The Second Viscosity of Liquids

Abstract

The second coefficient of viscosity is concerned with the viscous forces generated by compression (or dilatation). In the absence of knowledge of its magnitude in liquids it has been customary in hydrodynamics to assume that the coefficient of dilatational viscosity, ${n}^{\ensuremath{'}}$, could be approximated by the ideal gas value ${n}^{\ensuremath{'}}=\ensuremath{-}\frac{2n}{3}$, where $n$ is the coefficient of shear viscosity. A method has been developed for obtaining values for the dilatational viscosity which is based on Eckart's theory of acoustical streaming; the non-periodic motion of the fluid in the vicinity of a sound source is dependent on the two coefficients of viscosity. Values for the coefficient of dilatational viscosity for a variety of organic liquids and for water are given in the table. The coefficient of dilatational viscosity was found to be positive in sign and greater in magnitude than the shear viscosity. For example, the dilatational viscosity of water was found to be 2.4 centipoise and that for carbon disulfide greater than 200 centipoise. There is no correlation between the magnitude of the shear and dilatational viscosities for the liquids studied. Temperature variation measurements on water show that the temperature dependence of dilatational and shear viscosity in this substance is identical. Introduction of values for the dilatational viscosity into acoustical calculations eliminates the well-known discrepancy between theory and observation of sound absorption in liquids at very high frequencies.