 550ml mark
The vessel is stoppered and shaken to distribute the particles uniformly within the
medium
The pipette is then secured in its place and the whole assembly is kept undisturbed in
a constant temperature bath
At various time intervals, 10ml samples of the suspension are withdrawn through the
two-way stopcock into previously weighed china dishes
The samples are evaporated and weighed
The residue of dried sample obtained at a particular time is the weight fraction
having particles of sizes less than the size obtained by the stokes law calculation
for that time period of settling. The weight of each sample residue is therefore called
weight undersize and the sum of the successive weights is known as the cumulative
weight undersize
The cumulative weight undersize is then plotted on the probability scale against the
particle diameter on the log scale using a log-probability graph paper. Various
statistical diameters are then obtained from the plot

25. Advantages
Technique is simple and apparatus is inexpensive
The results obtained are precise provided the technique is adequately standardised
Disadvantages
Method is laborious since separate analysis are required for each experimental
point on the distribution curve
Very small particles cannot be determined accurately since their settling is unduly
prolonged and is subject to interference due to convection, diffusion and brownian
motion
Centrifugal methods are used for accelerating the rate of sedimentation for
minimizing the above effects
Particle number
Particle number (N) is defined as the number of particles per unit weight of a
powder
Mass = volume x density
N = 1gm of the powder/mass of one particle
N = 1/πdvn
3 ρ/6
N = 6/ πdvn
3 ρ

26. Particle volume
Electronic Scanning Zone (Coulter Counter)
Commonly known as the Coulter counter method
Considered to be the most accurate method for analyzing the particle size of a
sample
Size range: 0.4µm – 1600µm
Principle:
When a particle suspended in a conducting liquid passes through a small orifice, on
either side of which are electrodes, a change in electrical resistance occurs
It consists of two electrodes one of which is dipped into a beaker containing the
particle suspension in an electrolyte (such as 0.9% NaCl)
The other electrode is dipped into the electrolyte solution contained in a glass tube
which in turn is immersed into the beaker containing the particle suspension in the
electrolyte
The glass tube has a very small orifice at its lower end through which the particles
are sucked into the inner glass tube
However, for this method the sample is to be suspended in appropriate dilution in
an electrolyte solution followed by ultrasonication so as to break the agglomerates,
if formed

28. Powder samples are dispersed in the electrolyte to
form a very dilute suspension. A specific volume of
suspension is taken through the orifice. As the
volume of electrolyte fluid enters, it displaces some
volume which causes a change in electrical resistance
which is proportional to the volume of the particle.
This change in the resistance is then converted to
voltage pulse and then amplified and processed
electronically and the pulses which have values
within the pre-calibrated limits are used to split the
particle size distribution
Advantages
Particle size distribution results can be achieved in a
very short period of time with a single count taking
less than 30 seconds
It is reliable for counting 4000 particles in 1 second
Since the aperture is automatic , operator variability
is avoided
Disadvantages
Unsuitable for polar and highly water soluble
materials due to solvation
Aggregation of particles can give false results
It is a sophisticated and expensive method for
analysis

29. Functional schematic of the coulter
When stopcock F is opened, the mercury in the
manometer reservoir R is drawn upward by a
small vaccum pump connected to P, and the
resulting pressure head causes movement of
mercury column J after the stopcock is closed,
drawing sample suspension E from the sample
vessel through the hole in aperture wafer A
into sample tube B. The aperture wafer and
sample tube are made of dielectric materials
having an electrical resistivity much greater
than that of the suspending medium. Via H and
I electrodes C and D couple an electrical
current through the aperture and the resultant
signal pulses to an amplifier pulse counter (not
shown). The volume of sample to be analyzed
is determined by three control electrodes
(K,L,M) penetrating the wall of the manometer
tubing; when the flowing mercury causes
electrical contact between K and L, the pulse
counter starts, while mercury contact with M at
a calibrated distance from L terminates it.
The second stopcock G is only opened to fill or
flush the sample tube with clean suspending
media via O

