The present status of the controversy regarding the bulk viscosity of fluids

Abstract

Some years ago it was common for physicists to take the Stokes relation as obviously true. During the past two or three years many have come to hold the opposite view and to regard the Stokes relation as obviously false except for monatomic gases. Eight years of discomfort about the Stokes relation have brought me the conviction that nothing on either side of the argument is obvious. In most of what follows, the word viscosity shall refer only to the two coefficients μ and μ' which occur in Poisson’s dynamical equation, which is based upon the formula t i j = ( - p + μ' d k k ) d i j + 2μ d i j for the stress tensor t i j as a linear function of the rate of deformation tensor d i j . By their definition, these viscosities are for each fluid constants or functions of the thermodynamic state; they cannot depend upon the rate of deformation, the frequency of the motion, etc., for otherwise the linearity of the basic equation (1) would become meaningless.