Pharmaceutical Calculations

Table of Contents
1. Pharmaceutical Measurements
2. Aliquot Method
3. Density and Specific Gravity
4. Expression of Concentration
5. Dose Calculations
6. Dilution and Concentration
7. Unit Operations
8. Fluid Flow
9. Mass Transfer
10.Heat Transfer and Steam Properties
11.Evaporation
12.Drying
13.Filtration
14.Mixing
15.Solid Dosage Forms
16.Semisolid Dosage Forms
17.Size Reduction

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Pharmaceutical Measurements
Importance
• Essential for community and institutional pharmacies
• Critical for pharmaceutical research and development
• Required for manufacturing and quality control
• Pharmacists must accurately weigh, measure, and combine therapeutic
components
Volume Measurement
Instrument Selection: Choose graduate with capacity equal to or just exceeding
volume to be measured
Error Principle: Measuring small volumes in large graduates increases error
Precision Hierarchy: Micropipettes → Burettes → Calibrated vessels (increasing
capacity, decreasing precision)
Weight Measurement
Class A Prescription Balance: Required for all compounding
Sensitivity Requirement (SR): 6 mg or less with no load and 10g load
Minimum Weighable Amount: 120 mg (to avoid >5% error)
SR Definition: Load causing one division change on balance index plate
Key Formula
Smallest Quantity = (100% × SR) / Acceptable Error%
Example: SR = 6 mg, Error = 5% Smallest Quantity = (100% × 6 mg) / 5% = 120
mg

Aliquot Method
Definition
An aliquot is a fraction contained an exact number of times in another quantity.

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Weighing by Aliquot Method
Preliminary Step
Calculate minimum weighable quantity using sensitivity requirement.
Step 1: Select Multiple
Choose a multiple of desired quantity that exceeds minimum weighable amount.
Step 2: Dilute with Inert Substance
• Total mixture = Aliquot portion × Multiple
• Diluent needed = Total mixture - Drug weighed
Step 3: Weigh Aliquot Portion
Weigh 1/multiple of the total mixture to get desired quantity.
Example Problem
Given: Balance SR = 6 mg, need 4 mg atropine sulfate, 5% accuracy
Solution:
• Minimum weighable = 120 mg
• Multiple needed = 120/4 = 30
• Weigh 30 × 4 = 120 mg atropine sulfate
• Mix with diluent to make 30 × 120 = 3600 mg total
• Diluent needed = 3600 - 120 = 3480 mg lactose
• Final aliquot = 120 mg contains 4 mg atropine sulfate
Volume Aliquot Method
Same principle applies to volume measurements using compatible diluents.
Least Weighable Quantity Method
Alternative to aliquot method:
1. Weigh amount ≥ least weighable quantity
2. Dilute so predetermined quantity contains desired amount

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Density and Specific Gravity
Density
Definition: Mass per unit volume (g/mL or g/cc)
Water density: 1 g/mL at 4°C
Formula: Density = Mass/Volume
Example: Mercury density = 13.6 g/mL
Specific Gravity
Definition: Ratio of substance weight to equal volume of water
Formula: Specific Gravity = Weight of substance / Weight of equal volume of
water
Characteristics:
• Dimensionless (abstract number)
• Constant for each substance under controlled conditions
• Water specific gravity = 1
Measurement Methods
Pycnometer Method
1. Weigh empty pycnometer
2. Weigh filled with water
3. Calculate water weight by difference
4. Fill with test liquid and weigh
5. Calculate specific gravity
Example:
• Empty pycnometer = 120 g
• With water = 171 g
• With unknown liquid = 160 g

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 • Water weight = 171 - 120 = 51 g
• Liquid weight = 160 - 120 = 40 g
• Specific gravity = 40/51 = 0.78
Displacement (Plummet) Method
Based on Archimedes' principle:
1. Weigh plummet in air
2. Weigh plummet in water
3. Weigh plummet in test liquid
4. Calculate specific gravity
Pharmaceutical Applications
• Converting weight to volume and vice versa
• Automated TPN equipment calculations
• Urinalysis (normal urine sp gr: 1.010-1.025)
Specific Volume
Definition: Ratio of substance volume to equal weight of water
Relationship: Specific volume = 1/Specific gravity
Example: If 25g glycerin = 20 mL, 25g water = 25 mL
• Specific volume = 20/25 = 0.8

Expression of Concentration
Percentage Expressions
Weight-in-Volume (w/v)
Definition: Grams of constituent per 100 mL solution
Use: Powdered substances in liquid vehicles
Example: 5% w/v = 5g in 100 mL

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Volume-in-Volume (v/v)
Definition: mL of constituent per 100 mL solution
Use: Liquid components in liquid preparations
Example: 10% v/v = 10 mL in 100 mL
Weight-in-Weight (w/w)
Definition: Grams of constituent per 100 g preparation
Use: Solids mixed with solids/semisolids
Example: 2% w/w = 2g in 100g

Ratio Strength
Definition: Alternative expression of percentage
Conversion: 5% = 5:100 = 1:20
Interpretation:
• Solids in liquids: 1g in 1000 mL (1:1000)
• Liquids in liquids: 1 mL in 1000 mL
• Solids in solids: 1g in 1000g
Parts per Million (ppm) and Billion (ppb)
ppm: Parts per 1,000,000
ppb: Parts per 1,000,000,000
Example: Fluoride in water 1-4 ppm

Dose Calculations
Dose Definitions
Single dose: Amount taken at one time
Daily dose: Amount taken per day

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Total dose: Amount for entire therapy
Divided doses: Daily dose split into multiple administrations
Dosage regimen: Complete dosing schedule
Dosing Factors
• Patient age and weight
• Body surface area
• General health status
• Liver/kidney function
• Disease severity
• Route of administration
Important Dose Concepts
Usual adult dose: Standard effective amount
Usual pediatric dose: Standard amount for children
ED50: Median effective dose (50% of population)
TD50: Median toxic dose (50% of population)
MEC: Minimum effective concentration
MTC: Minimum toxic concentration
Loading dose: Initial higher dose to reach therapeutic level
Pediatric Considerations
Age groups: Neonate (0-1 month), Infant (1 month-1 year), Early childhood (1-5
years), Late childhood (6-12 years), Adolescence (13-17 years)
Special considerations: Underdeveloped organ systems, different metabolism
rates
Geriatric Considerations
• Start with lower doses
• Adjust based on response

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 • Consider multiple drug interactions
• Account for decreased organ function
Dose Calculation Formula
Number of doses = Total quantity / Size of dose
Examples
Example 1: How many 200 mg doses in 10g?
• 10g = 10,000 mg
• Doses = 10,000/200 = 50 doses

Example 2: Teaspoons per dose if 180 mL contains 18 doses?

