Lesson 1. Micromeritics and Powder Rheology

📋 Learning Objectives

By the end of this chapter, you will be able to:

✓ Understand fundamental and derived properties of particles
✓ Apply various methods for particle size determination
✓ Analyze powder flow properties and their measurement techniques
✓ Comprehend surface phenomena, rheology, and colloidal systems
✓ Evaluate diffusion processes and their pharmaceutical applications

🔍 Introduction to Micromeritics

Micromeritics is the science and technology which deals with small particles. There are two types of properties for a particle to characterize:

Fundamental Properties

Surface area, particle size and distribution, particle number, particle volume, particle shape.

Derived Properties

Porosity, density, bulkiness, flow ability (Flow property).

Particle Size and Particle Size Distribution

Particle size is quoted as the diameter of the sphere that has:
- Same weight (Weight based diameter)
- Same volume (Volume based diameter)
- Same surface (Area based diameter)
- Same drag coefficient/sedimentation velocity (Hydrodynamic or Aerodynamic based diameter)
Types of powders according to particle size:
- Monodisperse powder: All particles are of same size.
- Polydispersed powder: Particles of different size.
Average particle size: Average size of the particles which are distributed in the system.
- d_mean = (∑nd^p+f/∑nd^f)^1/p
- p = 1 – particle length, p = 2 – surface
- p = 3 – expression of volume
- p = +ve – arithmetic mean
- p = –ve – harmonic mean
- p = zero – geometric mean

💡 Methods for Particle Size Determination

Method	Size range	Instrument	Comment
Microscopy	0.2 to 100 micron	Optical microscope	Ferret, Martin and projected diameter measured
Sieving	50 to 1500 micron	Mechanical shaker
Sedimentation	1 to 200 micron	Anderson Pipette (Gravity sedimentation based)	Stoke diameter measured
Conductivity	0.5 to 500 micron	Coulter-Current or Royco/HIAC	Equivalent volume diameter measured

1. Microscopy

Range of analysis

By transmission electron microscope: 0.001–0.1 micron
By scanning electron microscope: 0.01–1000 micron
By light microscope: 1–1000 micron

Advantages

Easy and convenient
A size-frequency distribution curve can be plotted by counting the number of particles in a size range
Can detect the presence of agglomerates and particles of more than one component

Disadvantages

Diameter is obtained from only two dimensions—length and breadth
No estimation of the depth (thickness) of particle is available
The number of particles that must be counted to get a good estimate of the distribution makes the method slow and tedious

2. Sieving

This method utilizes a series of standard sieves calibrated by the National Bureau of Standards.
Range of analysis: We obtain particle size range 5–12000 µm.
Air jet sieving method: Another type of sieve analysis called air jet sieving, uses individual sieves rather than a complete nest of sieves. A reverser air jet circulator beneath the sieve mesh, blowing oversize particles away from the mesh to blocking. It is better than mechanically vibrated sieve analysis, although with finer particles agglomeration can become a problem.

3. Sedimentation

Particle size may be indirectly determined by measurement of rate of sedimentation in a Gravitational field.
A number of classical techniques based on sedimentation methods, utilizing devices such as the Anderson pipette or recording balances.
Stokes law of sedimentation:
- d_st = [18 η µ/(P_p – P_L) g ]^½
- Rate of settling = d² (ρ₁ – ρ₀) g/18 η
- where d is diameter of particle; ρ₁ is density of particle; ρ₀ is density of liquid and η is viscosity of liquid.
Used only for dilute suspension (less than 2% dispersed particles)

4-11. Other Methods

4. Elutriation

A procedure in which the fluid moves in the direction opposite to sedimentation movement so that in the gravitational force, the particle will move vertically downwards and fluid moves vertically upwards. If velocity of fluid is higher than the particle are carried upwards and vice versa.

5. Electronic scanning zone (coulter counter)

Particles are suspended in electrically conductive fluid. The suspension flows through suitable aperture with an immersed electrode on either side. When the particle passes, some resistance is seen and that change is measured as particle. Main advantages are: fastest counting, 1000 particles counted in one second, more reliable since number of particles are counted.