30. Particle shape
Particle shape is related to geometric shape and surface regularity
Particle shape will influence the surface area, flow of particles,
packing and compaction properties of the particles

31. It is possible to determine whether the shape of a particle is spherical or asymmetric
based on shape factor
A sphere has minimum surface area per unit volume. So these properties can be
compared for spheres and asymmetric particles in order to decide their shape
Property Sphere Particle
Surface area πds
2 αs x dp
2
volume (1/6) πds
3 αv x dp
3
αs = surface area factor
αv = volume factor for the asymmetric particles
Upon solving the appropriate properties
αs = πds
2 / dp
2 αv = πds
3 / 6dp
3
when ds is made equal to dp the relationship becomes,
αs = π = 3.124 and αv = π/6 = 0.524
Shape factor is the ratio of surface to volume factors then,
shape factor = αs / αv
3.124 / 0.524 = 6
The minimum possible value for shape factor is 6, which represents a sphere. If
the ratio exceeds this factor 6, the particle is considered as asymmetric

32. Particle surface area
Specific surface
It is defined as the surface area per unit volume (Sv) or per unit weight (Sw)
Derivation
The surface area per unit volume
Sv = surface area of particles / volume of particles
Sv = n αs d2 / n αv d3
sv = αs / αv d
Where n is the number of particles
The surface area per unit weight
Sw = Sv / ρ
ρ = true density of the particles
Substituting for Sv
Sw = αs / ρ αv dvs
dvs now defined as the volume surface diameter characteristic of specific
surface
For spherical or nearly spherical particles,
Sw = 6 / ρ dvs
(since αs / αv = 6 for a sphere)

33. SURFACE AREA DETERMINATION METHODS
Surface area of a powder can be determined directly by
1. Adsorption method
a. By using a solute which forms a monolayer
b. by using adsorption of gas on powder
2. Air-permeability method
1. Adsorption method
Particles with a large specific surface are good adsorbent for the adsorption of
gases and of solutes from solution
The amount of gas or solute adsorbed on the sample of powder to form a
monolayer is found out

34. By using a solute which forms a monolayer
Adsorption of a solute from its solution onto the surface of the sample powder
A solution of a suitable solute is prepared in a medium in which the adsorbent
powder is insoluble
A known amount of the sample powder is then added to the solution
Contents are stirred for a sufficient period of time
After attaining the equilibrium and the powder is filtered
Amount of solute remaining in the solution is determined
The difference between the quantity added and that remaining in the solution gives
the quantity that has been adsorbed and the specific surface area is determined
Ex: Methanolic solution of stearic acid used to determine surface area of powders
that are insoluble in methanol. Since stearic acid being a linear molecule its
molecules get adsorbed on the powder surface as a monolayer
Disadvantage: Accurate determination is difficult due to the adsorbed solvent
molecules on the powder prevent close packing of the adsorbed solute in the
formation of a monolayer
By using adsorption of gas on powder
Surface area determination BET (Brunauer-Emmett-Teller) Theory of adsorption
Most substances adsorb a monomolecular layer of gas under certain conditions of
partial pressure of gas and temperature
The adsorption process is carried out at liquid nitrogen temperature-196ºC

35. Instrument used : Quantasorb
The sample is first freed from interfering impurities such as air and moisture by
heating it in a continuous stream of helium. The presence of helium even at a
relatively high partial pressure, does not affect the adsorption of nitrogen.
The adsorption and desorption is measured with thermal conductivity detector
A mixture of helium and nitrogen is passed through the cell, containing powder
Nitrogen is adsorbate gas and helium is inert and is not adsorbed on surface
With the help of mathematical calculations and graph studies amount of nitrogen
adsorbed and thereby surface area is calculated
Once surface adsorption has reached equilibrium, the sample is heated and nitrogen
gas is desorbed. Its volume is measured

