Differential shear viscosity (source code)

= Differential shear viscosity
{title2=$\eta_d(s)=\frac{d}{ds}[s\mu(s)]=\mu(s)+s\mu'(s)$}

Differential shear viscosity measures the incremental shear-stress response around a given positive base <shear rate>. It differs from the secant <shear viscosity> mu. A regular locally stable stress-to-rate inversion needs positive differential viscosity. Zero differential viscosity makes a first-order stress perturbation singular, and negative differential viscosity identifies a decreasing constitutive branch.