6. Surface method

Take some powder and add air and liquid to it. Powder absorbs liquid and air’s mono-molecular layer on its surface. This absorbed volume can give mean of powder’s particle size.

8. Laser light scattering methods

In this method, the particle can be presented either in liquid or in air suspension. Both the large particle and small particle analysers are based on the interaction of laser light with particles. Royco/HIAC–based on light blockage principle.

9. X-ray diffraction method

An x-ray irradiation produces a highly specific diffraction pattern from a crystal of material. An X-ray diffraction pattern from the crystal is formed and recorded on photographic film. It is very sensitive and used in identification of polymorphs, but very expensive.

10. Cascade impaction

Size Range: 0.1-80 microns. It can be used to obtain the size distribution of an aerosol. Air samples are withdrawn through device with several stages where particles are deposited. This method is suitable to determine the distribution of particles of respirable size.

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Concept Check

Questions:

What is the difference between fundamental and derived properties of particles?
Which particle size analysis method would you choose for particles in the range of 0.5-5 microns?
What is the principle behind the Coulter counter method?

Show Answers

Answers:

Fundamental properties are intrinsic characteristics of particles like surface area, particle size, particle number, and shape. Derived properties are those calculated from fundamental properties, such as porosity, density, and flow ability.
For particles in the range of 0.5-5 microns, microscopy (especially electron microscopy) or conductivity methods like Coulter counter would be appropriate choices.
The Coulter counter works on the principle of electrical conductivity changes. Particles suspended in a conductive fluid pass through an aperture with electrodes on either side. As a particle passes through, it displaces its own volume of electrolyte, causing a measurable change in electrical resistance, which is proportional to the particle volume.

📚 Properties Affected by Particle Size

The properties of drug that are affected by particle size and particle size distribution include:

Surface area

As the particle size decreases, the surface area of the particle increases. Surface area is important for drug absorption, dissolution, solubility and bioavailability.

Effect on solubility: Log (S/S₀) = [2γ V/2.303 + RTr]
Where S = Solubility of small particle, S₀ = Solubility of large particle, Y = Surface tension, V = Molar volume, R = Gas volume, T = Absolute temperature, r = Radius of small particle

Effect on dissolution: Noyes Whitney equation dC/dt = KS(C_S-C_F)
Where dc/dt = rate of dissolution, K = dissolution rate constant, S = surface area, C_s = concentration of drug in immediate proximity of dissolving particle, C_f = concentration of drug in bulk fluid

Surface Area Determination

1. Adsorption method: Amount of the gas (Nitrogen or Argon gas) or liquid solute that is adsorbed onto sample of powder to form a monolayer is directly the function of surface area. Quantasorb instrument is used.

2. Air permeability method: The rate at which gas or liquid permeates a bed of powder is calculated. Resistance to flow of a fluid through a plug of compact powder is the surface area of powder.

Porosity

True volume: Volume of powder itself.
Granule volume: Volume of powder itself plus the volume of intra-particle space/pore.
Bulk volume: Volume of powder itself plus the volume of intra-particle space/pore plus volume of inter-particle space (Void).

Void Volume (V_v) = Bulk Volume (V_b) – True Volume (V_t)
Porosity (E) = V_v/V_b = (V_b – V_t)/V_b = (1 – V_t/V_b) × 100

Types of Density

Density Type	Measurement Method	Formula
True density	Helium pycnometer (Porous solid) Liquid displacement (Non-porous solid)	M/V_t
Granule density	Mercury displacement method	M/V_g
Bulk density	Graduated cylinder method based on tapping the powder from 1 inch height thrice in 2 min interval	M/V_b

Other Properties Affected by Particle Size

Bulkiness and packaging: As the particle size increases, the bulkiness decreases. It is a reciprocal of bulk density. Uniformity of powder blend is important. If not, then smaller particle takes place in space between larger particles that decreases bulkiness. Bulk property also important for packing criteria for powder.
Angle of repose and flow property: Particle size affects how powders flow, which is critical for manufacturing processes.
Hygroscopicity: The tendency to absorb moisture can be affected by particle size.
Electrostatic charge: Smaller particles may develop more electrostatic charge, affecting handling and mixing.

