Herschel–Bulkley fluid

Example

A Herschel–Bulkley fluid has a yield stress $\tau_0 \ge 0$, a consistency $k > 0$ and a flow index $n > 0$. In a simple shear flow with shear rate $\dot\gamma \ge 0$ and shear stress $\tau \ge 0$, its law is $$\dot\gamma = 0 \text{ if } \tau \le \tau_0, \qquad \tau = \tau_0 + k \dot\gamma^{\,n} \text{ if } \dot\gamma > 0.$$ For $\dot\gamma > 0$ the apparent viscosity is $\tau / \dot\gamma = \tau_0 / \dot\gamma + k \dot\gamma^{\,n - 1}$. Unless $\tau_0 = 0$ and $n = 1$, this depends on $\dot\gamma$, so the fluid is a non-Newtonian fluid.