## Bingham Plastic Model

The Bingham model is defined by the relationship;

Shear Stress = Yield Stress + (Plastic Viscosity x Shear Rate)

The major difference between this and Newtonian fluids is the presence of a Yield Stress or "Yield Point" (which is a measure of the electronic attractive forces in the fluid under flowing conditions). No bulk movement of the fluid occurs until this yield stress is overcome. Once the yield stress is exceeded, equal increments of shear stress produce equal increments of shear rate.

Shear Stress , t

Shear Stress , t

Apparent Viscosities y

ttM IL = Plastic LiM Y Viscosity

Apparent Viscosities y

### Flow Curve for a Bingham Plastic Fluid

Note that the apparent viscosity decreases with increased shear rate. This phenomenon is known as "shear thinning". As shear rates approach infinity, the apparent viscosity reaches a limit known as the Plastic Viscosity. This viscosity is the slope of the Bingham plastic line. The commonly used Fann V-G meter was specifically designed to measure viscosities for this model. As can be seen in the above illustration, this model does not accurately represent drilling fluids at low shear rates.

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