volume viscosity (dilatational viscosity)

https://doi.org/10.1351/goldbook.V06650
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.
Source:
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]