Bingham plastic

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A Bingham plastic is a viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress. It is used as a common mathematical model of mud flow in offshore engineering, and in the handling of slurries. A common example is toothpaste, which will not be extruded until a certain hydrostatic pressure is used on the tube. It then is pushed out as a solid plug.

[edit] Definition

The material is rigid for shear stress τ, less than a critical value τ0. Once the critical shear stress (or "yield stress") is exceeded, the material flows as a Newtonian fluid with incremental shear stress and shear rate, ∂u/∂y, (as defined in the article on viscosity) related by:

\frac {\partial u} {\partial y} = \left\{\begin{matrix} 0 &, \tau < \tau_0 \\ (\tau - \tau_0)/ {\mu} &, \tau \ge \tau_0 \end{matrix}\right.


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