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A solvable weak-potential model of a non-Newtonian fluid

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  • Rainwater, James C.
  • Hess, Siegfried

Abstract

A theoretical model is developed for a non-Newtonian fluid of spherical molecules interacting with a weak potential. The Kirkwood-Smoluchowski equation for planar Couette flow reduces in leading order in potential strength to a shear-diffusion equation with an inhomogeneous source term. The pressure tensor elements are calculated and, for a Gaussian potential, reduce to one-dimensional integrals which are evaluated numerically. The model reproduces several qualitative features of non-Newtonian liquids and the computer simulations of Evans and Hanley. These features include shear thinning, shear dilatancy, normal pressure differences, and dependence on shear rate to a half-integer power.

Suggested Citation

  • Rainwater, James C. & Hess, Siegfried, 1983. "A solvable weak-potential model of a non-Newtonian fluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 118(1), pages 371-382.
    • Handle: RePEc:eee:phsmap:v:118:y:1983:i:1:p:371-382
    DOI: 10.1016/0378-4371(83)90206-6
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