• Dose size = 180/18 = 10 mL = 2 teaspoons
Household Measurements
Teaspoon: ~5 mL (varies 3-7 mL)
Tablespoon: ~15 mL (varies 15-22 mL)
Drop: Variable, must be calibrated per dropper
Low-Dose and High-Dose Therapy
Low-dose: Aspirin 81 mg vs usual 325 mg
High-dose: Chemotherapy for cancer treatment
Fixed-Dose Combinations
Advantages: Convenience, compliance, cost
Disadvantages: Inflexibility in dosing

Dilution and Concentration

Basic Relationship
Dilution: Reducing concentration by adding solvent

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Concentration: Increasing strength by evaporation or adding active ingredient
Key principle: If quantity doubles, strength halves; if quantity halves, strength
doubles
Calculation Methods
1. Inverse proportion
2. Q₁C₁ = Q₂C₂ equation
3. Determine active ingredient quantity
Examples
Dilution Example
Problem: 500 mL of 15% v/v diluted to 1500 mL
• Using Q₁C₁ = Q₂C₂
• 500 × 15 = 1500 × x
• x = 5%
Concentration Example
Problem: 65% w/v syrup evaporated to 85% volume
• 100 mL → 85 mL
• 100 × 65 = 85 × x
• x = 76.47%
Stock Solutions
Concentrated solutions used to prepare weaker solutions.
Example: Use 1:50 stock to make 0.25% solution
• 1:50 = 2%
• 2%/0.25% = 30 mL/x mL
• x = 3.75 mL stock needed
Alcohol Dilution
Special consideration: Water-alcohol mixing causes volume contraction.

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Example: Make 50% v/v from 85% v/v
• Need 5000 mL final volume
• 85% × x = 50% × 5000
• x = 2941 mL of 85% alcohol
• Add water to make 5000 mL total
Acid Dilution
Concentrated acid: % w/w
Diluted acid: % w/v
Formula: Volume needed = (% w/v diluted × Volume needed) / (% w/w
concentrated × sp gr)
Solid Dilution
Trituration: 1:10 w/w dilution of potent drugs with lactose
Example: How much 1:10 trituration for 25 mg drug?
• 10g trituration contains 1g drug
• 1g/10g = 0.025g/x g
• x = 0.25g trituration needed
Alligation
Alligation Medial
Calculate weighted average of mixture.
Formula: % = (Σ(% × quantity)) / Total quantity × 100
Example: Mix 3000 mL 40%, 1000 mL 60%, 1000 mL 70%
• (0.40×3000 + 0.60×1000 + 0.70×1000) / 5000 = 0.50 = 50%
Alligation Alternate
Calculate proportions needed for desired strength.

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Method:
Higher % -------- (Desired % - Lower %) parts of higher %
\ /
Desired %
/ \
Lower % -------- (Higher % - Desired %) parts of lower %

Example: Mix 95% and 50% alcohol to get 70%

95% -------- 20 parts (70-50)
\ /
70%
/ \
50% -------- 25 parts (95-70)
Ratio = 20:25 = 4:5

Unit Operations
Definition
A unit operation is a process designed to achieve physical and/or chemical
property changes in raw materials.
Common Unit Operations
1. Size reduction
2. Size separation
3. Mixing
4. Filtration
5. Evaporation
6. Drying

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 7. Distillation
8. Extraction
9. Crystallization
10.Centrifugation
11.Compaction
Fundamental Principles
All unit operations are controlled by:
1. Fluid flow
2. Mass transfer
3. Heat transfer
Manufacturing Scale Benefits
Economic: Lower production costs
Accuracy: Better measurement precision
Greater scope: Complex processes possible
Standardization: Consistent formulations

Fluid Flow
Definition
Flow of substances that don't permanently resist distortion.
Types of Flow
1. Laminar (Streamline) Flow
Characteristics: Straight parallel paths, no mixing
Velocity: Low
Reynolds number: < 2000

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2. Transitional Flow
Characteristics: Wavy but parallel paths
Velocity: Moderate
Reynolds number: 2000-4000
3. Turbulent Flow
Characteristics: Complex mixing patterns
Velocity: High
Reynolds number: > 4000
Reynolds Number
Re = ρud/μ
Where:
• ρ = fluid density (kg/m³)
• u = fluid velocity (m/s)
• d = pipe diameter (m)
• μ = fluid viscosity (kg/m·s)
Factors Affecting Flow
Pipe diameter: Larger diameter → earlier turbulence
Fluid velocity: Higher velocity → turbulence
Fluid density: Higher density → earlier turbulence
Fluid viscosity: Lower viscosity → earlier turbulence
Boundary Layers
Definition: Regions near walls where velocity decreases
Characteristics: Turbulent → transitional → laminar → stationary
Control: Increased agitation reduces boundary layer thickness

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Velocity Distribution
Laminar: Parabolic profile, maximum at center
Turbulent: Flatter profile, more uniform velocity

Mass Transfer
Definition
Net movement of mass from one location/phase to another.
Mechanisms
1. Diffusion
Definition: Movement due to concentration gradient
Direction: High concentration → low concentration
Driving force: Concentration difference
2. Advection
Definition: Movement due to bulk fluid motion
Limitation: Cannot occur in solids
3. Convection
Definition: Combined diffusion and advection
Types: Natural (density/temperature changes) or forced (agitation)
Phase Interfaces
Solid/liquid: Dissolution, crystallization
Gas/liquid: Evaporation, condensation
Liquid/liquid: Extraction

