PREDICTIONS OF DRAG AND SHAPE OF A FLUID PARTICLE IN CREEPING FLOW BYUPPER BOUND APPROACH

Creeping motion of incompressible Newtonian media past axisymmetric fl uid and rigid particles has been analysed using the upper bound approa ch. The variational functional for the problem is identified as the mi nimum drag principle, in the absence of work against the interfacial t ension forces. Extensive theoretical predictions of drag and shape def ormation for bubbles rising in liquids and drops moving in another liq uid 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 theoret ical analyses available in the literature for the limiting cases.