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Concept Check

Questions:

How does particle size affect the surface area of a drug?
What is the relationship between bulk density, true density, and porosity?
Name three drugs whose bioavailability is increased by particle size reduction.

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Answers:

As particle size decreases, the surface area of the drug increases. This inverse relationship is important because increased surface area can lead to increased dissolution rate, which can enhance drug absorption and bioavailability.
Porosity (E) = (1 – V_t/V_b) × 100 or (1 – True density/Bulk density) × 100. True density is always greater than or equal to granule density, which is greater than bulk density.
Three drugs whose bioavailability is increased by particle size reduction are: Sulphadiazine, Phenothiazine, and Griseofulvin. Others include Tolbutamide, Nitrofurantoin, and Spironolactone.

👩‍⚕️ Powder Flow Properties

Powder flow property is critical for pharmaceutical manufacturing processes. Various methods are used to measure and evaluate flow properties:

1. Percent Compressibility

Compressibility is the ability of powder to decrease volume under pressure. Compressibility is a measure that is obtained from density determinations.

% Compressibility = (Tapped bulk density–poured or untapped or aerated Bulk density/Tapped bulk density) × 100

Compressibility measure gives idea about flow property of the granules as per CARR’S index which is as follows:

Carr’s Index (% compressibility)	Flow description
5–15	Excellent–free flowing granules
12–16	Good–free flowing powder granules
18–21	Fair powder granules
23–28	Poor–very fluid powders
28–35	Poor–fluid cohesive powder
35–38	Very poor–fluid cohesive
＞40	Extremely poor–cohesive powder

2. Hausner Ratio

It is a very important parameter to be measured since it affects the mass of uniformity of the dose. It is usually predicted from Hausner Ratio and Angle of Repose Measurement.

Hausner Ratio = Tapped Density/Bulk Density

Hausner Ratio	Type of Flow
Less than 1.25	Good Flow
1.25–1.5	Moderate
More than 1.5	Poor Flow

3. Angle of Repose

Angle of Repose (Φ) is the maximum angle between the surface of a pile of powder and horizontal plane. It is usually determined by Fixed Funnel Method and is the measure of the flowability of powder/granules.

Φ = tan^-1 (h/r) where,
h = height of heap of pile
r = radius of base of pile

Measurement methods:

Rotating Cylinder method
Tilted Box method
Fixed Cone Method

Angle of repose	Type of flow	Type of powder
＜25	Excellent	Non cohesive
25–30	Good	Cohesive
30–40	Passable	Cohesive
＞40	Very poor	Very cohesive

Factors Affecting Flowability

Particle size and distribution

Addition of small particles to larger particles which fill the void space reduce inter-particles cohesive force and reduces surface rugosity and acts as lubricant
Presence of particles of size smaller than 10 micron gives stickiness to material

Particle shape and surface roughness

Spherical shape is the best shape which gives the maximum flow rate
Irregular shape of particle in material causes the bridging in hopper
Roughness on the surface can cause mechanical hindrance to the flow of material

Density and porosity

More density and less porosity give better flow

Hygroscopicity

It reduces flow rate, because it increases adhesive and cohesive forces between particles

Electrostatic charge

More electrostatic charge reduces flowability

Methods of Improvement of Flowability

By addition of glidant: Flow can be improved by reducing adhesion and cohesion. Effectiveness of glidant is found to be dependent on particle size of material to which it is added. E.g., corn starch is more effective in coarser particle. Talc, silicon dioxide and Mg-stearate are effective in finer particles.
By size reduction or by addition of fine particles: Both should be up to optimum limit. Addition of fine particles to certain level improves flow.
By wet granulation: Gives regular shape and also removes the static charge of powder surface, thus improves the flow.
By removing static charge.
By densification with the help of slugging.
By using auger feed equipment.
By addition of flow activator: Powder flow property is impaired through increased moisture content of very fine MgO and may be used as a flow activator. MgO adsorbs water surrounding the moist particle.
For hygroscopic and moist powder: Use of silicon treated powder such as silicon coated talc or Na-bicarbonate may also be beneficial in improving the flowability of moist and hygroscopic powder.
By alterations of process condition: Used vibration assisted hopper, used force feeder.
By use of spray drying: Advantose 100 maltose powder has improved flow property and compressibility than MCC by using this process.

