A MODEL FOR MASS TRANSFER IN OSCILLATING-CIRCULATING LIQUID DROPS†

Velocity vector computations based upon flow-visualization techniques have enabled the development of a detailed model for flow patterns in a droplet-continuum system typical of liquid-liquid solvent extraction. Experiments show that the streamlines for flow in and around circulating droplets which are forced into regular oscillation by a pulsing electric field can be modeled as the vectorial sum of low-Reynolds-number internal circulation (Hadamard flow) and an oscillatory streaming caused by the prolate-to-oblate ellipsoidal shape changes of the droplet (Dirichlet flow). The convective-diffusion equations have been derived and numerically solved for mass transfer from both circulating droplets (Hadamard flow) and oscillating-circulating droplets (mixed Hadamard-Dirichlet flow). The resulting rate of mass transfer from an oscillating-circulating droplet is significantly greater than that from the equivalent circulating droplet. The rate of mass transfer is dependent upon oscillation frequency and amplitude, droplet Peclet number, the interphase distribution coefficient of the transferring species, and physical properties of each fluid phase.