AXIAL DROP MOTION IN ROTATING FLUIDS

A theoretical and experimental investigation of drop motion in rotatin g fluids is presented. The theory describing the vertical on-axis tran slation of an axisymmetric rigid body through a rapidly rotating low-v iscosity fluid is extended to the case of a buoyant deformable fluid d rop of arbitrary viscosity. In the case that inertial and viscous effe cts are negligible within the bulk external flow, motions are constrai ned to be two-dimensional in compliance with the Taylor-Proudman theor em, and the rising drop is circumscribed by a Taylor column. Calculati ons for the drop shape and rise speed decouple, so that theoretical pr edictions for both are obtained analytically. Drop shapes are set by a balance between centrifugal and interfacial tension forces, and corre spond to the family of prolate ellipsoids which would arise in the abs ence of drop translation. In the case of a drop rising through an unbo unded fluid, the Taylor column is dissipated at a distance determined by the outer fluid viscosity, and the rise speed corresponds to that o f an identically shaped rigid body. In the case of a drop rising throu gh a sufficiently shallow plane layer of fluid, the Taylor column exte nds to the boundaries. In such bounded systems, the rise speed depends further on the fluid and drop viscosities, which together prescribe t he efficiency of the Ekman transport over the drop and container surfa ces.A set of complementary experiments is also presented, which illust rate the effects of drop viscosity on steady drop motion in bounded ro tating systems. The experimental results provide qualitative agreement with the theoretical predictions; in particular, the poloidal circula tion observed inside low-viscosity drops is consistent with the presen ce of a double Ekman layer at the interface, and is opposite to that e xpected to arise in non-rotating systems. The steady rise speeds obser ved are larger than those predicted theoretically owing to the persist ence of finite inertial effects.