Here’s a simplified and easy-to-understand version of your text on Liquid Mixing:

Liquid Mixing

Mixing Mechanisms

There are four main ways that liquids are mixed:

1. Bulk Transport
This is when large parts of the liquid are moved from one place to another in the tank.
Just moving the liquid isn't enough — it needs to be moved in a way that the parts are
rearranged. This is usually done with paddles or blades that move the liquid in different
directions.

2. Turbulent Mixing
This happens when the liquid moves in a fast and random way, creating swirls (called
eddies). These eddies help mix the liquid well. Large eddies break into smaller ones,
which helps spread the particles and mix everything more evenly.

3. Laminar Mixing
This is a slow and smooth type of mixing, often seen with thick (viscous) liquids or gentle
stirring. The liquid flows in layers. If these layers are folded over and over, the area
between different layers increases, helping them mix better. But this process is slow and
often needs help from diffusion.

4. Molecular Diffusion
This happens at the smallest level, where molecules mix because of their natural
movement. It works better after the liquids are already somewhat mixed. Diffusion takes
time and works best with thin layers.

Mixing Equipment

Liquid mixing usually needs:

1. A Tank to hold the liquid

2. A Power Source to move the liquid (like an impeller, air jet, or liquid jet)

Extra parts like baffles and vanes help control the flow and improve mixing.

• Batch mixing is used for small amounts.

 • Continuous mixing is used for large amounts.

Types of Impellers (Mixers)

Impellers are blades that rotate in the liquid to mix it. They come in three main types:

1. Propellers

• Look like boat propellers (screw-shaped).

• Move liquid mostly in the up-down (axial) direction.

• Work best in thin liquids at high speeds.

• Create strong turbulence around the blades.

2. Turbines

• Blades are straight or tilted.

• Create radial (sideways) and tangential (circular) flow.

• Good for thick liquids.

• Can handle more viscous materials than propellers.

3. Paddles

• Flat, slow-moving blades (less than 50 rpm).

• Good for thick liquids and semisolids.

• Create mainly circular (tangential) flow.

• May leave unmixed areas, so ingredients should be added carefully.

Hybrid Mixers like Dispertron combine two blade types — one for large mixing and one for fine
mixing. They work well for very thick or sticky materials.

Jet Mixers

1. Air Jets

• Air is bubbled through the liquid from below.

• Bubbles lift the liquid, helping it move and mix.

 • Used only with non-foaming, non-reactive, and thin liquids.

2. Fluid Jets

• Liquid is pumped at high speed into the tank.

• Works like a propeller but doesn’t create circular flow.

• Helps mix while transferring the liquid.

Continuous or In-line Mixers

• These mix liquids continuously, instead of in batches.

• Work in pipes or chambers with little or no backflow.

• Use baffles, vanes, or screws inside to improve mixing.

• Need accurate control of how fast raw materials are added.

• Very efficient if operated correctly.

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Here’s a simplified version of the Practical Considerations: Vortexing section in easy and simple
words:

Practical Considerations in Liquid Mixing – Vortexing

What is Vortexing?

• When liquids are mixed using a vertical shaft impeller (a rotating mixer), a vortex
(whirlpool) can form in the center of the tank.

• This usually happens with turbine impellers that have blades set at 90° to the shaft.

• These impellers often cause the liquid to spin in a circle (tangential flow) instead of
mixing it properly.

Why is Vortexing a Problem?

1. Air gets pulled into the liquid, which:

o Causes foaming, especially if surfactants are present.

 o Reduces mixing efficiency.

o Can lead to oxidation (damage) of ingredients.

o Wastes the energy of the impeller.

2. Hard to Scale-Up:
When trying to produce the same product in larger tanks, vortexing makes it difficult to
match the flow patterns and tank designs, which are needed for consistent results.

How to Prevent Vortexing

You can avoid vortexing by:

1. Changing the impeller position:

o Off-center (not in the middle)

o Inclined (tilted)

o Side-entry (from the side)

These break the symmetry and help mix the liquid properly.

2. Using a Push-Pull Propeller:

o Two propellers on the same shaft spin in opposite directions.

o This cancels out the swirling effect and improves mixing.

3. Using Baffles:

o Baffles are flat plates fixed inside the tank wall.

o They break circular flow and create better up-and-down movement (axial flow).

o Baffles increase turbulence and help the impeller mix more efficiently.

4. Changing Tank Design:

o Tanks with special shapes (angled or asymmetrical) act like baffles.

o However, they may need more time to mix properly.

5. Diffuser or Stator Ring:

o A ring around the impeller creates strong turbulence, helpful for mixing or
making emulsions.
 6. Using a Closed Tank Filled to the Top:

o Helps avoid vortex and improves mixing in large batches.

o Reduces air contact and improves consistency.

7. Spraying from Inside:

o Spraying the outer liquid phase through nozzles can reduce splashing and
vortexing.

Drawbacks of Some Methods

• Side-entry mixers are hard to seal and may allow contamination.

• Baffles are difficult to clean, which is a problem when making sterile (germ-free)
products.

• If too many baffles are needed, it may be better to change the impeller instead.

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Here is a simplified, structured, and exam-ready summary of the topic "Semisolid Mixing" for
better understanding and memorization:

SEMISOLID MIXING

Mixing Mechanism

• Mixing depends on the characteristics (viscosity, form) of the material.