36. BET equation
Volume of nitrogen gas Vm in cm3 adsorbed
by 1 gm of the powder is
P / V(P0 – P) = 1 / Vm b + (b-1)p / Vm bP0
Where,
V = volume of gas in cm3 adsorbed per
gram of powder at pressure p
P0 = saturated vapour pressure of liquified
nitrogen at the temperature of the experiment
b = a constant and it gives the difference
between the heat of adsorption and the heat
of liquefaction of the nitrogen gas
The specific surface of the powder is
Sw = [Am N / (m / ρ)] Vm
Where,
m / ρ = molar volume of the gas which is
equal to 22,414 cm3 / mole
N = Avogadro’s number 6.02 x 1023
Am = area of a single close packed gas
molecule adsorbed as a monolayer on the
surface of the powder particles. For the
nitrogen the value is 16.2 x 10-16

37. Air-permeability method
Principle
The resistance offered to the flow of a fluid such as air, through a plug of
compacted powder is proportional to the surface area of the powder
Instrument used : Fisher subsieve sizer
Powder is packed in sample holder
Packing appears as series of capillaries at constant pressure
The diameter of capillaries related to average particle size
The internal surface of the capillaries is a function of the surface area of the
particles
According to Poiseuille’s equation
V = πd4 ∆Pt / 128 lղ
V is the volume of air flowing through a capillary of internal diameter d and
length l in t seconds under a pressure difference of ∆P
ղ viscosity of the fluid (air) in poise
When the air is allowed to pass through the plug of a compacted powder,
resistance to the flow of air occurs
This resistance is related to the surface area of the powder. As per

38. A is the cross sectional area of the plug
K is a constant
Ɛ is the porosity
 Flow rate of air is also affected by degree of compression and irregularities in
capillaries
 More compact the plug, lower the porosity
 As the porosity of powders decreases surface area of the powders decreases
 Greater the surface area greater the resistance
 Air-permeability is inversely proportional to the surface area
 Mainly used to control batch to batch variations in specific surface of powders

39. DERIVED PROPERTIES OF POWDER
Properties derived from fundamental properties are called derived properties
• Density
• Porosity
• Compressibility
• Packing arrangements
• Flow properties
Density
 Density is defined as weight per unit volume (W/V)
 During tapping, particles gradually pack more efficiently the powder volume
decreases and the tapped density increases
Bulk density
Bulk density = mass of powder / bulk volume
ρ = w / Vb
Bulk density depends primarily on particle size distribution, particle shape and
tendency of particles to adhere together
The bulk density value includes the volume of all of the pores within the powder
sample
Based on bulk density powders are classified as:
1. Heavy powders – smaller particles may sift between the larger particles- low bulk
volume- high bulk density
2. Light powders – when particles are packed loosely, lots of gaps between particles
-high bulk volume- low bulk density

40. Importance:
 Helps to check the uniformity of bulk chemicals
 In determination of size of capsule for a given dose of material. That is, higher
the bulk volume lower will be bulk density and bigger the size of capsule
size of capsule (capsule no.) is selected based on equation,
capsule volume = capsule fill weight of formulation / tapped bulk density
 Helps in selecting the proper size of a container, packing material, mixing
apparatus in the production of tablets and capsules
capacity of mixing bowl = weight of batch / bulk density
Bulk density apparatus
1. For the determination of the bulk density a weighed
quantity of the powder material (previously sieved) is
introduced into a graduated measuring cylinder
2. The cylinder is fixed on the bulk density apparatus and
the timer knob is set for 100 tappings
3. The volume occupied by the powder is noted
4. Another 50 taps continued and the final volume is
noted
5. The process of tapings continued until concurrent
volume is achieved
6. Final volume is the bulk volume and bulk density is
calculated

