W20N Rheology

Rheology

• Rheology is the study of how matter deforms and flows.
• Viscosity is the resistance of a fluid to flow.
• Rheological properties impact a material's processing and its performance in drug products.

Viscometry Testing

• Viscometry testing quantifies a fluid's resistance to flow.

Importance of Rheology

• Used for characterization and classification of materials.
• Rheological measurements describe the flow behaviour of liquids and semi-solids, like creams and ointments.
• Provides insights into viscosity, elasticity, and viscoelasticity.
• Can understand the structure of raw and finished products.
• Ensures physical stability, consistency in quality, patient compatibility, and drug bioavailability.
• Differences in rheological properties can indicate contamination, poor mixing, or variability.
• Impacts adhesive performance of transdermal patches
• Helps to find suitable equipment
• Optimizes flow, spreading and firmness
• Used to predict the behavior of materials under different conditions, such as temperature and pressure.
• Explores molecular structure, interactions, and new materials.

Rheology as Quality Control

• Rheology assesses processing and application characteristics like spreadability on skin or how well it pours.
• It identifies problems like particle sedimentation during storage
• It helps determine the adhesive properties for applications of patches on the skin

Newton's Experiment

• Shear stress is calculated as force divided by area
• Velocity of the top layer is displacement divided by time
• Shear strain is displacement divided by height
• Shear strain rate is the velocity of the top layer divided by the height

Viscometry Terms

• Shear stress (σ) is the torsional force applied per unit area, measured in N/m² or Pascals (Pa).
• Shear strain (γ) is the displacement divided by the sample height represented without units or in "% strain."
• Shear (strain) rate (γ') is the change in strain over time, measured in reciprocal seconds (s⁻¹).
• Viscosity (η) is shear stress divided by shear rate, denoted in Pascal-seconds (Pa·s) in SI units or Poise (P) in CGS units.
• Dynamic viscosity (η) is a measure of resistance to flow (or move)
• Kinematic viscosity is the dynamic viscosity divided by density.
• It represents a normalized value of viscosity and the velocity of the flow.

Newtonian Flow

• Newtonian fluids have constant viscosity regardless of the applied shear stress.
• These liquids follow Newton's law.
• The rate of flow (shear rate, is directly proportional to the shear stress.

Capillary and Falling Sphere Viscometers

• Capillary viscometers are utilized in the process.
• Falling Sphere viscometers are also known as single-point viscometers.
• The Ostwald U-tube viscometer measures laminar flow of a liquid under gravity's influence and records the time it takes to flow from one point to another to determine dynamic viscosity.
• Falling Sphere viscometers measure the time it takes for a sphere to fall through a fluid to determine viscosity using Stoke's law

Non-Newtonian Flow and Rotational Rheometer

• Pharmaceutical systems are often non-Newtonian due to their complexity and heterogeneity.
• The rate of flow (shear rate) is not directly proportional to the applied stress (shear stress).
• Three common behaviors include
  • Plastic
  • Pseudoplastic
  • Dilatant

Plastic Flow

• Describes concentrated, flocculated suspensions.
• A minimum shear stress must be applied before material will flow; that is known as yield value.
• Weak bonds between dispersed particles hold them together.
• Rheological properties can be modified using flocculating agents.
• Under certain conditions can also display pseudoplastic flow

Pseudoplastic Flow

• Cannot define viscosity unless shear stress/rate is specified.
• Usually associated with solutions of polymers, gums or pastes.
• Material flows as soon as shear stress is applied, but viscosity decreases as shear stress increases (Shear thinning)
• Applied force that is insufficient to break crosslinks will cause the material to flow.

Dilatant Flow

• Viscosity cannot be defined unless shear stress/rate is specified.
• Usually associated with concentrated deflocculated suspensions and pastes.
• At low shear rates, particles are separated and the liquid acts as a lubricant.
• At high shear rates, particles clump together, the liquid is no longer a lubricant, and viscosity increases
• Material flows as soon as shear stress is applied, but viscosity increase as shear stress increases (Shear thickening)

Non-Newtonian Studies

• Viscosity changes with applied stress.
• Instruments are needed to apply variable stress and measure corresponding strain

Rheometer

• Used to generates a stress/strain curve by increasing and then decreasing the applied stress.

Rheometer Components and Settings

• Upper mobile plate can be a parallel plate (stainless steel, titanium, etc.) or a cone plate
• Lower stationary plate supports the sample.
• Experimental settings include plate size, gap size between plates, and temperature.

Rheology Instrumentation

• Typical instruments include Cup and Bob and Rotational Rheometers.

Factors Affecting Viscosity

• Temperature: Viscosity decreases as temperature increases
• Pressure: Viscosity increases as pressure increases.
• Time: Affects viscosity in thixotropic systems.
• Shear stress
• Newtonian systems
  • Viscosity is shear rate independent
• Non-Newtonian systems
  • Viscosity depends on what we do to them

Newtonian Fluids

• Obey Newton’s Law of Flow where σ / γ’ = constant.
• The flow curve (rheogram) is linear, with dy/dx = viscosity.
• Dynamic viscosity (η) is the proportionality constant.