• Stages of mixing (based on liquid content added to a powder):

1. Powder State: Dry mixing resembles solid-solid mixing.

2. Pellet State: Small liquid forms pellets with powder, low homogenization.

3. Plastic State: Dough-like, shear force needed, fast homogenization.

4. Sticky State: Paste-like, easy flow, but slow homogenization.

5. Liquid State: Behaves like a fluid, rapid homogenization.

Mixing Equipment

Kneaders

• Used for tough, plastic masses.

• Provides shearing and folding action.

1. Sigma-Blade Mixer

• Two heavy, counter-rotating blades (speed ratio 2:1).

• Generates kneading and rolling action.

• Useful for high viscosity materials.

2. Planetary Mixer

• Mixing element rotates around the container + its own axis.

• Minimizes dead zones.

• Good for uniform mixing.

3. Mulling Mixers

• Provide kneading, shearing, smearing, and blending.

• Use weighted wheels to apply pressure.

• Best for deaggregating already mixed solids.

• May require final remixing if segregation occurs.

Mills

4. Roller Mill (3-Roller Type Preferred)

• Rollers rotate at different speeds, crush and shear material.

• Used for high-viscosity pastes.

• Ensures even distribution by passing material through fixed gaps.

5. Colloid Mill

• Rotor-stator design (3000–20000 rpm).

• Produces high shear → effective size reduction.

 • Used for semisolids/emulsions, not dry powders.

• Smooth vs rough surfaces:

o Smooth: Shearing.

o Rough: Eddy currents and impaction (for fibrous materials).

Mixer Selection Criteria

1. Physical Properties: Viscosity, density, miscibility.

2. Economic Considerations: Time, power cost.

3. Maintenance and Cost of equipment.

Mixing Based on Viscosity

1. Low Viscosity Systems

• Mix easily with high turbulence (e.g., air jets, fluid jets, high-speed propellers).

• Effective up to ~10 poise viscosity.

2. Intermediate Viscosity Systems

• Include emulsions and suspensions.

• Require moderate shear using turbines/propellers.

• Flat blade turbines:

o Good for emulsification.

o Produce radial flow, less affected by viscosity changes.

3. High Viscosity Systems

• Need strong shear forces.

• Equipment: Paddle mixers, sigma-blade mixers, muller mixers.

• If more fluid: Use colloid mill.

• Equipment must handle changing rheology and high stress.

Comparison of Equipment (Summary Table)

Equipment Best For Action

Sigma-Blade Mixer Thick pastes, doughs Kneading, shearing

Planetary Mixer Creams, ointments Dual rotation, uniform mixing

Mulling Mixer Pre-mixed solids with aggregates Smearing, kneading

Roller Mill Ointments, pastes Crushing + shearing

Colloid Mill Emulsions, viscous fluids High-speed shear dispersion

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Here is the meaning and summary of the provided material on Solid Mixing in simple and clear
language, suitable for study:

Meaning of Solid Mixing

Solid mixing is the process of combining different powdered or granular solids to form a uniform
mixture. Although solids may seem like liquids when poured, their mixing behavior is very
different and more complex. This is mainly due to the risk of segregation, where mixed powders
separate again during or after mixing.

Key Concepts Explained

Perfect Mix vs. Random Mix

• Perfect Mix: Every particle is exactly and evenly distributed. This is only theoretical and
cannot be achieved practically.

• Random Mix: A realistic goal where each type of particle has a probability of being
found at any location based on its proportion.

Mixing Mechanisms

Solid mixing involves different mechanisms:

1. Convective Mixing
 o Large groups of powder move from one place to another.

o Fastest and most efficient, but may not reach every part of the mixture evenly.

o Occurs via blades, screws, or bed inversion.

2. Shear Mixing

o Layers of powder slide over each other.

o Helps reduce differences between layers and break up large particles.

3. Diffusive Mixing

o Individual particles randomly move and change places.

o Works slowly and improves mixing on a smaller scale.

o Acts best with additional tools like baffles or irregular motion.

Types of Mixing Equipment

1. Tumblers / Blenders

• Rotate to cause tumbling and mixing.

• Use gentle forces (good for fragile powders).

• Common types:

o Twin-shell blender (“V” shaped)

o Double-cone blender

o Drum/Cube/Tetrahedral blenders

• Best speed: 30–100 rpm (too fast causes centrifugal sticking).

2. Agitator Mixers

• Use moving parts (blades, paddles, screws) inside a stationary container.

• Better for wet or sticky powders.

• Types:

o Ribbon Blender: Horizontal tank with helical blades.

o Planetary Mixer: Good for solid blending before liquid is added.

 o Nauta Mixer: Vertical screw in a cone that mixes in 3D motion.

3. Fluidized Air Mixer

• Uses a strong stream of air instead of blades.

• Powder floats and tumbles in the air for mixing.

Modern Mixers/Processors

1. Rapid Mixer-Granulators: Combine mixing and granulation quickly.

2. Lödige Mixer:

o Uses plow-shaped tools and high-speed choppers.

o Can mix and break lumps in 30–60 seconds.

3. Diosna Mixer:

o Vertical bowl with bottom mixer and side chopper.

o Breaks lumps while mixing.

4. Gral Mixer: Similar to Diosna, used in granulation.

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Here’s a summarized and organized version of your provided text on continuous mixers and
segregation during solids mixing, tailored for easy exam revision. Headings, bullet points, and
important terms are highlighted for clarity.

Continuous Mixers

❖ Characteristics

• Large mixers generally produce more variation in composition than smaller ones.

• Important in processes where uniformity is critical (e.g., tablets and capsules).

• Continuous mixing reduces blender volume requirements by ensuring steady mixing

and material flow.

• Work through impact or shearing, minimizing segregation.

 Types of Continuous Mixers

1. Blendex

• In-line continuous mixer with no moving parts.

