Micromeretics and powder rheology: Average particle size number and weight distribution, particle number and MCQs for GPAT, NIPER, Pharmacist and Drug Inspector exam

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Average particle size: Suppose that the particle size of a powder is analysed and the number of particles in each size range is determined, from the data, the average particle size of the powder may be calculated as

D_avg= n₁d₂ + n₂d₂ + n_nd_n / n₁+ n₂ + n_n

= Ɛ(nd) / Ɛ (n)

In the above calculation, only the total number and mean size of the particles have been considered for expressing the average particle size. The calculation can be modified to take into account the surface and volume of the particle also. Such a modified equation for calculation of the average particle size is derived by Edmundson:

d = Ɛ[(nd^p+f) / Ɛ(nd^f)]^1/p

where n is the number of particles in each size range, d the diameter of particles in a given size range (usually the midvalue), p an index related to the size of an individual particle and f the frequency index.

Value of p = 1 indicates particle length

p = 2 indicates particle surface

p = 3 indicates particle volume

Value of p = 0 indicates geometric mean

p = + indicates arithmetic mean

p = * indicates harmonic mean

For a collection of particles, the frequency with which a particle in a certain size range occurs is expressed as nd^f.

Value of f = 0 expresses size distribution in total number

f = 1 expresses size distribution in length

f = 2 expresses size distribution in surface

f = 3 expresses size distribution in volume

When the number (or weight) of particles lying within a certain size range is plotted against the mean particle size, a frequency distribution curve is obtained. Such histograms can give a visual representation of the distribution, which an average diameter cannot achieve. When the number of particles is plotted against the mean particle size, the curve is known as the number frequency distribution curve and when the weight of particles is plotted against the mean particle size, the curve is known as the weight distribution frequency curve.

When size distributions are not symmetrical, the frequency distribution curve of such populations exhibit skewness. If the distribution is skewed, it can be frequently made symmetric if the sizes are replaced by the logarithms of the sizes.

Positively skewed: Frequency curve with an elongated tail towards higher size ranges.
Negatively skewed: Frequency curve with an elongated tail towards lower size ranges.
Bimodal distribution: Frequency curve with more than one mode.

Particle Number:

Particle number, N, is defined as the number of particles per unit weight of a powder and can be obtained in the following manner. Assuming that the particles of the powder are spherical, the volume of a single particle is πdvn3p/6 and the mass (volume × density) is πdvn3p/6 g per particle, where dvn is the mean diameter based on volume and number and p is density of the particle.

The number of particles per gram can then be obtained from the following expression:

N = 1g of the powder / Mass of 1 particle

Or, N = 1 / πdvn³ p/6

Or, N = 6 / πdvn³ p

Multiple choice questions (MCQs)

1.The angle of repose value are utilized to

a)Measure the movement of granules from hopper to the table of tabletting/capsule machine

b)Select proper containers for capsules of a given mass of powders

c)Study of absorption of drugs

d)Understanding dissolution of medicaments

2.The term ‘light’ as applied to pharmaceutical powders means

a)Low bulk density

b)Low granule density

c)Low true density

d)Slightly colored

3.The type of particle diameter that is obtained by microscope method of evaluation is

a)Projected

b)Stokes

c)Volume

d)Volume-surface

4.Porosity of a porous powder is defined as

a)Bulk volume/void volume

b)Void volume/bulk volume

c)Void volume/true volume

d)True volume/bulk volume

5.Which equation is used to convert number distribution to weight distribution

a)Noyes Whitney equation

b)Hatch Choate equation

c)Henderson Hasselbalch equation

d)Higuchi equation

6.Coulter counter is used to determine

a)Particle volume

b)Particle number

c)Particle interaction

d)Viscosity

7.The ratio of void volume to bulk volume is known as

a)Bulk density

b)Tapped density

c)Porosity

d)Granule volume

8.If carr’s compressibility index value is in between 26 to 31, then flow will be

a)Poor

b)Excellent

c)Passable

d)Very, very poor

9.Hausner ratio is

a)Tapped density/bulk density

b)Bulk density/tapped density

c)Bulk volume/void volume

d)Void volume/bulk volume

10.The powder having low bulk density or large bulk volume is known as

a)Light powder

b)Heavy powder

c)Bulk powder

d)Granular powder

11.The term micromeretics was given by

a)M. Dalla Valle

b)James Kelvin

c)Wiliam Protector

d)Mahadeva Lai Schroff

12.Andreasen pipette is widely used method to determine particle size distribution by

a)Microscopy method

b)Sedimentation method

c)Sieving method

d)All of the above

13.Porosity is expressed in

a)Percentage

b)Millimeter

c)Gram/millimeter

d)Newton

14.Helium pycnometer is used to determine

a)Size

b)True density

c)Sedimentation rate

d)Surface area

15.The distance between two tangents on opposite sides of the particle parallel to some fixed direction

a)Feret’s diameter

b)Martin diameter

c)Projected

d)Stokes

Solutions:

a) Measure the movement of granules from hopper to the table of tabletting/capsule machine
b) Low granule density
a) Projected
b) Void volume/bulk volume
b) Hatch Choate equation
a) Particle volume
c) Porosity
a) Poor
a) Tapped density/bulk density
a) Light powder
a) J. M. Dalla Valle
b) Sedimentation method
a) Percentage
b) True density
a) Feret’s diameter