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Noyes-Whitney Equation
dW/dt = DA(C₁ - C₂)/L
Where:
• dW/dt = dissolution rate
• D = diffusion coefficient (m²/s)
• A = surface area
• C₁ = concentration at interface
• C₂ = bulk concentration
• L = boundary layer thickness
Factors Affecting Mass Transfer
Agitation: Reduces boundary layer thickness
Temperature: Increases diffusion coefficient
Surface area: More area = faster transfer
Concentration gradient: Larger gradient = faster transfer
Applications
Dissolution: Drug release from tablets
Drying: Moisture removal
Extraction: Separating components
Distillation: Separating by volatility
Equipment Design Considerations
1. Turbulent flow conditions
2. Maximum concentration gradients
3. Largest possible surface area
4. Optimal temperature control

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Key Formulas Summary
Calculations
Smallest weighable quantity: (100% × SR) / Error%
Percentage error: (Error × 100) / Quantity desired
Dilution: Q₁C₁ = Q₂C₂
Density: Mass/Volume
Specific gravity: Weight of substance / Weight of equal volume water
Dose calculations: Number of doses = Total quantity / Size of dose
Physical Properties
Reynolds number: Re = ρud/μ
Noyes-Whitney equation: dW/dt = DA(C₁ - C₂)/L
Alligation medial: % = Σ(% × quantity) / Total quantity × 100
Flow Characteristics
Laminar flow: Re < 2000
Transitional flow: Re = 2000-4000
Turbulent flow: Re > 4000

Heat Transfer and Steam Properties

Introduction to Heat Transfer
Heat is a form of energy associated with the disordered/chaotic movement of
molecules/ions. Although intangible, it can be accurately measured in:
• Joules (J) - SI unit
• Calories (cal) - 1 cal = 4.18 J (energy to raise 1g water by 1°C)
Temperature indicates internal energy - greater molecular motion = higher
internal energy = higher temperature.

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Heat transfer is the exchange/movement of heat energy that occurs spontaneously
wherever there is a temperature gradient.
Pharmaceutical Applications of Heat
Heat is essential in numerous pharmaceutical processes:
• Plant extraction and extract concentration/drying
• Chemical synthesis of medicinal compounds
• Pharmacy operations: melting, distillation, evaporation, concentration,
drying
• Industrial processes: gelatin capsules, ointments, creams, suppositories,
gels, powder drying, granulation, coating, ampoule sealing
• Sterilization: autoclaves (steam under pressure), ovens (dry heat), infrared
sterilizers, boilers (boiling water)
Methods of Heat Transfer
1. Conduction
• Definition: Heat transfer by direct contact of particles
• Mechanism: Adjacent atoms vibrate against each other; electrons move
atom to atom
• Characteristics: No mixing action; limited to solids and bound fluids;
slower than convection
• Governed by Fourier's Law: Rate of conduction ∝ area × temperature
gradient
Fourier's Law Equation:
Q = KA(t₁ - t₂)θ/L
Where:
• Q = quantity of heat
• K = thermal conductivity coefficient
• A = area
• (t₁ - t₂) = temperature difference

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 • θ = time
• L = thickness
Example Calculation: Stainless steel dish: A = 25 cm², L = 1 mm, T₁-T₂ = 10°C,
K = 17 W/mK
• Q/θ = 17 × 25×10⁻⁴ × 10 / 1×10⁻³ = 425 J/sec = 425 W
• In 4 minutes (240 s): Total heat = 425 × 240 = 102,000 J = 102 kJ
Thermal Conductivity Values:
Material K (W/mK)

Copper (pure) 386

Aluminum (pure) 204

Mild steel 43

Stainless steel 17

Glass 0.86

Water (20°C) 0.60

Air 0.03
2. Convection
• Definition: Heat transfer involving mixing of molecules in fluids
• Types:
o Natural convection: Density differences cause circulation (hot fluid
rises, cold sinks)
o Forced convection: Fluid forced to move (mixers, baffles, pumps)
• Characteristics: Forced convection > natural convection; turbulent flow
improves heat transfer
3. Radiation
• Definition: Energy transfer through space by electromagnetic radiation

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 • Mechanism: Hot body emits energy → transmitted through space →
absorbed by receiving body → manifested as heat
Steam as a Heating Medium
Advantages of Steam:
1. Raw material: Water is cheap and plentiful
2. Convenience: Easy to generate, distribute, and control
3. Cleanliness: Clean, odorless, tasteless; minimal contamination risk
4. High heat content: Latent heat enables rapid heating
5. Constant temperature: Heat released at constant temperature (useful for
control and sterilization)
Heat Content of Steam
Heating Process (1 kg water at atmospheric pressure):
1. Sensible Heat (0°C → 100°C):
o Specific heat capacity (S) = 4.2 kJ/kg·K
o Heat required = 4200 × 1 × 100 = 420,000 J = 420 kJ
2. Latent Heat of Vaporization (100°C water → 100°C steam):
o Latent heat (L) = 2.26 × 10⁶ J/kg = 2.26 MJ
o Dry saturated steam: All water converted to steam
3. Dryness Fraction: Weight fraction of steam in steam/water mixture
o Example: 50% converted = dryness fraction of 0.5
4. Superheated Steam: Steam above saturation temperature (gains sensible
heat)
Steam Tables (Pressure vs. Saturation Temperature)
Pressure (bar) Saturation Temperature (°C)

1 100.0

2 120.4

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Pressure (bar) Saturation Temperature (°C)

3 133.7

4 143.8
Example Calculation: Produce 13 kg dry saturated steam at 2 bar from water at
18.4°C:
• Saturation temperature at 2 bar = 120.4°C
• Sensible heat: 13 × 4210 × (120.4-18.4) = 5.582 × 10⁶ J
• Latent heat: 13 × 2.2 × 10⁶ = 2.86 × 10⁷ J
• Total: 5.582 × 10⁶ + 2.86 × 10⁷ = 3.418 × 10⁷ J = 34.18 MJ
Steam Condensation Process
• Superheated steam (200°C) → loses superheat → saturated steam
(100°C)
• Condensation begins → latent heat released → condensate formed
• Dryness fraction decreases as condensation continues
• Complete condensation → further cooling reduces temperature
Practical Steam Usage
Important Rules:
1. Pressure: Use lowest pressure giving suitable temperature gradient
2. Saturation: Use saturated steam (not superheated)
3. Dryness: Keep steam dry by minimizing heat losses
Steam Generation and Distribution:
• Central generation: High-pressure boiler for economy
• Distribution: Adequately sized, lagged (insulated) pipes
• Lagging materials: Asbestos, kieselguhr, aluminum foil, glass wool