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Concept Check

Questions:

What is the significance of Carr’s Index in powder flow evaluation?
How does particle shape affect powder flow?
Name three methods to improve the flowability of powders.

Show Answers

Answers:

Carr’s Index (% compressibility) provides a measure of powder flowability. Lower values (5-15%) indicate excellent flow, while higher values (>40%) indicate extremely poor, cohesive powder flow. It’s calculated from bulk density measurements before and after tapping.
Particle shape significantly affects powder flow. Spherical particles generally provide the best flow due to reduced interparticle contact and friction. Irregular particles can cause bridging in hoppers and mechanical hindrance to flow. As particles depart from spherical shape, flowability typically decreases.
Methods to improve flowability include: (1) Addition of glidants like talc or silicon dioxide, (2) Wet granulation to give regular shape and remove static charge, (3) Use of spray drying to improve flow properties, (4) Removing electrostatic charge, (5) Addition of flow activators like MgO for hygroscopic powders, and (6) Size modification or blending with optimal amounts of fine particles.

🔄 Rheology

Rheology is the science which deals with flow of liquid and deformation of solid.

Flow of Liquid

Newtonian flow
Non-Newtonian flow
- Plastic flow
- Pseudoplastic flow
- Dialatent flow

Deformation of Solid

Plastic – permanent and irreversible
Elastic – spontaneous and reversible

Newtonian Law of Viscosity

Shearing stress is directly proportional to Shearing Rate

F ∝ dv/dr
F = η dv/dr

Where,
F is Shearing stress = f/A force per unit area
Unit = newton per meter²
G = dv/dr = Shearing rate = change in velocity/change in distance
Unit = sec^-1

Viscosity

Viscosity: Property of a liquid which show index of resistance to flow.
Basic unit of viscosity: Poise (C.G.S. System)
Convenient unit of viscosity: centi poise (cp)
Dimension: dyne × sec/cm² or M L^-1 T^-1
Fluidity (φ): Reciprocal of viscosity
Unit is poise^-1
Φ = 1/η
Viscosity coefficient (η): = F/G = (f/a)/(dv/dr)
Kinematic viscosity: Viscosity is officially (IP) expressed as Kinematic viscosity.
Kinematic viscosity = η/ρ = Absolute viscosity of liquid/density of liquid
Unit–stoke or centistoke
Temperature and viscosity: On increasing T, viscosity of gas increases due to increased collision while viscosity of liquid is decreased.

Non-Newtonian Flow

Where there no direct relation between shear stress and shear rate. These are of three types:

1. Plastic flow

It is the Newtonian system at shear stress above yield value
Material does not begin to flow until a shearing stress corresponding to yield value exceeds
Associated with presence of flocculated particle in concentrated suspension and emulsion

2. Pseudoplastic flow

Here, yield value not associated. As applies shear stress increasing, viscosity decreases and disarranged molecules begin to align their long axes inline of molecules
Exhibits by natural and synthetic gum. E.g., tragacanth, CMC, Na-CMC

3. Dilatant flow

Opposite to pseudoplastic flow
Increase in the shear rate, increase in resistance to flow as viscosity increases
E.g., deflocculated suspension of Mg magma

Types of Flow and Examples

Type of flow	Example
Newtonian	Water, Glycerine, Benzene, Alcohol, Syrup solution, very dilute colloid solution
Plastic (Bingham body)	Suspension of ZnO in mineral oil Paint, Printing Inks and Firm jellies Flocculated suspension (1-10% solid content)
Pseudoplastic	Natural and synthetic gums, Polymers such as MC, CMC, Tragacanth, Sodium alginate, gelatin
Dilatant	De-flocculated suspension (more than 50% solid content) E.g., Concentrated titanium dioxide suspension

