Viscosity Concepts in Fluid Mechanics

Rheology

• Rheology is the science of deformation and flow, derived from the Greek word "rheos" meaning "stream."
• Rheology is important in characterizing and classifying materials, especially liquids and semisolids.
• Rheology helps understand raw materials, finished products, and quality control.
• This includes analyzing physical stability, consistency, patient compatibility, drug bioavailability, potential contamination, mixing quality, and variability.
• Rheology is used in process optimization, including selecting suitable equipment (e.g., toothpaste).
• It aids product development by optimizing flow, spreading, and firmness.
• Rheology is also used in predicting behavior under different conditions (e.g., temperature, pressure).
• Rheology is crucial for research and development related to exploring molecular structures, interactions, and new materials.

Viscometry Testing

• Viscometry is the measurement of a fluid's resistance to flow.
• Viscosity is a fluid's resistance to flow (e.g., viscous liquid versus a solid like a sponge).
• Important definitions:
  • Shear stress: force per area.
  • Strain: resultant displacement divided by sample height.
  • Shear rate: the rate of change of strain.
  • Viscosity: shear stress divided by shear rate.
• Units:
  • Pascal-second (Pa·s) is the SI unit for viscosity.
  • Poise (P) is the CGS unit for viscosity.
• Dynamic viscosity (η): Resistance of a substance to flow, and is calculated by dividing shear stress by shear rate.
• Kinematic viscosity (v): Normalised viscosity which is a measure of velocity of flow, and is found by dividing dynamic viscosity by density (ρ).

Learning Outcomes

• Rheological and rheological testing
• Introduction to viscometry
• Thixotropy and yield stress (shear-thinning, shaking in container, thickens back up when stopping).
• Oscillatory rheological testing
• Rheological viscoelasticity parameters

Rheology as Quality Control

• Rheology can describe and quantify product characteristics.
• Examples of process problems it can assess:
  • Spreadability on the skin
  • Pouring from containers
  • Particle sedimentation during storage.
  • Adhesive strength of patches to the skin

Newtonian Experiment

• Imagine a cube of liquid between two parallel plates.
• The bottom plate is fixed, and the top plate slides horizontally.
• Liquid molecules stick to both plates (intermolecular forces).
• Applying a force to the top plate causes it to move at a constant velocity.
• Bottom plate is stationary.
• Liquid layers move at different velocities, creating a velocity gradient (from zero at the bottom to V at the top).
• Internal resistance to flow is called shear stress, which is proportional to the velocity gradient.

Measuring Geometries

• Rotational rheometers are used for non-Newtonian flow measurement.
• They include parallel plates, cone and plate, and cup and bob designs.
• Essential parameters during testing also include plate size, gap size, and temperature.

Factors Affecting Viscosity

• Temperature and pressure affect viscosity in opposing ways. Increasing temperature lowers viscosity, and higher pressure increases viscosity.
• Time also affects viscosity: thixotropic systems are affected by time, changing viscosity over time.
• Shear Stress also affects viscosity: Newtonian materials exhibit stable viscosity no matter what shear stress is applied. Non-Newtonian materials viscosity changes based off level of applied shear stress

Newtonian Fluids

• Newton's Law defines flow as a constant ratio of stress to strain rate.
• Plots of Newtonian fluids show a linear relationship between shear stress and shear rate.
• Dynamic viscosity (η) is the constant of proportionality in Newton's Law
• Examples of Newtonian fluids are water, petrol, glycerol, and hydrogen gas (with varying viscosities).

Non-Newtonian Fluids

• Non-Newtonian fluids behave differently than Newtonian fluids, changing viscosity based on shear stress or time.
• Shear-dependent viscosity: There are three main types:
  • Shear thinning flow: (e.g. cream, suspensions) Viscosity decreases with increasing shear rate.
  • Shear thickening flow: (e.g. concentrated suspensions) Viscosity increases with increasing shear rate.
  • Bingham flow: (e.g. toothpaste) Viscosity remains constant below a certain shear stress value (yield stress). No flow until the yield stress is exceeded.
• Time-dependent viscosity: Thixotropy- Viscosity changes over time (e.g., bentonite, ketchup).

Viscoelasticity

• Many materials exhibit viscoelasticity, acting like viscous liquids in some circumstances and elastic solids in others.
• An example is a concentrated suspension. During storage, the suspension needs to act like a solid to prevent sedimentation; During application it needs to act like a fluid to be evenly applied (e.g. paint).
• Different testing modes include amplitude, frequency, temperature sweeps, and time experiments (e.g., thixotropy).

Oscillation

• Amplitude sweep: helps identify the linear viscoelastic region, important for understanding the material's inherent structural make up. Also can be used to test dispersion/suspension qualities.
• Frequency sweep: gives a unique fingerprint that shows relative process time behaviour- determines if material is elastic or viscous dominated during flow processes.
• Time experiment: determines rheological property of a thixotropic material.

Creep Test

• A constant stress over time is applied, and the resulting strain is measured.
• The stress needs to be low enough to not damage the material's internal structure yet high enough to cause changes in material flow.
• Stored energy changes in the material as the applied stress is removed; this is measured in creep compliance J (strain divided by stress).
• Examples of materials that demonstrate creep include adhesives and paints.