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

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  • OKUYAMA Masataka
    Department of Polymer Science, Faculty of Science, Osaka University
  • HIROSE Tatsuzo
    Department of Naval Architecture, Faculty of Engineering, Osaka University

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Other Title
  • 空孔生滅による液体の粘弾性の一般論
  • クウコウ ショウメツ ニ ヨル エキタイ ノ ネンダンセイ ノ イッパンロン
  • クウコウセイ ゲン ニ ヨル エキタイ ノ ネンダンセイ ノ イッパンロン

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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.<br>When pressure on liquid is anisotropic, time rate (frequency) of appearance of hole becomes also anisotropic.<br>From this point of view, a general relation between stress and deformation of liquid is derived.<br>[Ur]=vh/v0kT/hF≠/F0exp(-εj+εh/kT)[exp(-prvh/2kT)]-(pm/K2-θ)kT/hF≠/Fhexp(-εj/kT)[exp(prvh/2kT)]-1/3K2[pr]<br>[Ur]: tensor of time derivative of strain. Bracket means tensor. Subscript r means principal axes x, y, z of strain. v0, vh: volumes of a molecule and a hole, respectively. εj: activation energy for collapse of a hole. εh: energy for creation of a hole. F0, Fh, F≠: partition functions. pr: time derivative of pressure pr along each principal axis of strain. pm=Σr=x, y, zpr/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.

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