Creeping flow of a power law fluid past a fluid sphere

The stress variational principle is employed to obtain the lower bound for the drag offered by the creeping flow of a power law fluid past a Newtonian fluid sphere. In spite of the unprescribed interfacial velocity, a bound-on-bound approach yields bounds that are close to the upper bound obtained by Mohan (1974). Furthermore, for very viscous drops (solid behavior) the theory gives lower bounds that differ considerably from those of Wasserman & Slattery (1964) and show good agreement with the results of Yoshioka & Adachi (1973). The approach presented in this work provides an insight into the method of analyzing multiphase flow situations involving non-Newtonian fluids.