Viscosity Coefficients

Often viscosity is isotropic, meaning that it is the same in all directions. In such a case, only two of the six components of the strain rate tensor are independent, so two coefficients of viscosity can be used to describe the viscous behavior of the fluid. These two coefficients are related by -2/3. This relationship arises because the strain rate tensor has a simple form for isotropic fluids, and the viscosity is proportional to the magnitude of the rate of deformation of the fluid. Viscosity is multiplied by the strain rate tensor in the Navier-Stokes equations because viscosity is a scalar that describes the internal friction within a fluid and the strain rate tensor describes the rate of change of velocity in the fluid. The use of two coefficients of viscosity in the Navier-Stokes equations is a result of the symmetric form of the strain rate tensor and the isotropic nature of viscosity in many fluids.