 Yield-stress fluid

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,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.