41. True density
It is also known as absolute density
It is the density of the material itself
True density = weight of powder / true volume of powder
True volume is the volume obtained excluding the void volume (inter particle spaces)
and intra particle pores
Determination methods for true density
1. Gas displacement method (porous)
2. Liquid displacement method (non-porous)
1.Gas displacement method
Helium and nitrogen gases obey the idea gas law. Both gases do not adsorb on the
material. Helium is preferred because of its smaller size. Helium penetrates the
smallest pores and crevices
Helium pycnometer
It consists of a sample holder which can be
sealed after placing the sample
Valve is connected to the sample holder. It has
provisions for removing the air from the
sample holder and introducing the helium
A pressure detector in order to maintain preset
constant pressure
A piston to read the pressure related to the
volume of the powder

42. Working
volume of empty pycnometer determination
The air present in the sample holder is removed by applying vaccum
Helium gas is passed into the apparatus through the valve
Pressure is set with the help of movable piston
At this position, the reading on the scale denotes U1 – represents volume of empty
cell
calibration of pycnometer
Place a standard sample of known true volume ( Vc ) – stainless steel spheres in the
sample holder – it is sealed and air is removed
Same amount of helium gas is introduced
Pressure is adjusted with the help of piston
at this stage, the reading is denoted U2
The difference between U1 and U2 gives the volume occupied by the sphere
determination of volume of the sample
Stainless steel sphere is replaced by the test sample powder
Air in the pycnometer is replaced by same amount of helium gas
Pressure is adjusted with the help of piston
At this state piston reading is denoted by Us
The difference between U1 and Us gives the volume occupied by the sample
operating equation for the instrument
Vt = [ Vc / U1 - U2 ] U1 - Us
Vt is the true volume of the sample

43. 2. Liquid displacement method
Pycnometer or specific gravity bottle is used
A liquid in which the solid is insoluble is generally used. The powder whose
density is to be determined is added into the bottle of known volume and the
weight determined
Liquid in which the powder is introduced into the bottle, liquid fills up the void
spaces between the particles
bottle is again weighed
Contents of the bottle are emptied and only the liquid is filled into it and weighed
The true density is obtained as the ratio between the
weight of the material and the weight of the liquid it
displaces
True density = W2 – W1 / W4 – W2
Where,
W1 = weight of pycnometer
W2 = weight of pycnometer + sample
W3 = weight of sample ( W2 – W1 )
W4 = weight of pycnometer with powder and filled
with the solvent
W4 – W2 = weight of the liquid displaced by solids
(related to volume of liquid displaced

44. Granule density
It is determined for the granules that are employed in the manufacture of tablets
It is the ratio of the mass of the granular powder and the volume occupied by the
granular material together with its intraparticle spaces
Granule density = granule weight / granule volume
Method: Mercury displacement method
It is determined in a manner similar to liquid displacement method, mercury is
used as the displacement liquid since mercury fills the voids and does not enter
the internal pores of the particles.
Mercury has a high contact angle of 1400 and non-wetting property
Bulkiness
The reciprocal of bulk
density is known as bulk or
bulkiness or specific bulk
volume
Bulkiness increases with a
decrease in particle size
In a mixture of particles with
different sizes, the bulkiness
get reduced since the smaller
particles may sift between
the larger ones

45. Porosity
It is defined as the ratio of void volume to the bulk volume of the powder packing
For a non-porous material the bulk volume is equal to the true volume
Most pharmaceutical solids are porous i.e the bulk volume is greater than true volume
The volume of the spaces known as the void volume
Void volume v = Vb - Vp
Where, Vb = bulk volume Vp = true volume
Porosity or voids (ɛ) = void volume / bulk volume
ɛ = Vb – Vp / Vb
% ɛ = (1 – Vp / Vb ) 100
In general the porosities will be between 30-50%. They vary based on packing
arrangement

46. Importance:
• It influences the rate of
disintegration and dissolution
• Higher the porosity faster
the rate of dissolution
• It is applied in the studies
of adsorption and diffusion
of drug materials
Porosities Type of packing
26% Closed packing
48% Loose packing
30% If particles differ greatly in size distribution
50% Aggregates or flocculates
<1% Crystalline materials
Compressed under a force 1,00,000 lb/ sq. inch