• Consists of flow-twisting/splitting elements (e.g., tetrahedral chambers).

• Powders fall by gravity and mix through interfacial surface generation.

• Advantages: Efficient, no heat generation, no particle size reduction.

2. Barrel-Type Continuous Mixer

• Mixing through tumbling motion with baffles.

• Baffles redirect material flow, enhancing intense mixing.

3. Zig-Zag Continuous Blender

• Multiple “V”-shaped blenders in series.

• Each inversion splits material – one part moves forward, the other backward.

• Provides progressive mixing toward discharge end.

Practical Considerations: Segregation (Demixing)

❖ Causes of Segregation

Occurs due to differences in:

• Particle size

• Density

• Shape

• Surface charge

Driven by:

• Gravitational or centrifugal forces

• Shear gradients in the powder bed

 Types of Segregation

1. Radial Demixing

• Fine particles migrate to the center.

• Surrounded by coarse particles moving outward.

2. Axial Demixing

• Particles migrate along the axis of rotation.

• Causes band formation – distinct layers of materials.

3. Competitive Patterned Demixing

• Seen in complex tumblers.

• Arises due to interaction of surface flow and core structure.

Factors Affecting Demixing

1. Particle Size & Distribution

• Main cause of segregation.

• Percolation segregation: Small particles fall through voids.

• Trajectory segregation: Larger particles travel farther.

• Elutriation segregation: Dust particles get airborne and settle on top.

Remedies:

• Sieve to narrow size range.

• Mill particles below 30 μm.

• Granulate to combine different particles.

2. Particle Density

• Denser particles move downward.

• Same-size particles can still segregate due to mass differences.

Remedies:
 • Use excipients with similar density to active drug.

• Reduce size of denser components.

3. Particle Shape

• Spherical particles: Flow better but segregate more.

• Irregular/needle shapes: Interlock better, resist segregation.

Remedies:

• Controlled crystallization for desired shapes.

• Use shape factors to quantify influence.

4. Particle Charge

• Non-conductive particles can become electrostatically charged.

• Leads to clumping and poor mixing.

Remedies:

• Add surfactants to increase conductivity.

• Increase humidity (>40%) during mixing.

Practical Solutions to Minimize Segregation

• Ensure similarity in particle size, shape, and density.

• Use ordered mixing:

o Fine drug particles adhere to larger carrier particles.

o Improves homogeneity and stability.

• Spray drug solution onto carrier → dry → blend.

• Use geometric dilution for potent drugs.

• Control:

o Mixer volume (space for dilation)

 o Shear mechanism

o Mixing time

• Avoid post-mixing vibration or movement.

Mixing Measures

• Evaluation of mixing requires reliable measures.

• Degree of mixing assessed via variance, standard deviation, or concentration

uniformity.

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Here is a simplified and exam-friendly version of your notes on Continuous Mixers and
Segregation in Powder Mixing, with main points highlighted for easier studying:

Continuous Mixers

Continuous mixers are used to mix powders or granules continuously rather than in batches.
These mixers are especially helpful when:

• Small amounts of mixture need consistent composition (e.g., tablets or capsules).

• Reducing segregation and achieving uniformity is critical.

Key Point:

Larger mixers may cause greater variations in composition than smaller ones.

Types of Continuous Mixers

1. Blendex

• Design: No moving parts.

• Structure: Series of fixed twisting/splitting elements (tetrahedral chambers).

• Working: Powders fall freely through and are mixed by generating new interfacial
surfaces.
 • Features:

o Operates vertically.

o Number of chambers depends on mixing quality.

o No heat or particle size reduction.

• Ideal for: Free-flowing solids.

2. Barrel Type Continuous Mixer

• Working: Material tumbles and mixes as it moves through the barrel.

• Baffles: Cause some material to reverse direction, increasing mixing intensity.

• Mixing Mechanism: Tumbling + baffle-induced backward movement.

3. Zig-zag Continuous Blender

• Structure: Series of connected “V”-shaped blenders.

• Working:

o When inverted, material splits — one part moves forward, the other backward.

o Repeated motion enhances mixing towards the discharge end.

Practical Considerations: Segregation or Demixing

Segregation (Demixing) = Separation of powder components after mixing, leading to non-

uniform blends.

Causes of Segregation:

• Differences in: Particle size, shape, density, surface properties.

• Forces: Gravity, centrifugal, electrical, or magnetic fields.

• Motion: Shear rate gradients, especially in convective or shear-based mixers.

Important Concepts:

• Free-flowing, cohesionless powders are more prone to segregation.

• Powders with high cohesion or poor flow resist segregation.

Types of Segregation:
 1. Radial Demixing

o Fine particles move to center, larger particles to outer areas.

o Common in tumblers (See Fig. 1.25A).

2. Axial Demixing

o Grains migrate along the length of the tumbler.

o Results in band formation with clear separation.

3. Competitive Patterned Demixing

o Complex pattern due to interaction of:

▪ Surface flow of coarse grains.

▪ Radial core of fine grains.

▪ Mixer wall boundaries.

o Seen in complex tumbler geometries (See Fig. 1.25B).

Difference Between Demixing and Overblending

Aspect Demixing Overblending

Separation of components after

Definition Physical damage due to prolonged mixing
mixing

Loss of material properties (e.g.,

Effect Loss of uniformity
bioavailability)

Example Particle separation in tumblers Waxy lubricant coating particles excessively

Factors Affecting Demixing

1. Particle Size & Distribution:

o Larger size differences = higher segregation risk.

o Uniform size helps maintain mixture integrity.

