The dilatational properties of suspensions of gas bubbles in incompressible newtonian and non-newtonian fluids

Robert K. Prud'homme, R. Byron Bird

Research output: Contribution to journalArticle

31 Scopus citations

Abstract

We derive expressions for the dilatational properties of suspensions of gas bubbles in incompressible fluids, using a cell model for the suspension. A cell, consisting of a gas bubble centered in a spherical shell of incompressible fluid, is subjected to a purely dilatational boundary motion and the resulting stress at the cell boundary is obtained. The same dilatational boundary motion is prescribed at the boundary of an "equivalent" cell composed of a one-phase, uniformly compressible fluid with unknown dilatational properties. By specifying that the stress at the boundary of the one-phase cell is equal to the stress at the boundary of the two-phase suspension cell, we obtain expressions for the unknown dilatational properties as a function of observable properties of the suspension. The dilatational viscosity of a suspension with a Newtonian continuous phase and the analogous properties for suspensions with non-Newtonian continuous phases are obtained as functions of the boundary motion, volume fraction of gas, and properties of the incompressible continuous phase. Results are presented for continuous phases which are Newtonian fluids, second-order fluids, and Goddard-Miller model fluids.

Original languageEnglish (US)
Pages (from-to)261-279
Number of pages19
JournalJournal of Non-Newtonian Fluid Mechanics
Volume3
Issue number3
DOIs
StatePublished - Jan 1978
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Chemical Engineering(all)
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanical Engineering
  • Applied Mathematics

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