47. Packing arrangements
 The arrangement of particles in a powder influences the volume occupied by it.
Bulk density and porosity are subsequently affected
 Possible packing arrangements in powders
1. closest or rhombohedral packing
2. loosest or cubic packing
Theoretical porosity range: (30-50%)
Cubic : 48% Rhombohedral : 26%
Porosity < theoretical minimum (26%)- particles of varying sizes- smaller
particles fit in the void spaces
Porosity > theoretical maximum (48%)- powder contains floccules or aggregates-
large void spaces with entrapped air

48. Flow properties of powders
Powders may be free-flowing or cohesive (sticky)
Common manufacturing problems are attributes to powder flow
Uneven powder flow – excess entrapped air within powders- capping or
lamination
Uneven powder flow – 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 index
2. Hausner ratio
3. Angle of repose
Reasons for poor flow of powders
• Cohesiveness / stickiness between particles due to Van der Waals,
surface tension and electrostatic forces
Factors depend upon particle size and shape, density or porosity of the powder,
presence of adsorbed materials on the powder surface, presence of
moisture
Particles < 10 microns – more cohesive- due to larger surface area
• Adhesion between the particles and the container wall
• Friction between particles due to surface roughness
• Physical interlocking of particles of irregular shape
• Presence of moisture

49. Two indicators of flow properties are there
(i) Angle of repose
(ii) Flow rate
Angle of repose
This is the maximum angle possible between the
surface of heap (pile) of powder and the
horizontal plane
It helps in quantifying the frictional forces. The
frictional forces mainly contribute to improper
flow of powder
tanø = h / r
Where h = height of pile
r = radius of the base of pile

50. Flow rate measurement:
The flow rate of granules (less cohesive materials) may be assessed by passing the
powder through a circular orifice fitted in the base of a cylindrical container. The
powder is taken in the container and released through the orifice on the pan of a
balance. The weight of powder or granules falling per unit of time is recorded.
To improve the flow properties of granules a type of powders are used, they are
called glidants. Examples of glidants are talc, maize starch and magnesium
stearate
Angle of repose Powder flow
<25 Excellent
25-30 Good
30-40 Passable
40-50 Poor
>50 Very poor
Hausner’s ratio
It is related to interparticle friction
The powder with low interparticle friction, such as coarse spheres
Hausner’s ratio = tapped density / fluff density
More cohesive, less free flowing powders such as flakes
Between 1.25 and 1.5 added glidant normally improves flow
>1.5 added glidant doesn’t improve flow

51. Compressibility
Its also known as Carr’s consolidation index
It is indirectly related to flow rate, cohesiveness and particle size
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 measure
Fluff density = poured density or bulk density
Carr’s index = tapped density – fluff density / tapped density x 100
Carr’s index % Flow
5-15 Excellent
12-16 Good
18-21 Fair-passable
23-25 Poor
33-38 Very poor
>40 Very very poor
Hausner’s ratio Flow
<1.25 Good (20% carr’s index)
>1.5 Poor (33% carr’s index)

52. Improvement of flow properties
1. Altering the particle size
Increasing the average particle size of particles improves the flow properties due to
reduction in the cohesive forces
During tabletting fine powders are converted to coarse granules in order to impart
good flow properties to them
2. Removal or addition of fines
Small proportion of fines or granular mass – improve the flow properties by filling
up the pits and crevices on the surface of particles
Larger proportion of fines may retard the flow properties
3. Altering the particle shape and structure
Spherical particles tend to have better flowability as compared to irregular particles
Techniques used: spray drying, alterations in crystallisation conditions
4. Altering the surface forces
Reduction of electrostatic charges on particle surface by reducing frictional contacts
5. Removing extra moisture- by Drying
6. Adding flow activators or glidants
Glidants – starch, talc and magnesium stearate - form thin uniform film on the
surface of particles to reduce the adhesion cohesion between particles
Optimum concentration of glidants - 1%
Flow activator - colloidal silicon dioxide-reduces the bulk density of tightly packed
powders