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. In the classical case, by the equipartition theorem, at equilibrium, if particle collisions can transfer angular momentum as well as linear momentum, then these degrees of freedom will have the same average energy. 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.
Rotational viscosity has traditionally been thought to require rotational degrees of freedom for the fluid particles, such as in liquid crystals. In these fluids, the rotational degrees of freedom allow angular momentum to become a dynamical quantity that can be locally relaxed, leading to rotational viscosity. However, recent theoretical work has predicted that rotational viscosity ought to also be present in viscous electron fluids (see Gurzhi effect) in anisotropic metals. In these cases, the ionic lattice explicitly breaks rotational symmetry and applies torques to the electron fluid, implying non-conservation of angular momentum and hence rotational viscosity.