No abstract

for spherical drops or bubbles supporting interfacial tension gradients and translating in creeping flow in an electric field imposed in the direction of translation. In particular, the case in which a trace of surfactant is present is considered, and it is found that such material may produce quasistagnant zones along the interface either near the poles or the equator. Terminal velocities may be either increased or decreased relative to the value obtained in the absence of the electric field, SCOPEEarlier work has shown the ability of electric fields to generate circulatory flows in drops or bubbles that are either stationary or translating by gravity, and experimental results suggest the importance of such flows in enhancing the rate of mass or heat exchange between a drop and its surroundings. On the other hand, the effect of interfacial tension gradients, particularly as caused by the presence of traces of surfactant, has been thoroughly investigated and shown (in the usual case) to retard significantly interfacial velocity in the rear stagnation region and to reduce terminal velocity. The present work examines theoretically the combined effects of an interfacial tension gradient, drop translation, and an electric field on the flow structure of a drop or bubble and its surroundings. The simultaneous consideration of all three of these effects is necessary to the assessment of the promise of electric fields for enhancing mass or heat exchange rates in, for example, liquid extraction or directcontact heat transfer operations.

No abstract

a = CD(NRe,t)' = functional form in Eq. 7 = porosity t P = density P = viscosity P NOTATION = drag coefficient = particle diameter = a function appearing in Eq. 4 = acceleration resulting from gravity = Reynolds number defined by Eq. 2 = Reynolds number for a suspension defined by Eq. 9 = Reynolds number based on terminal velocity, defined . = Pm/Pe by Eq. 6 = Ps/Pe = superficial liquid velocity = o r / ut = terminal velocity of a particle in an infinite medium = relative velocity between liquid and particles Subscripts i = ith particle species e = liquid m = mixture or suspension S = solid LITERATURE CITED Garside, J., and M. R. AIDibouni, "Velocity-Voidage Relationships for Fluidization and Sedimentation in Solid Liquid Systems," Ind. Eng. Chem.