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your understanding.

Here's a simplified and exam-friendly explanation of your notes on Continuous Mixers and
Factors Affecting Demixing in Powder Mixing – ideal for your Pharm D midterm prep:

Continuous Mixers

• Definition: Devices that mix powders continuously rather than in batches.

• Key point: Larger mixers often produce more variation in the mix than smaller ones –
critical when uniformity (like in tablets/capsules) is needed.

Types of Continuous Mixers:

1. Blendex

• No moving parts.

• Uses fixed flow-splitting elements to mix powders.

• Powders fall freely and are mixed by generating new surfaces (interfacial surface
generation).

• No heat or particle size change – good for sensitive powders.

2. Barrel Type Continuous Mixer

• Uses tumbling motion and baffles to mix powders.

• Baffles push part of the material backwards → creates intense mixing.

• Effective for cohesive or less free-flowing materials.

3. Zig-zag Continuous Blender

• Series of “V”-shaped blenders.

• As it inverts, material splits → some moves forward, some backward.

• This zig-zag action ensures better distribution.

Segregation or Demixing

• Segregation = Unintentional separation of powder components after mixing.

 • Causes non-uniformity, especially in free-flowing powders.

• Occurs during mixing and after (during transfer, discharge, etc.).

Causes of Segregation:

Type of Segregation Description

Percolation Smaller particles fall through gaps between larger ones.

Trajectory Larger/heavier particles move farther due to momentum.

Elutriation (Dusting Out) Fine particles float in air currents and settle later on top.

Demixing Patterns (Fig. 1.25A & B):

1. Radial Demixing: Fine grains move to the center; coarse grains move to the outer edge.

2. Axial Demixing: Grains in the center migrate along the tumbler's axis, forming bands.

3. Competitive Patterned Demixing: Seen in complex geometries – mix of radial and

surface segregation.

Factors Affecting Demixing

1. Particle Size & Size Distribution

• Main cause of segregation.

• Remedies:

o Use similar-sized particles (sieve if needed).

o Mill to reduce size to <30 μm.

o Use granulation to combine ingredients into same-size granules.

2. Particle Density

• Heavier (denser) particles sink even if size is same.

• Remedies:

o Choose excipients with similar densities.

o Reduce particle size of denser ingredients.

3. Particle Shape

• Spherical particles flow and mix well but segregate easily.

• Irregular/needle-shaped particles reduce segregation by interlocking.

• Shape factors (αs) describe the irregularity of shape and help estimate behavior during
mixing.

• Remedy: Control crystal shape during production.

4. Particle Charge

• Non-conductive particles can build up electrostatic charges, affecting how they mix.

• Not elaborated in this extract, but it usually increases clumping or repulsion.

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Here's a simplified, exam-friendly summary of the given text on powder mixing, segregation,
and evaluation of mixing quality:

Powder Mixing and Segregation

Issues During Mixing

• Clumping: Agitation can cause powders to clump.

• Surface charging: Particles may become electrostatically charged during mixing,

reducing inter-particulate diffusion and promoting segregation.

Nature of Surface Charges

• Total net charge of a powder bed may be zero even if individual particles are highly
charged.

• Particles can have:

o Single or multiple charges (positive or negative).

• Measuring net charge helps assess charge separation risk.

Preventing Charge Separation

 • Add surfactants to increase surface conductivity.

• Mix under high humidity (>40%).

Preventing Segregation

• It's almost impossible to remove all causes of segregation.

• Best approach: Improve the powder properties, not the mixer.

Key Adjustments:

1. Make particles similar in:

o Size

o Shape

o Density

2. Use selective excipients:

o Inert materials that stick to the drug improve homogeneity.

o Called ordered mixing (aka adhesive or interactive mixing).

o Example: Steroids stick better to lipid-like carriers.

⚠ Caution:

• Waxy excipients may affect tablet disintegration or dissolution.

Solution-Based Ordered Mixing

• Dissolve drug in dilute solution.

• Spray it onto an excipient.

• Dry and then mix with rest of the batch.

Mixing Techniques

• Choose:

o Appropriate mixer volume (allows powder bed expansion).

 o Correct mixing mechanism (enough shear force).

o Adequate mixing time.

• Geometric dilution is essential:

o Gradually double the amount of the second component while mixing (50:50
ratios).

Mixing Measures

1. Scale & Intensity of Segregation (Danckwerts' Concept):

• Scale of Segregation: Size of lumps (linear or volume scale).

• Intensity of Segregation: Composition variation among samples.

o Ideal value: Zero (perfect mixing).

o Reduced scale = better diffusion = lower intensity.

2. Scale of Scrutiny

• Smallest region to detect imperfections.

• Depends on product use:

o For tablets: Tablet weight = scale of scrutiny.

o Must be small enough to detect variation but large enough to represent the
region.

• Limited by particle size.

Example: Binomial Distribution in Powder Mixing

• Binary mixture (A:B = 3:7).

• 500-pellet capsule = random selection.

• Mean number of A pellets = 150.

• Standard deviation (σ) = 10.2.

• So, 68% of capsules will contain:

 o Between 140 to 160 A pellets (±1σ).

Conclusion: Larger sample size = less % variation.

Sampling Techniques

• Accurate sampling is crucial to assess mixing quality.

• Use:

o Sampling during discharge or

o Sampling thief:

▪ Tool with two tubes (inner & outer).

▪ Holes align to collect samples when rotated.

▪ Best for free-flowing powders.