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Steam Usage Methods:
1. Direct use: Live steam blown directly into material
o Advantage: Greater heat transfer efficiency
o Disadvantage: Condensate enters material
2. Indirect use: Steam jacket or coils
o Advantage: No condensate contamination
o Method: Large surface area for heat transfer
Steam Jacket Systems
Components:
1. Reducing valve
2. Pressure gauge
3. Temperature gauge
4. Safety valve
5. Control valve
6. Temperature probe
7. Temperature controller
8. Steam trap
9. Air vent
10.Stirrer
11.Homogenizer
Steam Traps (remove condensate and air, retain steam):
1. Float-type mechanical: Depends on condensate level
2. Balanced pressure thermostatic: Operates below saturation temperature

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Design Considerations for Heating Equipment
Critical Factors:
1. Area: Maximize surface area for heat transfer
2. Temperature gradient: Balance efficiency with product stability
3. Materials: Select appropriate thermal conductivity
4. Surface layers: Minimize resistance
5. Air removal: Critical for steam systems
6. Cleanliness: Keep surfaces free from deposits/scale
7. Condensate removal: Ensure proper drainage
8. Liquid circulation: Promote turbulent flow, avoid stagnation

Evaporation
Definition and Purpose
Evaporation is the removal of liquid from a solution by boiling in a suitable vessel
and withdrawing vapor, leaving concentrated residue.
Practical Definition: While true evaporation occurs below boiling point, industrial
evaporation involves boiling for faster processing.
Purpose:
• Form concentrated solutions
• Obtain solid solutes from dilute solutions
Mechanism of Evaporation
When heat is applied to a solution:
1. Molecular motion increases
2. Surface molecules overcome surface tension
3. Molecules evaporate (surface molecules have less cohesive force)
4. Rate controlled by heat transfer rate

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Factors Affecting Evaporation Rate
1. Temperature
• Relationship: Rate directly proportional to temperature
• Limitation: Thermolabile substances require low temperatures
• Examples: Glycosides, alkaloids decompose <100°C; hormones, enzymes
more heat-sensitive; antibiotics may require freeze-drying
• Principle: Short exposure to high temperature may be less destructive than
long exposure to low temperature
2. Surface Area and Agitation
• Surface area: Rate directly proportional to exposed area
• Agitation/stirring: Necessary because it:
o Decreases boundary layer thickness
o Increases heat and mass transfer rates
3. Atmospheric and Vapor Pressure
• Atmospheric pressure: Rate inversely proportional to external pressure
• Vapor pressure: Rate directly proportional to liquid's vapor pressure
4. Type of Product
• Determines method and apparatus selection
• Examples: Evaporating pans for dry products, film evaporators for liquid
products
5. Effect of Concentration
As concentration increases:
• Boiling point elevation: Higher solids proportion raises boiling point
• Increased risk: Greater damage to thermolabile constituents
• Reduced temperature gradient: Decreases heat transfer driving force
• Increased viscosity: Causes thicker boundary layers

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 • Solid deposition: May build up on heating surfaces, reducing heat transfer
• Solution: Ensure turbulent flow conditions
Types of Evaporators
I. Natural Circulation Evaporators
a) Evaporating Pans
• Advantages: Easy to use, clean, and maintain
• Disadvantages: Open system causes slow evaporation due to atmospheric
saturation; limited to aqueous liquids
b) Evaporating Still
• Design: Covered pan connected to condenser
• Features: Receiver and vacuum pump can be fitted
• Advantage: Reduced pressure operation allows lower temperatures for
thermolabile materials
c) Short Tube Evaporator (Calandria)
• Advantage: Tubular design increases heating area 10-15 times compared to
external jacket
• Disadvantages: Complicated, expensive to construct, clean, and maintain
• Applications: Large-quantity extracts (cascara), general products (sugar,
salt, caustic soda)
II. Film Evaporators
Long-tube Evaporator (Climbing Film)
• Characteristic: Liquor residence time only few seconds
• Advantage: Ideal for thermolabile substances (vitamins, fruit juices)
• Mechanism: Liquid climbs tube walls as thin film
III. Forced Circulation Evaporators
Standard Forced Circulation
• Design: Calandria supplemented by pump

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 • Applications: Syrups, gelatin solutions
• Advantages: Rapid liquid movement improves heat transfer, especially for:
o Viscous liquids
o Materials depositing solids
o Foaming materials
o Thermolabile materials (insulin, liver extracts)
Rotary Evaporators
• Features: Vacuum operation, rotating flask
• Advantages:
o Rapid liquid movement improves heat transfer
o Lower pressure reduces boiling points
o Suitable for thermolabile materials
o Solvent recovery capability
o Safety for organic solvents
Vacuum Evaporators
• Principle: Lowering pressure reduces boiling points
• Applications: Thermolabile materials, solvent recovery

Drying
Definition and Importance
Drying is the vaporization and removal of water/other liquids from solutions,
suspensions, or solid-liquid mixtures to form dry solids.
Importance of Drying:
1. Preservation: Prevents fungal/bacterial deterioration
2. Stabilization: Essential for moisture-sensitive materials (aspirin, ascorbic
acid)

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 3. Size reduction preparation: Removes moisture to make materials brittle
4. Property improvement: Enhances handling characteristics (bulk density,
powder flow, compaction)
Theory of Drying
Drying involves both heat transfer and mass transfer:
Heat Transfer: Required to supply latent heat for moisture vaporization Mass
Transfer: Involves:
• Water diffusion through material to evaporating surface
• Evaporation from surface
• Vapor diffusion into air stream
General Principles for Efficient Drying
1. Large surface area for heat transfer
2. Efficient heat transfer per unit area
3. Efficient mass transfer (sufficient turbulence, minimize boundary layers)
4. Efficient vapor removal (low humidity air at adequate velocity)
Important Definitions
Absolute Humidity: Weight of water vapor per unit weight of dry air
Relative Humidity (RH): Ratio of partial vapor pressure to saturation vapor
pressure at same temperature (expressed as percentage)
Saturation Humidity: Absolute humidity when partial pressure equals vapor
pressure of free water
Dew Point: Temperature at which air-water mixture becomes saturated
Moisture Content:
Moisture Content = (Loss in weight / Initial weight) × 100%
Example: 5g moist solid → 3g dry weight Moisture content = (5-3)/5 × 100% =
40%

