Enhancement of transport from drops by steady and modulated electric fields

摘要

We consider the problem of transport of heat or mass from circulating droplets that are both settling and subject to an axial electric field. The electric field can be either steady or oscillatory in time and drives an electrohydrodynamic flow, called the Taylor circulation, which augments the Hadamard circulation caused by steady translation. The problem is governed by four dimensionless groups: the Peclet number Pe, the dimensionless amplitudes of both the steady and unsteady electric field, and the dimensionless frequency omega of the modulation. The convective diffusion equation is solved numerically by an efficient finite-difference scheme that allows a wide range of parameters-in particular, very large Peclet numbers-to be covered. The results are characterized by the asymptotic rate of extraction of heat or mass from the droplet, which is found to be exponential in time. The enhancement factor, defined as the ratio of this rate to that of a stagnant drop, is studied as a function of parameters. For steady drops, we find that transport remains diffusion controlled, but the enhancement factor is significantly higher with the Taylor flow than without. For modulated electric field the enhancement factor is not a simple function of parameters and exhibits spectral "resonant peaks" at particular values of omega for which the enhancement factor is extremely large. Movies of the simulations are used to study the underlying time-periodic spatial structures of the concentration field (so-called strange eigenmodes) and the complex time dependence that is responsible for these resonances.