The Second Coefficient of Viscosity of Liquids and Gases

The classical theory of the dynamics of viscous fluids is based on the assumption that there is only one fundamental coefficient of viscosity, $\mu$, the coefficient of shear viscosity. The other quantity, ${\mu }^{\prime }$, the second coefficient of viscosity, is assumed to be equal to $-\frac{2\mu }{3}$ in order that $\kappa (=\frac{(2\mathrm{}\mu +3\mathrm{}{\mu }^{\prime })}{3})$, the coefficient of bulk viscosity, should be zero. In making this assumption classical hydrodynamics parts company from classical elasticity, in which two fundamental quantities, the Lamé constants $\lambda$ and $\mu$, are introduced.