Mechanism of dispersed‐phase mass transfer in viscous, single‐drop extraction systems

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Abstract
The theory of solute extraction in viscous single‐drop systems is extended to show (1) the dependence of the asymptotic Nusselt number on the Peclet number from NPe = 0, the molecular diffusion limit, to NPe = ∞, the Kronig and Brink limit, and (2) the dependence of the diffusion entry region Nusselt number on the Peclet number and the initial concentration profile.A numerical solution of the diffusion equation, limited to dilute solute concentrations and solute transport by viscous convection and molecular diffusion, is presented from which the nature of the Nusselt number is deduced. The observed oscillatory behavior of the Nusselt number in the diffusion entry region, as NPe → ∞, is given a simple physical interpretation in terms of the circulation period of the drop liquid.The model is based upon the Hadamard stream function which theoretically is limited to creeping flow; however some experimental evidence indicates that flow fields similar to the Hadamard stream function exist at continuous phase Reynolds numbers of the order of ten.

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