Power-law

A Power-law Fluid is a generalized non-Newtonian fluid where the shear stress, \(\tau\), is related to the shear rate, \(\dot{\gamma}\) , such that:

\[\tau=\rho K \dot{\gamma}^n\]

where \(\rho\) is the fluid density, \(K\) is the flow consistency, and \(n\) is the fluid behavior index. The units on \(\rho\) are taken to be \(kg/m^3\), the units on \(K\) are taken to be \(m^2/s^{2-n}\), and \(n\) is dimensionless. From this constitutive relationship, the apparent viscosity \(\nu_a\) of a power-law fluid is then defined as:

\[\nu_a=K\dot{\gamma}^{n-1}\]

where the units \(\nu_a\) are \(m^2/s\). This definition of apparent viscosity is used to calculate the spatiotemporal variation in viscosity across the fluid volume due to spatiotemporal variations in strain rate.

Property Grid

Fluid Properties

Rheology Type

Apply Power-law rheology. Local fluid viscosity is calculated from the local shear rate using a user-defined flow consistency index, flow behavior index, and yield stress.

Density

kg/m 3 | The density of the fluid.

Yield Stress

Pa | Yield shear stress.

Power Law K

m 2 /s 2-n | Flow consistency index.

Power Law N

Flow behavior index n.

Rheology Limits

These are user defined limits that provide a lower and upper bound on the viscosity realized in the simulation. Appropriate limits can help maintain simulation stability and maximize the allowable simulation time step.

Min Viscosity

m 2 /s | The minimum fluid viscosity realized in the simulation.

Max Viscosity

m 2 /s | The maximum fluid viscosity realized in the simulation.