TY - JOUR

T1 - The dilatational properties of suspensions of gas bubbles in incompressible newtonian and non-newtonian fluids

AU - Prud'homme, Robert K.

AU - Bird, R. Byron

N1 - Funding Information:
The authors would like to acknowledge support received from the National Science Foundation Grant ENG 75-01092 and from the Vilas Trust Fund administered through the University of Wisconsin. In addition the authors would like to thank the University of Wisconsin Mathematics Research Center for support provided to one of us (R.K.P.) as a graduate fellow.

PY - 1978/1

Y1 - 1978/1

N2 - 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.

AB - 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.

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U2 - 10.1016/0377-0257(78)87004-9

DO - 10.1016/0377-0257(78)87004-9

M3 - Article

AN - SCOPUS:0017923363

SN - 0377-0257

VL - 3

SP - 261

EP - 279

JO - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

IS - 3

ER -