Analytical solutions to Stokes-type flows of inhomogeneous fluids

Mehrdad Massoudi, Ashuwin Vaidya

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Abstract

In this paper, we study the unsteady motion of an inhomogeneous incompressible viscous fluid, where the viscosity varies spatially according to various models. We study the Stokes-type flow for these types of fluids where in the first case the flow between two parallel plates is examined with one of the plates oscillating and in the second case when the flow is caused by a pulsatile pressure gradient. A general argument establishes the existence of oscillatory solutions to our problem. Exact solutions are obtained in terms of some special functions and comparisons are made with the cases of constant viscosity and the slow flow regimes.

Original languageEnglish
Pages (from-to)6314-6329
Number of pages16
JournalApplied Mathematics and Computation
Volume218
Issue number11
DOIs
Publication statusPublished - 5 Feb 2012

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Keywords

  • Non-homogenous fluids
  • Oscillating plate
  • Stokes second problem
  • Variable viscosity

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