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Classification of Pharmaceutical Driers
1. Convective Drying of Wet Solids
a) Fixed (Static) Bed Convective Drying
• Tray Dryer: Used for crude drugs, chemicals, powders, granules
b) Dynamic Convective Driers
• Fluidized-bed Dryers:
o Particles suspended in upward gas stream
o Random lifting and falling motion
o Mixture acts like boiling liquid
Advantages of Fluidized-bed Dryers:
• Efficient heat/mass transfer → high drying rates
• Uniform, precisely controlled temperature
• Turbulence creates spherical, free-flowing products
• Disadvantage: Produces fines and dust (segregation, contamination risk)
2. Conductive Drying of Wet Solids
Vacuum Oven:
• Operating pressure: 0.03-0.06 bar
• Boiling point: Water boils at 25-35°C
• Applications: Unstable materials, thermolabile substances
• Advantages: Low temperature operation, reduced oxidation risk (e.g.,
penicillins)
3. Radiation Drying of Wet Solids
Infrared (IR) Radiation:
• Absorbed quickly, poor penetration
• Rarely used for pharmaceutical products

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Microwaves:
• Frequency: 960 and 2450 MHz
• Generated by: Magnetron
• Penetration: Excellent, uniform heat generation within solid
Advantages of Microwave Drying:
1. Rapid drying at low temperatures
2. High thermal efficiency (casing and air remain cool)
3. Stationary bed (no dust/attrition problems)
Disadvantages:
1. Smaller batch sizes than fluidized-bed dryers
2. Radiation shielding required (eye and reproductive organ protection)
4. Driers for Dilute Solutions and Suspensions
Drum Dryer:
• Mechanism: Spreads liquid over large heated surface
• Advantages: Rapid drying, vacuum jacket option for temperature reduction
• Critical factors: Feed rate, film thickness, drum speed, temperature
• Applications: Starch products, ferrous salts, kaolin/zinc oxide suspensions
Spray Dryer:
• Mechanism: Atomizes liquid to small droplets for large surface area
• Particle formation: Hollow spheres (outer crust forms first, internal liquid
vaporizes)
Advantages of Spray Drying:
• Uniform appearance
• Rapid drying
• High bulk density, rapid dissolution
• Uniform, free-flowing, spherical particles

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 • Ideal for tablet manufacture
5. Freeze Drying
Process:
1. Freeze initial solution/suspension
2. Reduce pressure above frozen state
3. Remove water by sublimation
Applications: Extremely heat-sensitive materials (proteins, blood products)
Advantages: Minimal damage to sensitive compounds

Filtration
Definitions and Classifications
Unit Operation: Process designed to achieve physical/chemical property changes
in raw materials
Clarification: Processes involving solid-fluid or fluid-fluid separation
Filtration: Separation of insoluble solid or fluid from fluid using porous medium
Filtration Types:
1. Solid/fluid filtration
o Solid/liquid filtration
o Solid/gas filtration
2. Fluid/fluid filtration
Pharmaceutical Applications
1. Appearance improvement of solutions
2. Irritant removal (e.g., from eye drops)
3. Sterilization where heat treatment inappropriate
4. Air purification for manufacturing areas (HEPA filters)

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Mechanisms of Filtration
1. Straining/Sieving
• Physical size exclusion
• Particles larger than pores retained
2. Impingement
• Particles collide with filter medium
• Captured by physical contact
3. Attractive Forces
• Electrostatic, van der Waals forces
• Chemical attraction between particles and medium
4. Auto-filtration
• Retained particles form additional filter layer
• Improves subsequent filtration efficiency
Factors Affecting Filtration Rate
Darcy's Equation:
V/t = (k × A × ΔP) / (η × L)
Where:
• V/t = filtration rate (volume/time)
• k = permeability of filter medium
• A = area available for filtration
• ΔP = pressure difference across filter bed
• η = viscosity of filtrate
• L = thickness of filter medium and deposited cake

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Filter Media
Ideal Properties:
• Deliver clear filtrate at suitable rate
• Withstand mechanical stress without rupturing
• No chemical/physical interactions with filtrate components
Classification:
1. Woven Filters:
• Wire screening: Stainless steel (durable, clog-resistant, easily cleaned)
• Fabrics: Cotton, wool, nylon (nylon preferred for pharmaceuticals)
2. Non-woven Filters:
• Filter paper: Controlled porosity, limited absorption, low cost
3. Membrane Filters:
• Materials: Cellulose esters, nylon, Teflon, PVC
• Structure: Thin membrane with millions of pores/cm²
• Applications: Microfiltration, sterile solution preparation
4. Porous Plates:
• Types: Perforated metal/rubber, natural materials (stone, porcelain,
ceramics), sintered glass
Filter Aids
Purpose: Prevent medium blockage, form open porous cake, reduce flow
resistance
Requirements: Inert, insoluble, incompressible, irregular shape
Examples:
1. Diatomite (Kieselguhr): Natural siliceous deposits
2. Perlite: Aluminum silicate
3. Cellulose and Asbestos

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Methods to Increase Filtration Rate
1. Increase filtration area
2. Increase pressure difference (vacuum or positive pressure)
3. Decrease filtrate viscosity (dilution, heating)
4. Increase cake permeability (filter aids)
5. Decrease cake thickness (large surface area)
Filtration Equipment
Small Scale:
• Buchner funnel and vacuum flask
Large Scale:
• Gravity filters
• Vacuum filters (rotary vacuum filter)
• Pressure filters (Meta filter)
• HEPA filters

Mixing
Definition and Purpose
Mixing is a unit operation treating two or more components from
unmixed/partially mixed state so each unit lies as close as possible to units of other
components.
Pharmaceutical Importance: Most products contain multiple components
requiring mixing for:
• Even active component distribution
• Uniform appearance
• Correct release site and rate

