Rheology
Introduction: Rheology is the study of the flow and deformation of matter from solids to gases. It describes the relationship between force, deformation and time. It comes from the Greek "rheos" that means to flow. The consistency of different products describes fluid rheology. Fluid rheology is studied by viscosity (η) and elasticity. Viscosity is the resistance to flow and elasticity is usually stickiness.
Common to liquids, solids and substances in between the former two is that if a stress is applied to them, they will strain. Stress may be visualized by placing a small amount of fluid between two parallel plates. When one plate slides over the other, forces act on the fluid dependent upon the rate of the plate movement. This causes a shear stress on the liquid. Recall laminar flow of fluids through a tubular vessel. Strain is the response to the stress. If solids are elastic, they deform and return to their original shape. Since fluids are not elastic and, hence, viscous, their deformation is irreversible.
For practical purposes,
there are three types of fluids:
- Newtonian Fluids
- Non-Newtonian Fluids, Time Independent
- Non-Newtonian Fluids, Time Dependent
The viscosity of Newtonian fluids is dependent only on temperature. Examples of Newtonian fluids are water, milk, sugar water, mineral oil, ethyl alcohol. The viscosity of non-Newtonian time Independent fluids is dependent on temperature and shear rate. The flow behavior of these fluids may be classified as follows
Shear Thinning:
- aka: pseudo plastic
- Viscosity goes down with increased shear rate
E.g., paint, shampoo, ketchup, fruit juice concentrates
Shear Thickening:
- aka: dilatant
- Viscosity increases with increased shear rate
E.g., wet sand, concentrated starch suspensions
Plastic:
- aka: Bingham Plastic Fluid
- Requires a threshold shear stress before flow occurs -- this is called a yield value
E.g., tomato paste, tooth paste, hand cream, grease
Types of Rheometers:
Concentric Cylinder Rheometers:
- Two concentric cylinders of radii R_{1} and R_{2}.
- A relative angular velocity (Ω) of one cylinder with respect to another one.
- The shear stress (σ) at any cylindrical surface of radius (r) is σ= G/2πr^{2 }
Where G: “is the torque per unit length acting on the liquid cylindrical surface of radius r”.
The strain rate: y = where; ω: Is the relative angular velocity between i.e.: the inner cylinder and the liquid cylindrical surface of radius (r)
Concentric Cylinder Rheometer: The narrow gap concentric cylinder rheometer:
- The length (L) of the cylinders is much larger than the radii; L >>R_{1}, R_{2}
- The ratio of inner cylinder to outer cylinder radii is greater than 0.97.
- The shear stress: σ= G/2πR_{a}^{2 }
^{Ra: represents “some average radius” which can be equal [(R1 R2)/2]}
Rheometers Uses:
- Viscosities.
- Shear stress with respect to shear strain rate behavior.
- Pressure gradient of the fluid.
- Velocity profile.
- Storage and Loss modulus