Predictions of drag and shape of a fluid particle in creeping flow by upper bound approach

Abstract

Creeping motion of incompressible Newtonian media past axisymmetric fluid and rigid particles has been analysed using the upper bound approach. The variational functional for the problem is identified as the minimum drag principle, in the absence of work against the interfacial tension forces. Extensive theoretical predictions of drag and shape deformation for bubbles rising in liquids and drops moving in another liquid or gas, are obtained by suitable choices of viscosity and density ratios and for wide ranges of kinematic parameters, namely, the Froude number and Weber number. Comparisons are presented with other theoretical analyses available in the literature for the limiting cases.