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Types of Mixtures
1. Positive Mixtures
• Characteristics: Mix spontaneously and irreversibly by diffusion
• Examples: Gases, miscible liquids
• Tendency: Approach perfect mix
2. Negative Mixtures
• Characteristics: Components tend to separate
• Requirement: Continuous energy input to maintain dispersion
• Examples: Suspensions, emulsions, creams
3. Neutral Mixtures
• Characteristics: Static behavior - no tendency to mix or segregate
spontaneously
• Examples: Mixed powders, pastes, ointments
Mixing Quality Definitions
Perfect Mix: Each unit in contact with units of all other components (theoretical
ideal, not practical)
Random Mix: Equal probability of selecting any particle type at all positions
(proportion equals total mix proportion)
Scale of Scrutiny
Definition: Weight/volume of dosage unit dictating how closely mix must be
examined
Importance: Ensures each dosage unit contains correct amount/concentration
Example: 200mg tablet → 200mg sample scale of scrutiny
Evaluation of Mixing
Purposes:
1. Indicate degree/extent of mixing
2. Follow mixing process

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 3. Assess mixer efficiency
4. Determine required mixing time
Mixing Index (M):
M = S_ACT / S_R
Where:
• S_ACT = standard deviation of actual samples
• S_R = standard deviation of random mix samples
Interpretation:
• Start: High S_ACT, low M
• Progress: S_ACT decreases, M approaches 1
• Random mix: S_ACT = S_R, M = 1
Requirements for Evaluation:
1. Sufficient samples (~10) using sampling thief
2. Suitable analytical technique
Mechanisms of Powder Mixing
1. Convection
• Bulk movement of powder groups
• Transfer of relatively large amounts
2. Shear
• Slip planes development
• Intermediate-scale mixing
3. Diffusion
• Individual particle movement
• Final stage of mixing process
Note: All three mechanisms occur simultaneously, depending on mixer type,
conditions, and powder flowability.

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Liquid Mixing Mechanisms
1. Bulk Transport
• Large-scale fluid movement
• Gross circulation patterns
2. Turbulent Mixing
• Chaotic fluid motion
• Rapid mixing mechanism
3. Molecular Diffusion
• Individual molecule movement
• Slow but thorough mixing
Powder Segregation (Demixing)
Definition: Opposite of mixing - components separate out
Causes:
• Particle size variation
• Density differences
• Shape differences
• Vibration/movement
Consequences:
• Content uniformity variations
• Weight variation test failures
Approaches to Eliminate Segregation:
1. Size fraction selection: Sieving to narrow particle size ranges
2. Controlled crystallization: Specific crystal shape/size
3. Density matching: Select similar density excipients
4. Granulation: Size enlargement

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 5. Minimize vibration: Reduce post-mixing movement
6. Ordered mixing: Create adhesive interactions
Ordered Mixing
Alternative names: Adhesive mixing, interactive mixing
Mechanism: Small particles adsorb onto "active sites" of larger carrier particles
Applications:
• Oral antibiotic dry suspensions
• Dry powder inhaler formulations
Mixing Equipment
Powder Mixing:
1. Tumbling Mixers/Blenders:
• Mechanism: Vessel rotation causes powder movement until angle of repose
exceeded
• Designs: Y-cone, rotating cube, V-shape double-cone
• Advantage: Gentle mixing action
2. High-speed Mixer-Granulators:
• Function: Intensive mixing with simultaneous granulation
• Applications: Wet granulation processes
Liquid Mixing:
Propeller Mixers:
• Unbaffled tanks: May cause undesirable vortexing and aeration
• Baffled tanks: Prevent vortexing, improve mixing efficiency, reduce
oxidation risk
Semisolid Mixing:
1. Sigma Blade Mixers:
• Design: Two sigma-shaped blades in trough

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 • Action: Kneading and shearing
• Applications: Heavy pastes, doughs
2. Planetary Mixers:
• Design: Blade orbits around vessel while rotating
• Action: Thorough mixing of viscous materials
• Applications: Ointments, creams, pastes
Construction Note: Semisolid mixers require heavier construction to handle high-
consistency materials.

Solid Dosage Forms

TABLETS
Definition: Unit dose of one or more medicaments prepared by compression or
mold method
Common Excipients:
• Diluents - Provide bulkiness to tablet
• Disintegrants - Ensure tablet breaks up in digestive tract
• Binders - Important for powder granulation
• Glidants and Lubricants - Provide good flow and ensure efficient
tabletting
• Sweeteners and Flavors - Mask taste of APIs
• Pigments - Make uncoated tablets visually attractive
Coating Benefits:
• Mask taste
• Smooth tablet for easy swallowing
• Extend shelf life
• Prevent gastric degradation of drug

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BUCCAL AND SUBLINGUAL TABLETS
Buccal Tablets: Placed between gum and cheek Sublingual Tablets: Placed under
tongue
Advantages:
• Rapid dissolution in mouth
• Absorbed through mucous membrane
• Drug reaches systemic circulation without gastric juice interference
• Bypasses liver metabolizing enzymes
Examples: Vasodilators, Steroidal hormones
EFFERVESCENT TABLETS
Composition: Uncoated tablets containing acid substances (citric and tartaric
acids) and carbonates/bicarbonates
Mechanism: React rapidly with water, releasing CO₂
Benefits:
• Immediate dissolution/dispersion
• Pleasant taste of carbonated drink
CHEWABLE TABLETS
Use: Chewed prior to swallowing Target Population: Children (e.g., vitamin
products)
CAPSULES
Definition: Solid unit dosage form containing solid, semi-solid, or liquid fill in
gelatin shell
Common Excipients:
• Gelatin - Gelling agent
• Plasticizers - Ensure elasticity/mechanical stability
• Additional Additives - Preservatives, coloring, opacifying agents
Types:

