Power-law fluid

Example

A power-law fluid (Ostwald–de Waele fluid) has two constants, the consistency $K > 0$ and the flow index $n > 0$. In a simple shear flow with shear rate $\dot\gamma > 0$ its shear stress is $$\tau = K \dot\gamma^{\,n}.$$ Its apparent viscosity is $\eta(\dot\gamma) = \tau / \dot\gamma = K \dot\gamma^{\,n - 1}$. For $n = 1$ this is the constant $K$, and the fluid is Newtonian. For $n \ne 1$ the apparent viscosity depends on $\dot\gamma$, so the fluid is a non-Newtonian fluid. If $n < 1$ the viscosity decreases as $\dot\gamma$ grows (shear-thinning, or pseudoplastic); if $n > 1$ it increases (shear-thickening, or dilatant).