Yield-stress fluid
= Yield-stress fluid
{wiki}
A <yield-stress fluid> can sustain a finite <shear stress> without steady <flow>, but flows when the applied loading exceeds its <yield stress>. The ideal <Bingham plastic> treats the unyielded region as rigid and gives, after yield,
$$
\tau=\tau_y\operatorname{sgn}(\dot\gamma)+\eta_p\dot\gamma.
$$
Here $\dot\gamma$ is the <shear rate>, $\tau_y$ the <yield stress> and $\eta_p$ the post-yield <dynamic viscosity>. Real materials can undergo small <elastic> <deformations> below the flow threshold; an ideal rigid branch does not describe every part of their response.
A pressure-driven experiment makes the spatial distinction visible. Where the local <shear stress> is below threshold, a <plug flow of a yield-stress fluid> can move without internal shearing, while adjacent yielded layers deform. If every point remains below threshold and the walls have no <wall slip>, the ideal material does not flow. Slowly evolving microstructure and <thixotropy> make the apparent threshold depend on preparation, waiting <time> and the loading protocol.