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 • Hard gelatin capsules - For dry powder ingredients
• Soft gelatin capsules - For semi-solid and ingredients dissolved/suspended
in oil
LOZENGES
Definition: Solid preparation for medicating mouth and throat for slow
administration
Composition: Sugar and gum (provides strength, cohesiveness, and facilitates
slow release)
Uses: Indigestion or cough remedies
PASTILLES
Definition: Solid medicated pill/candy designed to dissolve slowly in mouth
Characteristics: Softer than lozenges
Base Components: Glycerol, gelatin, acacia, sugar
DENTAL CONES
Definition: Tablet intended for placement in empty socket after tooth extraction
Purpose: Prevent local multiplication of pathogenic bacteria
Excipients: Lactose, sodium bicarbonate, sodium chloride
Active Ingredients: May contain antibiotics or antiseptics
PILLS
Definition: Solid oral dosage form of spherical masses from APIs with inert
excipients
Current Status: Rarely used
ORAL GRANULES
Definition: Solid, dry aggregates of powder particles with irregular shape
Packaging: Often supplied in single-dose sachets
Administration Methods:
• Placed under tongue and swallowed with water

39
 • Dissolved in water before taking
• Effervescent granules - Evolve CO₂ when added to water
ORAL POWDER
Definition: Multi-dose preparations of solid, loose, dry particles of varying
fineness
Components:
• One or more active ingredients
• Excipients (if necessary)
• Coloring matter and flavoring substances
Typical Use: Non-potent medicaments (e.g., antacids)
Dosing: Patient measures by volume using 5 mL medicine spoon

Semisolid Dosage Forms

SUPPOSITORIES
Definition: Semisolid dosage forms for insertion into body orifices where they
melt, soften, or dissolve
Routes of Administration:
• Rectal - Most common
• Vaginal - For contraceptives, antiseptics, pathogen treatment
• Urethral - Antibacterial, local anesthetic
Shape Variations: Depend on density of base, medicaments, and manufacturer
Applications
Local Action:
• Rectal - Relieve constipation, hemorrhoid pain/irritation/inflammation
• Vaginal - Contraceptives, antiseptics, antimicrobials
• Urethral - Antibacterial, local anesthetic for examination

40
Systemic Action:
• Relief of nausea/vomiting, tranquilizer
• Narcotic analgesia
• Migraine syndrome relief
• Anti-inflammatory, analgesic, antipyretic
Advantages over Oral Therapy:
• Avoid gastric pH and enzymatic destruction
• Reduce stomach irritation
• Bypass portal circulation (avoid liver metabolism)
• Convenient for patients unable/unwilling to swallow
• Effective for patients with vomiting episodes
Suppository Ingredients
Components: Drug + Base + Adjuvants
Affecting Factors:
• Physicochemical nature of drug
• Nature of suppository vehicle
• Drug release capacity
• Clinical desired effects
• Drug solubility (lipid vs water)
• Particle size of dispersed drug
Base Requirements
Essential Properties:
• Solid at room temperature
• Softens/melts/dissolves at body temperature
• Appropriate hydrophilic/hydrophobic character

41
 • Melting point near solidifying point
• Easily ejectable from mold
• Non-irritating to mucous membranes
Base Classification
Fatty/Oleaginous Bases: Water-repelling, oil-based Water-Soluble/Water-
Miscible Bases: Dissolve in body fluids
Preparation Methods
• Compression method
• Fusion/Mold method
OINTMENTS
Definition: Semisolid preparations for external application
Composition: Drug substance + Bases + Adjuvants
Ointment Base Classification
Hydrocarbon Bases (Oleaginous):
• Water-free
• Retained on skin for prolonged periods
• Prevent moisture escape (occlusive dressing)
• Difficult to wash off
• Don't dry out or change with aging
Key Hydrocarbon Bases:
• Petrolatum - Semisolid hydrocarbons from petroleum (Vaseline)
• Paraffin - Solid hydrocarbons, colorless/white, hardens bases
• Liquid Paraffin - Colorless, odorless oil, adjusts viscosity
• Hydrophilic Petrolatum - Can absorb water, forms W/O emulsion
• Anhydrous Lanolin - <0.25% water, mixes with 2× weight water
• Lanolin - W/O emulsion with 25-30% water

42
 • Beeswax/Spermaceti - Weak surfactants, stabilization agents
• Mineral Oil - Levigating substance for solid incorporation
Absorption Bases:
• Type 1 - Permit aqueous solution incorporation → W/O emulsions
• Type 2 - Already W/O emulsions, accept additional aqueous solutions
• Useful as emollients
• Not easily water-washable
• Useful for incorporating aqueous drug solutions
Water-Removable Bases:
• O/W emulsions
• Water-washable
• Can be diluted with water/aqueous solutions
• Absorb serious discharges in dermatologic conditions
• May enhance drug absorption
Emulsifying Agents:
• Sodium lauryl sulfate - O/W emulsion
• Stearyl/Cetyl alcohol - Oleaginous phase, improves stabilization
• Glyceryl monostearate - Weak W/O emulsifier, stabilization
• Spans - W/O emulsifying agents
• Tweens - O/W emulsifying agents
• Preservatives - Methylparaben, propylparaben
Water-Soluble Bases:
• Contain only water-soluble components
• Water washable
• Soften greatly with water addition

43
 • Better for non-aqueous/solid substance incorporation
Base Selection Factors
• Desired drug release rate
• Percutaneous absorption enhancement
• Moisture occlusion advisability
• Drug stability (short/long-term)
• Drug influence on base consistency
• Patient factors
Preparation Methods
• Incorporation method
• Fusion method
• Emulsification method
OPHTHALMIC OINTMENTS
Definition: Semisolid preparations for eye application under aseptic conditions
Advantages: Increased ocular contact time vs solutions
Disadvantages: Blurred vision as base melts and spreads
Base Requirements:
• Non-irritating to eye
• Permit drug diffusion through eye secretions
• Melting point close to body temperature
• Usually petrolatum + liquid petrolatum mixtures
• May include lanolin for water-miscible properties
CREAMS
Definition: Semisolid preparations containing medicinal agents in O/W or W/O
emulsion
Applications: Topical skin, rectal, vaginal products

