Shear rate

The shear rate ( older, non DIN -compliant names: shear rate, shear rate, shear rate ) is a term used in fluid dynamics, which describes the spatial variation of the flow rate. Since friction forces are present in real fluids, represents a different flow rate at different locations also a transfer of power. In the rheology of the shear rate thus serves as a measure of the mechanical stress to which a sample is subjected at a rheological measurement.

The shear rate used in the rheology of the definition of the viscosity, that is the coefficient of proportionality between shear stress and shear rate. Considering this is a laminar flow.

Symbol: (gamma point); earlier: D

The dimension of the shear rate is the reciprocal of the time: the normal unit therefore.

The shear rate is calculated from the ratio between the speed difference of two adjacent liquid layers and their spacing. In mathematical terms, is the shear rate, the gradient of the velocity field. In the case of laminar flow ( the coordinate h is perpendicular to the flow direction):

In the general case, since the speed and distance are both vector quantities, the shear rate is a second order tensor

Due to symmetry considerations, however, a odere several components of the tensor are identically zero in many problems. So, for example, limits the shear velocity of a current flowing in a direction parallel to the z- axis tube liquid on the tensor elements and who is simplified in the representation in cylindrical coordinates on. For all other components is either zero velocity or its derivative.

So-called shear thinning fluids and other substances (such as plastics) change their viscosity as a function of shear rate. The higher the shear rate, the lower the viscosity. Can be measured, the viscosity of a liquid, a polymer solution or paste at different shear rates using a viscometer.

At Newtonian materials, the viscosity is not dependent of the shear rate. Dilatant materials show a slope of the viscosity at shear rate becomes larger.

In Newtonian fluids there is a linear relationship between the shear stress and the shear rate. Is given by: wherein the dynamic viscosity.