Methods of Viscosity Determination

Type of fluid	Method of determination
Newtonian fluid	Capillary viscometer (Ostwald viscometer) Falling and Rising body (Sphere)
Non-Newtonian fluid	Cup and bob viscometer Cone and Plate viscometer

Time-dependent Viscosity

Thixotropy (Gel-Sol transformation)

Gel→Sol→Gel

Plastic system–Bentonite (Magma)gel, petrolatum
Pseudoplastic system–dispersion of synthetic suspending agent

Anti-Thixotropy (Negative thixotropy) or Rheopexy (Sol-Gel transformation)

Sol→Gel→Sol

E.g., magnesia magma, Flocculated suspension (1–10% solid content)

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Concept Check

Questions:

What is the difference between Newtonian and non-Newtonian flow?
Which type of flow is exhibited by natural gums like tragacanth?
What is thixotropy and give an example of a thixotropic system?

Show Answers

Answers:

In Newtonian flow, there is a direct proportional relationship between shear stress and shear rate (F = η dv/dr), resulting in a constant viscosity regardless of the applied force. In non-Newtonian flow, there is no direct relationship between shear stress and shear rate, and viscosity changes with applied force.
Natural gums like tragacanth, CMC, and sodium alginate exhibit pseudoplastic flow. As shear stress increases, viscosity decreases as disarranged molecules begin to align.
Thixotropy is a time-dependent behavior where a gel transforms to a sol when stress is applied and reverts back to a gel when the stress is removed (Gel→Sol→Gel). Examples of thixotropic systems include bentonite gel, petrolatum, and dispersions of synthetic suspending agents.

🧩 Surface and Interfacial Phenomena

Surface Tension (ST)

Force per unit length acting at surface at right angle (N/meter) or (Dyne/cm)
Indicates strength of Cohesive force (force between like molecules)
Examples: Formation of spherical globules in emulsion, Shape of falling water drop, Shape of mercury drop on flat surface, Rise in capillary tube

Interfacial Tension (IT)

Force per unit length acting at interface at right angle (N/m)
Indicates strength of adhesive force (force between unlike molecules)

Factors affecting ST and IT

Temperature: T increases → Kinetic Energy increases → weakening of cohesive forces, hence ST decreases.
Electrolytes
Surface Active agents

Determination of ST and IT

Capillary rise method: Only ST can be determined.

Based on Young–Laplace Equation
P = 2Ƴ/r
P = hρg
So Ƴ = h ρ g × r/2
Where Ƴ is surface tension, ρ is density of liquid, h is height occupied by liquid, r is inside radius of capillary tube.
DuNouy Tensiometer: Both ST and IT can be determined.
Bubble pressure
Drop weight or Drop count method: Both ST and IT can be determined.

Instrument used: Stalagmometer
Mg = 2 π r × Ƴ

Wetting

Intimate contact between solid and liquid or liquid and liquid.

Application

Initial step in preparation of emulsion and suspension
In granulation process
Film coating requires wetting and spreading of liquid over tablet surface

Surfactant used for wetting of powder

Has HLB 7 to 9
Functions via:
1. Lowering Interfacial tension
2. Lowering of Contact angle between solid and liquid
3. Dispersing air and permit intimate contact

Contact angle

Angle between liquid droplet and surface over which it spreads
Indicator of evaluating the efficiency of a wetting agent
Normally lies between 0 to 180 degree
Zero(0) degree means complete (Significant) wetting so Cos θ = 1
180 degree means insignificant wetting

Surfactant (Surface Active Agent)

Amphiphilic molecules that are partitioned at interface and decrease interfacial tension of solution.

Polar head group orient towards polar region of solution.
Non-polar group orient towards non-polar region.
Polar group or hydrophilic part of surfactant provides much greater barrier than non-polar (hydrophobic) portion.

HLB scale

Arbitary scale devised by Griffin
Indicates extent of hydrophilic-lipophilic balance
Range 1(Oleic acid) to 40 (Sodium Lauryl Sulphate)
Higher the HLB, more will be the hydrophilicity of compound

HLB value	Category
1–3	Anti-foaming agent
3–8	w/o emulsifier
7–9	Wetting and spreading agent
8	Foaming agent
8–16	o/w emulsifier
13–16	Detergent
16–18	Solubilizing agent

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Concept Check

Questions:

What is the difference between surface tension and interfacial tension?
How does temperature affect surface tension?
What HLB range is appropriate for a wetting agent?

