The Second Viscosity Coefficient in Rheological Systems

Abstract

Viscosity in liquids may be regarded as that property which corresponds to elasticity in solid systems, and the coefficient of viscosity is expected to show as many independent components as the modulus of elasticity. For isotropic systems two components are expected. These two components are denoted by η and ξ. The Stokes relationship between the two coefficients, viz. ζ=-⅔η is compared with the Cauchy-Poisson relationship between the two moduli of elasticity of an isotropic solid, and is claimed as of no more general application. Indeed, experience in sound absorption leads to the conclusion that ζ»η and many measurements on the viscosity of plastic materials appear tacitly to assume that ζ=∞. ζ, however, has a finite value for systems which undergo a progressive change in density at constant pressure. For such systems it is shown that the coefficient of viscosity, as determined by a tensile testing method, while always less than that as determined by torsion testing methods is greater than two-thirds of the latter value. The bulk viscosity, measured by the bulk stress required to produce a progressive density change, is shown to be related to the difference between the shear (or torsional) and the tensile (or flexural) viscosities. Measurements of all three viscosities carried out on a specimen of solid carbon dioxide gives a satisfactory agreement with the theory of small deformations. The values recorded are : Coefficient of viscous traction 10.5 x 101° poises, Torsional viscosity 4.2 x lof0 poises, Bulk viscosity 5.4 x 1010 poises (measured), or 7.0 x 10lU poises (computed). Both flexural and torsional flow curves are of the Bingham type. Corrected yield points are 6.9 x 10⁶ baryes for tensile stress and 4.8 x 10⁶ baryes for shear stress.