Non-Newtonian Fluids

• Exhibit shear stress-dependent viscosity.
  • Shear-thinning (pseudoplastic) flow (e.g., cream)
    • Begins as soon as shear stress is applied.
    • Viscosity is high at low shear rates and vice versa.
    • Described by Power Law equations: σ / η γ’ where n < 1.
    • Observed in polymer solutions (e.g., gels formulations).
  • Shear-thickening (dilatant) flow (e.g., concentrated suspension corn starch, plaster)
    • Opposite behavior to shear-thinning
    • Viscosity is high at high shear rates and vice versa.
    • Described by the Power Law equation: σ / η γ’n where n > 1.
  • Bingham flow (e.g., toothpaste high yield stress)
    • High/thick viscosity
    • Needs applied pressure to initiate flow.
    • Described by equation σ = σ y + η γ’.

Time-Dependent Viscosity

• Includes thixotropic flow (e.g., bentonite, ketchup).

Thixotropic Behavior

• It is time-dependent shear-thinning (pseudoplastic) behaviour
• When mixed constantly, viscosity decreases until it becomes a liquid
• Resets after application stops, thickening and behaving like a solid.

Hysteresis Loop

• It measures area that indicates how thixotropic the material is

Yield Stress

• Flow does not occur until a certain shear stress is applied

Viscoelasticity

• Materials exhibit both viscous (liquid-like) and elastic (solid-like) behaviors.
  • An example of Viscoelasticity is concentrated suspension

Concentrated Suspension Example

• Requires solid-like behaviour to prevent sedimentation during storage.
• Requires fluid-like behaviour when applied to flow through brush bristles.

Oscillation Principles

• The input stress and measured strain are exactly in phase.
• Therefore the phase angle is zero (0
• Phase Angle of Purely Viscous Material
• The stress and strain are ¼ of a cycle out of phase
• Therefore, the phase angle is 90°

Phase Angle

• It is used as a measure of elasticity; a higher value indicates more viscous behavior, while a lower one indicates more elastic properties

Complex Modulus

• It equals to Stress/ Strain
• It is mathematically derived from the ratio of the stress and strain amplitudes.

Oscillation Parameters

• Loss (Viscous) Modulus can indicate liquid-like nature.
  • Equation: Stress/Strain x sin (δ).
• Storage (Elastic) Modulus indicates solid-like nature.
  • Equation: Stress/Strain x cos (δ).
• Dynamic viscosity can be related to shear viscosity.
  • Equation G’’/Frequency

Test Modes

• Rotational rheometers can be are operated in Viscometry (shear), Oscillation, and Creep and Recovery.

Wet Sponge Model

• Dry = elastic solid (storage modulus).
• If add water (inelastic, viscous/loss modulus) – complex viscoelastic behaviour (complex modulus – vector sum of moduli)
• Soak with honey – higher complex modulus

Rheological behavior

• It is a characteristic of cosmetic ingredients/ finished products

Material/Product Rheological Classification

• Liquid
  • Viscous or newtonian
• Semisolids
  • viscoelastic and non-Newtonian, shear-thinning creams and ointments.
• Solid
  • Elastic

Behavior

• Viscoelastic behavior combines viscous and elastic properties.
  • Viscous Behavior
    • Materials that flow, i.e liquids
  • Elastic behaviour:
    • Structured materials that deform reversibly, i.e solids
    • Polymer melts, polymer gels, creams

Oscillation Measurement

• Used for measurements on suspensions
• Amplitude Sweep
  • Two suspensions either remains a continuous phase or produces a supernatant layer
  • Measures linear viscoelastic region
  • Measures dispersion/suspension stability
• Frequency Sweep allows to identify a unique fingerprint and behavior
  • Shows relative process time behavior
  • Behaves as a solid that is elastically dominated (G’ > G’’)
  • Behave as a liquid that is viscously dominated (G’ < G’’)

Temperature and Time Experiments

• Sweep is used for temperature experiments, while measurements are used for thixotropic and time based experiments.

Viscoelasticity Measurements: Creep Test

• Aims to characterize by applying constant stress (σ) over period of time t.
  • Observe and monitor resulting in strain
  • Stress should be low enough to not destruct the internal structure
  • The viscoelastic material stores some of the enery and dissipates(loses) the rest.
    • If stress is removed the energy is restored: rest state
• Creep compliance J= Strain/ Stress; or = /δ
• Creep can described by Burgus model
  • AB: immediate elastic response
  • BC: viscoelastic response
  • CD: steady state viscous response
  • DE: elastic recovery equal to AB
  • Part of structure that can not be recovered is lost energy during viscous flow