Apparent viscosity (sometimes denoted η)[1] is a rheological property calculated from rheometer readings performed by a Mud engineer on drilling fluid. It is normally abbreviated as AV. It is expressed in cP (centipoise). Centipoise is the amount of force required to move one layer of fluid in relation to another. One centipoise is equal to one hundredth of a poise. A more conventional unit is the SI derived unit mPa·s (millipascal-second; 1 mPa·s = 1 cP).

## Definition

In non-Newtonian fluids, the shear stress due to viscosity, $$\tau_{xy}$$, is modeled by

$\tau_{xy} = k \left (\frac{du}{dy}\right ) ^n$

where

• k is the consistency index
• n is the flow behavior index
• du/dy is the shear rate, with velocity u and position y

To ensure that $$\tau_{xy}$$ has the same sign as du/dy, this is often written as

$\tau_{yx} = k \left | \frac{du}{dy} \right | ^{n-1} \frac{du}{dy} = \eta \frac{du}{dy}$

where the term

$\eta = k \left | \frac{du}{dy} \right | ^{n-1}$

is defined as the apparent viscosity.[1]

## Scope

For this article, apparent viscosity is described, as used in drilling fluid applications in the Oil exploration industry. There may be other applications in other fields of study such as fluid mechanics (The study of the movement of fluid) or fluid dynamics (The study of the flow of fluid).

## Application

The apparent viscosity is but one of many calculations derived from tests performed on the drilling fluid. These calculations and tests help the mud engineer develop and maintain the properties of the drilling fluid to the specifications required.

## References

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