volume viscosity (dilatational viscosity)

A quantity ζ which enters into equations at any point where the flow involves a change in volume, i.e. is dilatational. If the deformation is purely dilatational, the average of three @[email protected] components is: \[\sigma =\frac{1}{3}\ (\sigma _{xx}+\sigma _{yy}+\sigma _{zz})=- p+\zeta \ (\frac{\partial v_{x}}{\partial x}+\frac{\partial v_{y}}{\partial y}+\frac{\partial v_{z}}{\partial z})\] where \(p\) is the hydrostatic pressure at the point considered in the absence of motion.
PAC, 1979, 51, 1213. (Terminology and Symbols in Colloid and Surface Chemistry Part 1.13. Definitions, Terminology and Symbols for Rheological Properties) on page 1216 [Terms] [Paper]