Volume viscosity

Volume viscosity (also called bulk viscosity, or second viscosity or, dilatational viscosity) is a material property relevant for characterizing fluid flow. Common symbols are ${\displaystyle \zeta ,\mu ',\mu _{\mathrm {b} },\kappa }$ or ${\displaystyle \xi }$. It has dimensions (mass / (length × time)), and the corresponding SI unit is the pascal-second (Pa·s).

Like other material properties (e.g. density, shear viscosity, and thermal conductivity) the value of volume viscosity is specific to each fluid and depends additionally on the fluid state, particularly its temperature and pressure. Physically, volume viscosity represents the irreversible resistance, over and above the reversible resistance caused by isentropic bulk modulus, to a compression or expansion of a fluid.^[1] At the molecular level, it stems from the finite time required for energy injected in the system to be distributed among the rotational and vibrational degrees of freedom of molecular motion.^[2]

Knowledge of the volume viscosity is important for understanding a variety of fluid phenomena, including sound attenuation in polyatomic gases (e.g. Stokes's law), propagation of shock waves, and dynamics of liquids containing gas bubbles. In many fluid dynamics problems, however, its effect can be neglected. For instance, it is 0 in a monatomic gas at low density (unless the gas is moderately relativistic^[3]), whereas in an incompressible flow the volume viscosity is superfluous since it does not appear in the equation of motion.^[4]

Volume viscosity was introduced in 1879 by Sir Horace Lamb in his famous work Hydrodynamics.^[5] Although relatively obscure in the scientific literature at large, volume viscosity is discussed in depth in many important works on fluid mechanics,^[1][6][7] fluid acoustics,^{[8][9][10][2]} theory of liquids,^[11][12] rheology,^[13] and relativistic hydrodynamics.^[3]