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Here is a summarized and exam-focused breakdown of the passage you provided. The content is
divided into major headings with bullet points and simplified wording for better retention and
easier studying:

Sampling and Visualization of Powders

Powder Sampling Techniques:

• Sampling thief: Used to extract samples from within powder beds (Fig. 1.26).

• Refer to Table 1.2 for various sampling techniques (e.g., thief, rotary samplers, etc.).

Visualization Techniques:

• Diffusing Wave Spectroscopy – Detects movement fluctuations inside the bed.

• Positron Emission Tomography (PET) – Tracks individual grains during flow.

• Magnetic Resonance Imaging (MRI) – Detects hydrogen-containing grains.

• X-ray Tomography – Tracks radio-opaque particles in flow.

Mixer Selection

Ideal Mixer Characteristics:

• Mixes quickly with gentle action (avoids product damage).

• Dust-tight, easy to clean/discharge, low maintenance and power.

Types of Mixers:

1. Rotating Shell Mixers:

o Poor cross-flow unless baffled or inclined.

2. Cubical/Polyhedron Mixers:

o Sliding motion, not efficient for mixing.

3. Double Cone & Twin-Shell Blenders:

o Rolling motion, recommended for precision blending.

4. Agitator Mixers:

o Shear action breaks agglomerates.

o Ribbon Mixers: Not precise, hard to clean, high power.

o Sigma/Planetary Mixers: Good for cohesive powders; heat build-up possible.

o Blendex: Suitable for batch/continuous mixing, minimal heat or size change.

Material Property Considerations

Cohesive Powders:

• Stick-slip flow occurs in non-tacky 50–300 µm grains.

• Below 100 µm: Cohesion dominates; particles form aggregates.

Solution:

• High shear mixers or mills to break aggregates.

• Use high shear pre-blending with part of the excipient.

Power Requirement in Solids Mixing

Key Points:

• Cannot predict power needs accurately like fluids.

• Optimal mixing = minimal power use + correct operation.

• Overmixing causes segregation or particle breakdown:

o May result in unwanted fines.

o Especially problematic during scale-up from lab to production.

Mixer Loading Effects

• Horizontal Layering: Promotes faster mixing.

• Side-by-Side Loading: Slower and inefficient.

Scale-Up of Mixing

Objective:

• Move process from lab → pilot → production using empirical methods and
dimensionless numbers.

Important Dimensionless Numbers:

1. Reynolds Number (Re):

o Ratio of inertial to viscous forces.

o High Re = Turbulent flow; Low Re = Laminar flow.

2. Froude Number (Fr):

o Ratio of inertial to gravitational forces.

o Important in powder systems.

3. Power Number (Pn):

o Describes how much power is needed to achieve flow.

Equations:
 • Laminar Flow (Re low):

P=Gg−1ηω2d3P = Gg^{-1} ηω^2 d^3

Power ∝ viscosity; not dependent on density.

• Turbulent Flow (Re high):

P=Gg−1ζω3d5P = Gg^{-1} ζω^3 d^5

Power ∝ density; viscosity has no effect.

Scale-Up Rule:

• Must maintain geometric similarity.

• Power requirements increase dramatically with changes in impeller speed and size.

Example Calculation Summary

Scenario:

• Mixer changes from 15 cm to 23 cm propeller, and speed is doubled.

Result:

• Increased mixing speed requires significantly more power.

• Decision: Weigh benefit of faster mixing against power cost.

Key Takeaways for Exam:

• Proper mixer type depends on material properties.

• Overmixing can lead to segregation and fines formation.

• Scale-up relies on Re, Fr, and Pn to predict behavior.

• Power input differs under laminar vs. turbulent conditions.

• Mixer loading pattern influences mixing efficiency.

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numerical examples.
Here's a clear and concise summary of the provided content about milling and theory of
comminution in pharmaceuticals:

Milling in Pharmaceuticals

Definition: Milling (also called comminution, grinding, pulverization, etc.) is the mechanical
process of reducing particle size to enhance pharmaceutical formulation and effectiveness.

Purpose of Milling

• Few pharmaceutical materials are available in optimum size → need size reduction.

• Enhances dissolution, absorption, mixing, extraction, drying, flow, and appearance.

Milling Classifications (based on mesh size)

Type Mesh Size Particle Size

Coarse > 20 mesh > 840 µm

Intermediate 20–200 mesh 74–840 µm

Fine < 200 mesh < 74 µm

Pharmaceutical Applications of Size Reduction

1. Dissolution & Bioavailability: Increases surface area → faster dissolution (e.g.,

griseofulvin).

2. Pulmonary/Transdermal Delivery: Particle size affects absorption and retention.

3. Extraction: Smaller particles → faster/more complete leaching.

4. Drying: Faster drying due to reduced diffusion distance.

5. Flowability: More uniform flow and filling.

6. Mixing: Uniform distribution in blends, improves dose accuracy.

7. Formulation:
 o Ointments: Smoother texture

o Suspensions: Reduced sedimentation rate

o Lubricants: Require fine particle coating

Theory of Comminution

Stress-Strain Behavior

• Hooke’s Law: Initial linear region – reversible deformation.

• Yield Point: Start of permanent deformation.

• Fracture Point: Irreversible particle breakage.

• Area under curve = energy required for fracture.

Crack Formation & Fracture

• Fracture starts at flaws/cracks in particles.

• Bigger particles with cracks break easily.

• Fine grinding needs more energy due to fewer cracks.

Efficiency of Milling

• < 1% of total energy goes into creating new surfaces.

• Rest is lost as:

o Heat

o Vibration

o Friction

o Motor inefficiency

Griffith Theory (on fracture)

• Stress focuses at the tip of microscopic flaws.

