Bulk viscosity

Volume viscosity (also called second viscosity or bulk viscosity or dilatational viscosity) becomes important only for such effects where fluid compressibility is essential. Dilatational viscosity is a measure of the viscous forces and viscous forces depend on the rate of compression or dilatation. Dilatational viscosity is zero for Monatomic gases at low density. For an incompressible liquid the dilatational viscosity is neglected. The dilatational viscosity is important in describing sound absorption in polyatomic gases and in describing the fluid dynamics of liquids containing gas bubbles.

The negative-one-third of the trace of the Cauchy stress tensor at the equilibrium is often identified with the thermodynamic pressure,

which only depends upon the equilibrium state potentials like temperature and density (equation of state). In general, the trace of the stress tensor is the sum of thermodynamic pressure contribution and another contribution which is proportional to the divergence of the velocity field. This constant of proportionality is called the volume viscosity.

Volume viscosity appears in the Navier-Stokes equation if it is written for compressible fluid, as described in the most books on general hydrodynamics ^, and acoustics ^, .

If ${\displaystyle \mu }$ and ${\displaystyle \zeta }$ are assumed constant,

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