Viscosity is usually described as the property of a fluid which determines the rate at which local momentum differences are equilibrated.
Rotational viscosity is a property of a fluid which determines the rate at which local angular momentum differences are equilibrated.
If there is a lack of equilibrium between these degrees of freedom, then the rate of equilibration will be determined by the rotational viscosity coefficient.
However, recent theoretical work[2] has predicted that rotational viscosity ought to also be present in viscous electron fluids (see Gurzhi effect) in anisotropic metals.
As a tensor, the equation for the conservation of angular momentum for a simple fluid with no external forces is written: where
) and intrinsic angular momentum density due to the rotation of the fluid particles about their center of mass (
If, however, the internal rotational degrees of freedom of the particles are coupled to the flow (via the velocity term in the above equation), then the total pressure tensor will not be symmetric, with its antisymmetric component describing the rate of angular momentum exchange between the flow and the particle rotation.
In the linear approximation for this transport of angular momentum, the rate of flow is written:[1]: p.308 where