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Advantages: Easier to spread and remove than ointments
Consistency: Relatively soft, spreadable
Examples:
• O/W cream - Hydrophilic ointment
• W/O cream - Cold cream
• "Cream" without qualification - Generally water-washable
Cream Preparation
Components: Oils (mineral/vegetable), fatty alcohols, fatty acids, fatty esters
Emulsifying Agents: Non-ionic surfactants, soaps
Process:
1. Separate components into lipid and aqueous portions
2. Heat both phases above highest melting point
3. Mix phases
4. Stir until ambient temperature/congealed
5. Continue mixing during cooling
6. May use high shear homogenizers
GELS
Definition: Clear, transparent, non-greasy semisolids with solubilized actives in
aqueous vehicle rendered jelly-like by gelling agent
Gelling Agents:
• Synthetic macromolecules - Carbomer
• Cellulose derivatives - Carboxymethyl cellulose, hydroxypropyl cellulose
• Natural gums - Tragacanth
Carbomers: High molecular weight, water-soluble acrylic acid polymers
• Types: 910, 934, 940 (different viscosities)
• Concentration: 0.5-2% in water

45
 • Carbomer 940: Highest viscosity (40,000-60,000 centipoises at 0.5%)
Applications: Lubricants, medicated applications (skin, eye, nose, vagina, rectum)
Additional Components:
• Solvents (alcohol, propylene glycol)
• Antimicrobial preservatives (methyl/propyl parabens)
• Stabilizers (edetate disodium)
Advantages:
• Easy application
• Pleasant cooling effect from water evaporation
• Easily removed by washing
Characteristics:
• May thicken on standing (thixotropic)
• Must shake before use
• Single-phase - Uniform macromolecule distribution
• Two-phase - Floccules of distinct particles (magma)
PASTES
Definition: Semisolid preparations for skin application with larger proportion of
solids (~25%) than ointments
Characteristics: Stiffer than ointments
Preparation: Same as ointments (direct mixing or heat softening)
Levigating Agent: Often use portion of base rather than liquid
Advantages:
• Remain in place after application
• Effectively absorb serious secretions
• Protective due to stiffness and impermeability
Limitations: Not suitable for hairy body parts

46
Example: Zinc oxide paste (25% zinc oxide + 25% starch + white petrolatum)

Size Reduction
DEFINITION
Size Reduction: Process of reducing particle size to finer state of subdivision
Alternative Terms: Comminution, Pulverization
METHODS
Precipitation Method:
• Substance dissolved in appropriate solvent
• Suitable for raw material production
Mechanical Process:
• Solids - Cutting, grinding, milling
• Liquids - Atomization, emulsification
PHARMACEUTICAL APPLICATIONS
Benefits:
• Increased surface area → rapid dissolution and absorption
• Facilitates extraction of crude drugs
• Enhances evaporation and drying rate
• Improves mixing uniformity of solid ingredients
• Enhances physical stability and elegance of suspensions, emulsions, creams,
ointments, pastes
• Reduces irritation
Examples: Glibenclamide, Griseofulvin benefit from size reduction
DISADVANTAGES
• Volatile Loss - Volatile constituents may be lost (avoid heavy grinding of
clove, cinnamon)

47
 • Increased Reactivity - Enhanced oxidation and hydrolysis (store in closed
containers, cool places)
FACTORS AFFECTING SIZE REDUCTION
Material Properties:
• Hardness - Mohs scale (Diamond >7, Talc <3)
• Toughness and Abrasiveness
• Stickiness and Slipperiness
• Material Structure and Softening Temperature
Moisture Content:
• <5% - Suitable for dry grinding
• >50% - Required for wet grinding
MECHANISMS OF SIZE REDUCTION
Cutting: Material cut by sharp blade
Compression: Material crushed by pressure application
Impact: Material hit by high-speed object or strikes stationary surface
Attrition: Pressure with relative surface movement creating shear forces
EQUIPMENT CLASSIFICATION
Cutting Methods
Cutter Mill:
• Series of knives on horizontal rotor vs stationary knives
• Few millimeter clearance
• Screen retains material until sufficient size reduction
• Uses: Coarse size reduction of dried granulations, fibrous crude drugs
Compression Methods
Mortar and Pestle:
• Mortar - Bowl (wood, ceramic, glass, stone)

48
 • Pestle - Heavy club-shaped crushing tool
Comminution Techniques:
• Trituration - Continuous rubbing/grinding (hard, fracturable powders)
• Pulverization by Intervention - Uses intervening solvent (alcohol, acetone)
for hard crystalline/gummy substances
• Levigation - Reduces particle size with small amount of viscous liquid
(mineral oil, glycerin)
End-Runner and Edge-Runner Mills:
• Mechanized mortar and pestle
• End-runner - Weighted pestle turned by friction
• Edge-runner - Horizontal pestle against powder bed
Impact Methods
Hammer Mills:
• Four or more hinged hammers on central shaft
• Rigid metal case enclosure
• Screen retains particles until adequate comminution
• Produces narrow size distributions
Vibration Mills:
• 80% filled with porcelain/steel balls
• Whole mill body vibrated
• Size reduction by repeated impaction
• Particles fall through base screen
Attrition Methods
Roller Mills:
• Two or three porcelain/metal rolls
• Horizontal mounting with adjustable gap (20μm minimum)

49
 • Different rotation speeds create shear
• Uses: Suspensions, pastes, ointments
Combined Impact and Attrition Methods
Ball Mill:
• Hollow cylinder rotating on horizontal axis
• Contains balls (30-50% volume)
• Multiple ball sizes improve efficiency
• Critical Factor: Rotation speed
Speed Effects:
• Low speed - Balls slide back with minimal reduction
• High speed - Centrifugal force, no reduction
• Optimal - 2/3 critical velocity produces cascading action
Fluid Energy Mill (Micronizer):
• Hollow toroid (20-200 mm diameter)
• High-pressure air jets create turbulence
• Particle-particle collisions cause fracture
• Size reduction by impact and attrition

Key Classifications Summary

Tablet Types
• Standard tablets
• Buccal/Sublingual
• Effervescent
• Chewable
• Dental cones

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Capsule Types
• Hard gelatin (dry powders)
• Soft gelatin (semi-solids, oils)
Suppository Bases
• Fatty/Oleaginous
• Water-soluble/Water-miscible
Ointment Bases
• Hydrocarbon (oleaginous)
• Absorption
• Water-removable
• Water-soluble
Size Reduction Mechanisms
• Cutting
• Compression
• Impact
• Attrition
Size Reduction Equipment
• Cutting - Cutter mills
• Compression - Mortar/pestle, runner mills
• Impact - Hammer mills, vibration mills
• Attrition - Roller mills
• Combined - Ball mills, fluid energy mills

51