Show Answers

Answers:

Surface tension (ST) is the force per unit length acting at a surface at right angles, indicating the strength of cohesive forces between like molecules. Interfacial tension (IT) is the force per unit length acting at an interface between two immiscible phases, indicating the strength of adhesive forces between unlike molecules. Generally, ST is greater than IT.
As temperature increases, surface tension decreases. This happens because higher temperature increases the kinetic energy of molecules, which weakens the cohesive forces between them.
Wetting agents typically have an HLB (Hydrophilic-Lipophilic Balance) value in the range of 7 to 9.

🔬 Colloids and Adsorption

Colloids

Types of Dispersion

Molecular (less than 0.1nm)
Colloidal (particle size 0.5 to 1 nm and show Tyndall effect, scattering of light)
Coarse dispersion (>0.5 micron)

Dispersions are also thermodynamically unstable because dispersed particles aggregate and settle.

Important Colloidal Terms

Peptization: Breakdown of aggregates into particles of colloidal size.
Amphiphiles: Molecules or ions which have affinity for both polar and non-polar solvents.
Critical micelle concentration (CMC): Concentration of surfactant at which micelle formation starts.
Krafft point (K_t): Temperature at which the solubility of the surfactants is equal to the CMC and above which sudden rise in solubility results.
Electrodialysis: Diffusion of ions or molecules is enhanced by applying a potential difference across the membrane.

Types of Colloids

Lyophilic vs. Lyophobic Colloids

Lyophilic colloid	Lyophobic colloid
Stable towards prolong dialysis	Not stable
Weak Tyndall effect	Strong Tyndall effect
Act as protective colloid	Do not act as protective colloid
Easy to prepare due to affinity towards solvent	Difficult to prepare due to lower affinity towards solvent

Association Colloids

Type	Example	Counter ion
Cationic type	Cetyl trimethyl ammonium bromide (Cetrimide)	Bromide ion
Anionic type	Sodium lauryl sulphate	Sodium ion
Non-ionic type	Poly oxyethylene lauryl ether	–
Ampholytic (Zwitter ionic)	Lecithin	–

Adsorption

Adsorption is the process in which matter is extracted from one phase and concentrated at the surface of a second phase. (Interface accumulation). This is a surface phenomenon as opposed to absorption where matter changes solution phase.

Adsorbate: material being adsorbed.
Adsorbent: material doing the adsorbing. Examples are activated carbon or ion-exchange resin.

Types of adsorption

Exchange adsorption (ion exchange): Electrostatic due to charged sites on the surface. Adsorption goes up as ionic charge goes up and as hydrated radius goes down.
Physical adsorption: Van der Waals attraction between adsorbate and adsorbent. The attraction is not fixed to a specific site and the adsorbate is relatively free to move on the surface. This is relatively weak, reversible adsorption, capable of multilayer adsorption.
Chemical adsorption: Some degree of chemical bonding between adsorbate and adsorbent characterized by strong attractiveness. Adsorbed molecules are not free to move on the surface. There is a high degree of specificity and typically, a monolayer is formed. The process is seldom reversible.

Adsorption Isotherm Models

Langmuir isotherm: Assumes monolayer coverage and constant binding energy between surface and adsorbate.
BET (Brunauer, Emmett and Teller) isotherm: A more general, multi-layer model. It assumes that a Langmuir isotherm applies to each layer and that no transmigration occurs between layers.
Freundlich isotherm: For heterogeneous surface energies in which the energy term varies as a function of surface coverage.

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Concept Check

Questions:

What is the difference between lyophilic and lyophobic colloids?
What is the Tyndall effect and why does it occur in colloids?
Explain the difference between physical and chemical adsorption.

