Yield-stress fluid

A yield-stress fluid behaves as a rigid material below a critical shear stress and flows once that stress is exceeded.

A Bingham plastic has $\dot{\gamma }=0$ for $|\tau |<{\tau }_c$ and $\tau ={\tau }_c\mathrm{sgn}\dot{\gamma }+\mu \dot{\gamma }$ after yield.

A thin Bingham layer of thickness $h$ between a stationary wall and a moving body gives $u_b=(h/\mu )(|{\tau }_b|-{\tau }_c{)}_{+}\mathrm{sgn}{\tau }_b$.

A Herschel–Bulkley fluid is unyielded for $|\tau |\le {\tau }_y$ and obeys $\tau =\mathrm{sgn}(\dot{\gamma })({\tau }_y+K|\dot{\gamma }{|}^n)$ after yield. The parameters $K$ and $n$ are its consistency and power-law index.

Where the stress in a yield-stress fluid remains below the yield stress, the shear rate vanishes and the material moves as an undeformed plug bounded by yielded layers.

A slump test releases a known volume of material and infers its yield stress from the dimensions of the final gravity-supported deposit.