• Fracture stress (T) is related to:

T=2YεπcT = \sqrt{\frac{2Y\varepsilon}{\pi c}}

Where:
 o Y = Young’s modulus

o ε = surface energy

o c = crack depth

Energy Requirements

• Energy required is proportional to new surface area formed.

• Energy formula:

E′=E(1D2−1D1)E' = E \left(\frac{1}{\sqrt{D_2}} - \frac{1}{\sqrt{D_1}}\right)

Where:

o D₁ = feed size

o D₂ = product size

o E = total energy input

Key Factors Influencing Milling

• Material type: Brittle vs plastic

• Force type & application rate

• Crystalline vs amorphous structures

• Presence of flaws and cracks

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Here's a simplified and exam-focused summary of your content on "Mechanisms of

Comminution and Mills", ideal for Pharm D revision:

Mechanisms of Comminution (Size Reduction)

Mills reduce particle size by four main mechanisms:

1. Cutting
 o Force applied over a narrow area using sharp edges (e.g., knives or blades).

o Best for tough, fibrous materials.

2. Compression

o Material crushed between two surfaces (e.g., rollers or mullers).

o Used for brittle solids.

3. Impact

o High-speed collision causes internal stress and fracture.

o Common in hammer mills.

4. Attrition

o Shearing between two surfaces moving relative to each other.

o Produces fine particles.

Types of Milling Operations

• Open-circuit milling: Material passes once through the mill.

• Closed-circuit milling: Uses a classifier to return oversized particles for further grinding
— ideal for fine/ultrafine particles.

Types of Mills Used in Pharmaceuticals

1. Cutter Mill

• Mechanism: Cutting/shearing

• Construction: Rotor with knives (200–900 rpm), stationary knives, and a screen.

• Use: Tough, fibrous materials

• Output size: Up to 80 mesh

• Special note: Disc mills use rotating discs with cutting teeth.

2. Roller Mill
 • Mechanism: Compression + shearing

• Construction: Two to five rollers operating at different speeds.

• Use: Ointments, pastes (Triple roller mill discussed under semi-solid mixing)

3. Colloid Mill

• Mechanism: Shearing

• Construction: Two surfaces (one rotating), used for wet grinding

• Use: Produces fine dispersions (not true colloids)

• Note: Common in ointment/paste mixing

4. Edge-Runner and End-Runner Mills

• Mechanism: Compression + shearing

• Edge-Runner: Heavy wheels rotate over material in a pan

• End-Runner: Rotating pan with a heavy pestle

• Use: Wet grinding of viscous materials (e.g., ointments), moderately fine powders

5. Hammer Mill

• Mechanism: Impact

• Construction: High-speed rotor (up to 10,000 rpm) with swinging hammers

• Working: Material thrown outwards, impacted by hammers, and passed through a

screen

• Speed Control:

o Low speed = blending (not grinding)

o High speed = effective impact (best for brittle materials)

o Speed affects particle size: Higher speed → smaller particles

• Screen types:
 o Round holes: Strong, for fibrous materials

o Herringbone: For crystalline substances

o Jump-gap: For abrasive/clogging materials

• Applications:

o Milling of dry powders, ointments, slurries

o Wet granulation (at 2,450 rpm using knife edges)

o Dried granules (at 1,000–2,450 rpm)

• Advantages:

o Compact, high capacity

o Produces 20–40 µm particles

o Narrow particle size range

o Easy to clean and change settings

o Can be closed system (safe and dust-free)

• Limitation:

o Not ideal for ultrafine particles without classification system

Key Figures Explained

• Fig 2.8: Shows how higher speed leads to finer particles in hammer mill.

• Fig 2.9: Thicker screens at the same speed give smaller particles.

• Fig 2.10: Shows particle size comparison with different screen sizes.

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Here's a summarized and well-organized comparison of the Pin Mill, Ball Mill, Vibro-Energy
Mill, and Fluid-Energy Mill based on construction, working, advantages, and disadvantages for
your study:
 Pin Mill

Construction:

• Two horizontal steel plates with vertical pins arranged in concentric circles.

• Pins intermesh; feed enters through the center of the stator.

Working:

• Feed propelled by centrifugal motion through intermeshing pins.

• Size reduction occurs via impact and attrition.

• Final particle size depends on rotor speed, feed rate, and airflow.

Advantages:

• Clog-free due to absence of screens.

• Achieves finer particle size than rotor-stator mills.

• Suitable for heat-sensitive, soft, non-abrasive powders.

• Fineness adjustable via different pin arrangements.

Disadvantages:

• Not suitable for hard or abrasive materials.

• Scale-up may be limited by difficulty in maintaining rotor speed.

Ball Mill

Construction:

• Horizontally rotating cylindrical vessel partially filled with steel balls or rods.

• Variants: Pebble mill (uses pebbles), Rod mill (uses rods), Tube mill (longer than wide),
Conical mill (tapered end).

Working:

• Impact + attrition are primary forces.

• At low speeds: sliding occurs.

• At optimum speeds: cascading leads to effective grinding.

 • At critical speed: balls centrifuge and no grinding occurs.

Advantages:

• Can operate in batch or continuous mode, wet or dry.

• Suitable for sterile and sealed operations.

• Effective for fine grinding of hard and abrasive materials.

• Can use wetting agents for better efficiency.

Disadvantages:

• Slow process.

• Not energy efficient.

• Not suitable for very fine particles (<10 µm).

Vibro-Energy Mill (Vibratory Mill)

Construction:

• Annular grinding chamber supported on springs.

