Derivation of an Unified Equation on Shear and Bulk Viscoelasticity of Liquid from the Viewpoint of Hole Theory

Abstract

The present authors consider that both shear flow and volume change are ascribed to the appearance and disappearance of holes. Number of holes decreases with increasing pressure and increases with decreasing pressure.
When pressure on liquid is anisotropic, time rate (frequency) of appearance of hole becomes also anisotropic.
From this point of view, a general relation between stress and deformation of liquid is derived.
[U_r]=v_h/v₀kT/hF≠/F₀exp(-ε_j+ε_h/kT)[exp(-p_rv_h/2kT)]-(p_m/K₂-θ)kT/hF≠/F_hexp(-ε_j/kT)[exp(p_rv_h/2kT)]-1/3K₂[p_r]
[U_r]: tensor of time derivative of strain. Bracket means tensor. Subscript r means principal axes x, y, z of strain. v₀, v_h: volumes of a molecule and a hole, respectively. ε_j: activation energy for collapse of a hole. ε_h: energy for creation of a hole. F₀, F_h, F≠: partition functions. p_r: time derivative of pressure p_r along each principal axis of strain. p_m=Σr=x, y, zp_r/3. θ: bulk strain both by the appearance and disappearance of hole and by the change of inter-molecular distance. K₂: bulk elasticity only by the change of inter-molecular distance. Further from the relation, complex shear viscosity and complex bulk viscosity can be derived. So present theory comprises Hirai-Eyring theory on bulk viscosity (1958) as a special case. If the mechanisms of shear viscosity and bulk viscosity are the same (i.e. the appearance and disappearance of hole), the empirical rule that their activation energies are much the same becoms self-evident.