FST 311

Food Rheology

Overview of Rheology

• Definition: Rheology is a science that studies the deformation of materials, including their flow characteristics.
• Importance: Understanding rheological properties is essential for various engineering calculations and processes in food engineering. It helps in determining pump sizes, pipe designs, and energy requirements.
• Applications: Rheological models obtained from experimental measurements can significantly aid in the design and processing of food engineering materials.

Key Concepts in Rheology

Rheological Properties

• Materials can be characterized by their different flow behaviors, which include:
  • Elastic (Solid-like behavior): Retains shape when stress is applied.
  • Plastic (Yield stress behavior): Requires a minimum stress to start flowing.
  • Viscous (Liquid-like behavior): Flows continuously under stress.
  • Viscoelasticity: Exhibits both viscous and elastic characteristics.

Classification of Deformation

• Elastic Deformation: Deformation is reversible when stress is removed.
• Plastic Deformation: Permanent changes in shape occur when stress exceeds a certain yield point.

Flow of Materials

Newtonian Fluids

• Definition: Fluids that obey Newton's law of viscosity.
• Newton's Law of Viscosity: $\tau_{yz} = -\mu \frac{dv}{dy}$
  • Where:
  • $\tau_{yz}$ = Shear stress (N/m²)
  • $\mu$ = Dynamic viscosity (Pa·s)
  • $\frac{dv}{dy}$ = Shear rate (1/s)
• Steady State Flow: Involves a linear velocity gradient when flow is established.

Non-Newtonian Fluids

• Definition: Fluids that do not follow Newton's law of viscosity.
• Types of Non-Newtonian Fluids:
  • Shear-thinning (Pseudoplastic): Viscosity decreases with increased shear rate (e.g., paint, ketchup).
  • Shear-thickening (Dilatant): Viscosity increases with increased shear rate (e.g., cornstarch in water).
  • Bingham Plastic Fluids: Require a yield stress to flow. For example, toothpaste.

Viscosity Measurement Techniques

Capillary Flow Viscometers

• Usage: Suitable for low-viscosity Newtonian fluids.
• Measurement principle: The time taken for a fluid to flow through a capillary tube is measured.
• Flow Rate Formula: $V = \pi r^2 L$
  • $V$ = Flow rate
  • $r$ = Radius of the capillary
  • $L$ = Length of the fluid column

Rotational Viscometers

• Types: Searle system and Couette system.
• Application: Measures viscosity by rotating a cylinder in a fluid.
• Equation: $\tau = \frac{M}{2\pi h r^2}$
  • Where:
  • $M$ = Torque
  • $h$ = Height of the cylinder
  • $r$ = Radius of the cylinder

Mathematical Relationships in Rheology

Shear Stress vs. Shear Rate for Non-Newtonian Fluids

• Bingham Plastic: $\tau<em>{yz} = \tau</em>0 + k \left(\frac{dv}{dy}\right)$
  • Where:
  • $\tau_0$ = Yield stress
  • $k$ = Consistency coefficient

Power Law Model for Non-Newtonian Fluids

• General form: $\tau_{yz} = k \left(\frac{dv}{dy}\right)^n$
  • Where:
  • $n$ = Flow behavior index; $n < 1$ for shear-thinning, $n > 1$ for shear-thickening.

Time Dependency of Fluids

• Thixotropic Fluids: Viscosity decreases with time under constant shear rate.
• Rheopectic Fluids: Viscosity increases with time under constant shear rate.
• Measurement: Evaluate the behavior of materials under constant stress or shear rates over time.

Practical Implications in Food Engineering

Example of Non-Newtonian Behavior

• Bingham Fluid Behavior in Food: Tomato paste and mayonnaise exhibit behavior typical of Bingham plastic fluids.
• Analysis of Food Products: The rheological behavior can greatly influence processing techniques and consumer acceptance.

Summary and Conclusion

• Understanding the rheological properties of food materials is crucial for their processing and application. This includes recognizing how their properties change under varying conditions of stress and shear.