Stability of the plane Couette flow of a disperse medium with a finite volume fraction of the particles

S. A. Boronin

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

The linear hydrodynamic stability of the plane Couette flow of a suspension with a finite volume fraction of the particles is considered. The two-phase medium flow is described within the framework of the model of mutually penetrating continua which allows for the finiteness of the volume occupied by the particles. In the main flow the phase velocities are the same, while gravity is not taken into account. The stability of disperse flows with both uniform and nonuniform particle distributions is studied. The linearized system of the equations of suspension motion with the no-slip boundary conditions imposed on solid walls is reduced to the eigenvalue problem for an ordinary differential fourth-order equation in the stream function. The eigenvalues are sought using the orthogonolization method. The parametric investigation of the stability characteristics of the disperse flow is performed. It is shown that in the case of the uniform spatial distribution of the particles in the main flow, the presence of an admixture in the flow leads to a slight variation in the wave decay rates, while the flow remains stable for any permissible combinations of the dimensionless governing parameters. In the case of nonuniform distribution of inclusions the flow loses stability already for low Reynolds numbers on a wide range of the dimensionless governing parameters.

Original languageEnglish
Pages (from-to)64-71
Number of pages8
JournalFluid Dynamics
Volume46
Issue number1
DOIs
Publication statusPublished - Feb 2011
Externally publishedYes

Keywords

  • orthogonolization method
  • stability
  • stratified flows
  • suspension
  • volume fraction of particles

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