• Cylindrical grinding media (usually porcelain or stainless steel balls).

• Operates via three-dimensional vibration.

Working:

• Oscillation produces attrition and some impact.

• Generates low heat.

• Produces narrow particle size distribution.

Advantages:

• Faster and more efficient than ball mills.

• Lower operating temperatures.

• Produces uniform particle size distribution.

Disadvantages:

• Complex construction.
 • Not effective for resilient (elastic) materials.

• Limited impact force compared to ball mill.

Fluid-Energy Mill (Micronizer)

Construction:

• Compressed air/steam enters through nozzles in a grinding chamber.

• Feed introduced via venturi injector.

• Product exits through cyclone separator.

Working:

• Interparticulate attrition and impact from air/steam turbulence.

• Internal classification allows only fine particles to exit.

• Particle size: 1–20 μm.

Advantages:

• Ideal for thermolabile substances (air expansion cools system).

• Can produce ultra-fine particles quickly.

• No moving parts in contact with product = low contamination.

Disadvantages:

• High capital and operating costs.

• Not suitable for materials prone to caking.

• Requires premilling of feed (20–100 mesh).

Summary Table

Feature Pin Mill Ball Mill Vibro-Energy Mill Fluid-Energy Mill

Impact +
Size Reduction Impact + Attrition Attrition (mainly) Attrition + Impact
Attrition
Feature Pin Mill Ball Mill Vibro-Energy Mill Fluid-Energy Mill

Fine with narrow

Fineness Fine Medium to Fine Ultra-fine (1–20 µm)
distribution

Heat Low due to air

Low Moderate Very Low
Generation expansion

Material Soft, non- Not for resilient Thermolabile, high-

Hard, abrasive
Suitability abrasive materials value materials

Operation Batch / Continuous,

Continuous Batch Continuous
Mode Wet / Dry

Cost Moderate Low Moderate High

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Here's a simplified and exam-focused summary of the topic Wet and Dry Milling and
Homogenization from your study material:

Wet and Dry Milling (Size Reduction)

Dry Milling

• Medium: Air (compressible).

• Used when: The product degrades in water.

• Size limit: ~100 µm (finer milling causes caking).

• Grinding aids: May be added (<0.1%) to prevent ball coating and improve output (e.g.,
oleic acid, triethanolamine salts).

• Advantages: Simpler process; no drying needed.

• Disadvantages: Dust hazards; limited size reduction; equipment wear.

Wet Milling

• Medium: Liquid (incompressible).

• Used when: Very fine size is needed (limit ~10 µm).

 • Advantages: Better control of particle size, reduces dust, and safer for hazardous drugs.

• Disadvantages: Requires drying step later; potential for flocculation.

Comparison Table

Feature Dry Milling Wet Milling

Medium Air Liquid

Energy Transfer Collision-based Collision + shear forces

Dampening Weak Strong

Particle size limit ~100 µm ~10 µm

Dust hazard High Low

Power consumption Often higher Lower (due to slower mill speeds)

Selection of Mill

Factors to Consider:

1. Material Properties: Size, moisture, hardness, melting point, toxicity.

2. Product Specs: Desired particle size, moisture sensitivity, and shape.

3. Mill Capabilities: Wet/dry options, safety, ease of cleaning, speed.

4. Production Needs: Capacity, batch/continuous process, cost.

5. Auxiliary Equipment: Dust collectors, feeders, temperature control.

Examples of Mills Used for Different Materials

Material Suitable Mills

Antibiotics Ball, hammer, colloid, fluid-energy

Ascorbic acid Ball, roller, hammer, fluid-energy

Caffeine Roller, hammer

Sugar Hammer, fluid-energy

Material Suitable Mills

Urea Ball, hammer, fluid-energy

Homogenization

Homogenization reduces particle size in suspensions and emulsions using mechanical forces
like:

• Shear

• Turbulence

• Impact

• Cavitation

Types of Homogenizers

1. Simple Homogenizer

o Uses high-pressure to force liquids through a small orifice.

o Reduces size by hydraulic shear and turbulence.

2. Silverson Homogenizer

o Has a rotor–stator system with fine tolerances.

o Produces high shear; discharge grids control final particle size.

3. Ultrasonic (Rapisonic) Homogenizer

o Uses ultrasound waves to create cavitation and shear.

o Suitable for fine emulsions and nanoparticle dispersions.

4. High-Pressure Homogenizer

o Fluid is forced at high pressure through a narrow gap.

o Useful for liposomes, nanoemulsions, cell disruption.

o Multiple passes can improve uniformity.

Let me know if you want a chart or diagram summary, MCQs, or quick revision notes.
Here’s a summarized and simplified version of your text, with key points highlighted for easy
understanding and revision:

1. Microfluidizer

• A high-pressure homogenizer used to reduce droplet or particle size in emulsions and

suspensions.

• Works by forcing the pre-homogenized liquid through ceramic micro-channels in an

interaction chamber.

• The liquid splits into two high-velocity streams that recombine, producing:

o Shear

o Impact

o Cavitation (formation and collapse of vapor bubbles)

• Can reduce particles to nanosize (<1 μm).

• Advantages: Highly efficient, easy to scale up, ideal for parenteral emulsions.

2. Low-pressure Cyclone Emulsifier

• Uses a positive-displacement pump to push fluid into a special chamber with tangential
entry.

• Fluid forms spiraling layers that create shear as it moves to the center.

• Operates at low pressure (around 200 psig).

• No moving or adjustable parts.

• Suitable for emulsions with 2–10 μm droplet size.

• Handles viscosity in the range of 1–2000 centipoise.