Show Answers

Answers:

Lyophilic colloids (“solvent-loving”) have a strong affinity for the dispersion medium, are stable towards dialysis, show weak Tyndall effect, and are easy to prepare. Examples include natural gums and proteins. Lyophobic colloids (“solvent-hating”) have low affinity for the dispersion medium, are unstable towards dialysis, show strong Tyndall effect, and are difficult to prepare. Examples include metal sols like gold and silver.
The Tyndall effect is the scattering of light by colloidal particles when a beam of light passes through a colloidal dispersion. It occurs because colloidal particles are large enough to scatter light but small enough to remain suspended in the dispersion medium. This effect makes the path of light visible and helps identify colloidal systems.
Physical adsorption (physisorption) involves Van der Waals forces between adsorbate and adsorbent. It’s relatively weak, reversible, not site-specific, and can form multiple layers. Chemical adsorption (chemisorption) involves chemical bonding between adsorbate and adsorbent. It’s stronger, often irreversible, highly specific, and typically forms only a monolayer. Physisorption can occur at low temperatures while chemisorption requires higher activation energy.

🧪 Diffusion

Diffusion is the random movement of molecules but has a net direction towards regions of lower concentration in order to reach equilibrium.

Simple Diffusion

Rate of diffusion is directly proportional to the concentration gradient by the Fick’s equation:

dn/dt = P × A × (dC/dx)

Where A is the membrane surface area and P is the permeability constant. P is a constant relating the ease of entry of a molecule into the cell depending on the molecule’s size and lipid solubility. C is concentration of diffusing molecules (mol/cm³), x is thickness or width of membrane (cm) and t is time (sec).

Facilitated Diffusion

Facilitated diffusion involves a limited number of carrier proteins. At low concentrations, molecules pass through the carrier proteins similar to simple diffusion. At high solute concentrations, all the proteins are occupied with the diffusing molecules.

dn/dt = V_max/(1 + K/(dC/dx))

Where V_max is saturation constant (mol/cm³/sec) and K is constant determining speed of saturation (mol/cm³).

Fick’s Laws of Diffusion

Fick’s First Law

J = -D (∂C(x,t)/∂x)

Where J is the flux, D is the diffusion constant for the material that is diffusing in the specific solvent, and ∂C(x, t)/∂x is the concentration gradient.

Fick’s Second Law

∂C(x, t)/∂t = ∂(D∂C(x, t)/∂x)/∂x

If the diffusion coefficient is independent of position, this simplifies to:

∂C(x,t)/∂t = D ∂²C(x, t)/∂x²

Diffusion Cell

A diffusion cell consists of a donor chamber and receptor chamber (2 chambers) with a membrane clamped in between.

Vertical diffusion cell (Franz diffusion cell)
Horizontal diffusion cell

The diffusion cell donor chamber contains a known concentration of a solute (donor solution). The receptor solution is contained in the receptor chamber on the other side of the membrane. When the diffusion experiment begins, the solute in the donor solution diffuses through the membrane and into the receptor solution. The receptor solution is periodically removed for analysis and replaced with new receptor solution. The results of the analysis can be used to calculate the diffusion coefficient.

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Concept Check

Questions:

What is the difference between simple diffusion and facilitated diffusion?
What does Fick’s First Law of diffusion describe?
What is the purpose of a diffusion cell?

Show Answers

Answers:

Simple diffusion occurs when molecules pass directly through a membrane along a concentration gradient without assistance. It follows Fick’s law with a linear relationship between diffusion rate and concentration gradient. Facilitated diffusion involves carrier proteins that help molecules cross the membrane. At low concentrations it behaves like simple diffusion, but at high concentrations, it shows saturation kinetics as all carrier proteins become occupied.
Fick’s First Law describes how the rate of diffusion (flux) is proportional to the concentration gradient. It states that the flux (J) equals the diffusion coefficient (D) multiplied by the negative concentration gradient (-∂C/∂x). The negative sign indicates that diffusion occurs from regions of higher concentration to regions of lower concentration.
A diffusion cell is used to measure the rate of diffusion of substances through membranes. It consists of donor and receptor chambers separated by a membrane. By analyzing how quickly a substance moves from the donor chamber to the receptor chamber, researchers can calculate diffusion coefficients and study factors affecting permeability, which is important in pharmaceutical research for drug delivery systems and formulation development.

