Shear rate

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Shear rate is a measure of the rate of shear deformation:

$\dot \gamma_{ij}=\frac {\partial v_i} {\partial x_j} + \frac{\partial v_j} {\partial x_i}$

For the simple shear case, it is just a gradient of velocity in a flowing material. The SI unit of measurement for shear rate is sec^-1, expressed as "reciprocal seconds" or "inverse seconds."^[1]

For a Newtonian fluid wall Shear stress ( $τ w$ ) can be related to shear rate by $\tau_{w} = {\dot \gamma_{x} \mu}$ , where $μ$ is the Viscosity of the fluid. For Non-Newtonian fluids, there are different constitutive laws depending on the fluid, which relates the stress tensor to the shear rate tensor.