3. Particle Size and Size Distribution

• Irregular particles are measured statistically by equivalent diameters.

• Equivalent diameters are based on volume, surface area, or sedimentation behavior.

 • Commonly used diameter:

o Stokes' diameter: Based on sedimentation rate (using Stokes’ Law).

4. Types of Diameters

• Arithmetic Mean Diameter: Average of all particle sizes.

• Geometric Mean Diameter: nth root of product of n diameters.

• Median Diameter (d₅₀): 50% of particles are smaller than this size.

• Surface Mean Diameter: Based on total surface area.

• Volume Mean Diameter: Based on total volume.

5. Data Representation

• Tabular form (e.g., Table 2.5) is most precise.

• Graphical representation makes data easier to interpret:

o Histogram or bar graph

o Size-frequency curve: Shows % of particles in each size group.

o Cumulative plot: Used to find median diameter.

6. Size-Frequency and Normal Distribution

• Normal distribution (Gaussian): Symmetrical bell-shaped curve.

• Skewed distribution: More small particles; common in milled powders.

• Skewed data often becomes normal when log of particle size is used.

7. Probability Plots

• Arithmetic-probability plot: Straight line if distribution is normal.

• Log-probability plot: Straight line if data is log-normally distributed.

• Median from both plots = 50% mark.

 • Standard deviation:

o σ = 84.13% size – 50% size

o σ = 50% size – 15.87% size

8. Hatch-Choate Equations

• Relate different types of diameters using:

o Geometric mean diameter (d₍geo₎)

o Geometric standard deviation (σ₍geo₎)

• Example for mean surface diameter (dₛ):

o log dₛ = log d₍geo₎ − 4.606(log² σ₍geo₎)

9. Methods of Particle Size Determination

Method Property Measured Examples

Microscopy Number of particles Optical or electron microscopy

Sieving, sedimentation Weight of particles Sieve analysis, sedimentation rate

Coulter counter Volume of particles Electrical sensing zone

Light scattering Optical behavior Dynamic/laser light scattering

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Here is a simplified and well-organized summary of the particle size measurement methods
described in your provided text:

Particle Size Distribution Measurement Methods

1. Microscopy

• Principle: Direct visualization of particles under a microscope.

• Size range:
 o Ordinary microscope: 0.4 – 150 μm.

o With UV light: down to 0.1 μm.

o Ultramicroscope (dark field): 0.01 – 0.2 μm.

• Measurement tools:

o Filar micrometer eyepiece or eyepiece graticules (grids).

• Procedure:

o Measure diameter by shifting hairline across particle edges.

o Use of calibrated stage micrometer for magnification.

• Particle Count Recommendation:

o Wide distribution: >625 particles.

o Narrow distribution: ≥200 particles.

• Limitations:

o Operator-dependent.

o Time-consuming.

o Subject to human error.

• Improvement tools: Photomicrographs, projections, automatic scanners.

2. Sieving

• Principle: Particles separated based on their ability to pass through mesh screens.

• Size range: 10 – 2000 μm (generally effective above 50 μm).

• Standards:

o Tyler Standard Scale: Based on 200 mesh (0.0029”).

o US Standard Scale: Based on 18 mesh (1 mm).

• Procedure:

o Series of sieves with decreasing openings.

o Shake sample mechanically; weigh retained material.

 • Factors affecting performance:

o Motion type (vibratory > rotary).

o Sieving time.

o Load per sieve.

• Results:

o Particle size = mean of sieve openings.

o Weight data can be converted to number distribution using Hatch-Choate

equations.

3. Sedimentation

• Principle: Settling rate of particles in a fluid depends on their size (Stokes’ Law).

• Size range: 1 – 200 μm.

• Key equation:

d=18ηx(ρ−ρ0)gtd = \sqrt{\frac{18ηx}{(ρ - ρ_0)gt}}

• Method: Andreasen Pipet.

o Withdraw samples at different times from a fixed depth.

o Dry and weigh particles (gives cumulative undersize distribution).

• Analysis:

o Plot log size vs. % less than stated size.

o Determine geometric mean diameter and standard deviation.

o Convert to number distribution using Hatch-Choate equations.

4. Centrifugation

• Principle: Similar to sedimentation but uses centrifugal force.

• Application: For very small particles (too slow to settle by gravity).

• Advantages:
 o Faster than sedimentation.

o Reduces Brownian motion effects.

• Calculation: Modified Stokes’ law using centrifugal acceleration.

5. Elutriation

• Principle: Fluid flow opposes sedimentation; particles rise or fall depending on flow
velocity.

• Mechanism:

o Particles move upward if fluid velocity > settling velocity.

o Multiple columns with increasing diameter = separation by decreasing size.

• Unique Point: Separation based on fluid velocity, not time.

6. Coulter Counter

• Principle: Electrical resistance change as particles pass through an aperture.

• Range: 0.5 – 1000 μm.

• How it works:

o Particles suspended in conducting fluid.

o Each particle displaces electrolyte → voltage pulse.

o Pulse size ∝ particle volume.

• Advantages:

o Measures particle volume directly.

o Very rapid and accurate.

o Operator-independent and reproducible.

7. Dynamic Light Scattering (DLS)

• Principle: Measures particle motion (Brownian motion) via scattered light to determine
size.
 • Best for: Nanosized particles (not affected by settling).

• How it works:

o Uses laser light.

o Measures fluctuation in scattered light frequency.

o Correlates with particle diffusion speed → size.

• Advantages:

o Simple, non-invasive.

o Suitable for colloidal dispersions.

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revision.