📋 Chapter Summary

✓
Micromeritics deals with small particles and involves understanding both fundamental properties (surface area, particle size, shape) and derived properties (porosity, density, flow ability).
✓
Particle size determination methods include microscopy, sieving, sedimentation, and electronic scanning zone techniques, each with specific applications and size ranges.
✓
Powder flow properties can be measured using Carr’s index, Hausner ratio, and angle of repose, which are crucial for pharmaceutical manufacturing processes.
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Rheology encompasses Newtonian and non-Newtonian flow behaviors, with pharmaceutical systems exhibiting plastic, pseudoplastic, or dilatant flow depending on their composition.
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Surface and interfacial phenomena, including surface tension and wetting, significantly impact pharmaceutical formulations, especially in emulsions and suspensions.
✓
Colloidal systems are important in pharmaceuticals, with properties depending on whether they are lyophilic or lyophobic, and stabilized through various mechanisms.
✓
Diffusion processes, governed by Fick’s laws, are fundamental to drug delivery and dissolution, involving both simple and facilitated mechanisms.

🔄 Multiple Choice Questions

Following are used for particle size analysis

P. Coulter counter Q. BET N₂ adsorption R. XRPD S. HIAC counter

(a) Q and S

(b) P and S

(c) Q, R and S

(d) R and S
Which instrument is used for the determination of shear rate/shear stress?

(a) Ultrasonifier

(b) Rotational viscometer

(c) Accela cota

(d) Chilsonator
Colloid particle have …………… type of rheology.

(a) Newtonian flow

(b) Pseudoplastic flow

(c) Non-Newtonian flow

(d) Dilatant
Wetting agent has …………… HLB value.

(a) 1 to 3

(b) 3 to 6

(c) 7 to 9

(d) 8 to 18
Carr’s compressibility index gives an idea about

(a) Flow property of powders

(b) Cohesiveness of powders

(c) Both

(d) None

Essentials of Pharmacy

Curriculum

Lesson 1. Micromeritics and Powder Rheology

📋 Learning Objectives

🔍 Introduction to Micromeritics

Fundamental Properties

Derived Properties

Particle Size and Particle Size Distribution

💡 Methods for Particle Size Determination

1. Microscopy

Range of analysis

Advantages

Disadvantages

2. Sieving

3. Sedimentation

4-11. Other Methods

4. Elutriation

5. Electronic scanning zone (coulter counter)

6. Surface method

8. Laser light scattering methods

9. X-ray diffraction method

10. Cascade impaction

? Concept Check

Questions:

Answers:

📚 Properties Affected by Particle Size

Surface area

Surface Area Determination

Porosity

Types of Density

Other Properties Affected by Particle Size

? Concept Check

Questions:

Answers:

👩‍⚕️ Powder Flow Properties

1. Percent Compressibility

2. Hausner Ratio

3. Angle of Repose

Factors Affecting Flowability

Particle size and distribution

Particle shape and surface roughness

Density and porosity

Hygroscopicity

Electrostatic charge

Methods of Improvement of Flowability

? Concept Check

Questions:

Answers:

🔄 Rheology

Flow of Liquid

Deformation of Solid

Newtonian Law of Viscosity

Viscosity

Non-Newtonian Flow

1. Plastic flow

2. Pseudoplastic flow

3. Dilatant flow

Types of Flow and Examples

Methods of Viscosity Determination

Time-dependent Viscosity

Thixotropy (Gel-Sol transformation)

Anti-Thixotropy (Negative thixotropy) or Rheopexy (Sol-Gel transformation)

? Concept Check

Questions:

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🧩 Surface and Interfacial Phenomena

Surface Tension (ST)

Interfacial Tension (IT)

Factors affecting ST and IT

Determination of ST and IT

Wetting

Application

Surfactant used for wetting of powder

Contact angle

Surfactant (Surface Active Agent)

HLB scale

? Concept Check

Questions:

Answers:

🔬 Colloids and Adsorption

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