The Taylor–Melcher leaky dielectric model as a macroscale electrokinetic description

While the Taylor–Melcher electrohydrodynamic model entails ionic charge carriers, it addresses neither ionic transport within the liquids nor the formation of diffuse space-charge layers about their common interface. Moreover, as this model is hinged upon the presence of non-zero interfacial-charge density, it appears to be in contradiction with the aggregate electro-neutrality implied by ionic screening. Following a brief synopsis published by Baygents these conditions, together with the simplified transport within the bulk domains, constitute the requisite macroscale description. This description essentially coincides with the familiar equations of Melcher its asymptotic correction provides the ‘interfacial’ surface-charge density appearing in the Taylor–Melcher model. Our unified electrohydrodynamic treatment provides a reinterpretation of both the Taylor–Melcher conductivity-ratio parameter and the electrical Reynolds number. The latter, expressed in terms of fundamental electrokinetic properties, becomes O (1) only for intense applied fields, comparable with the transverse field within the space-charge layers; at this limit the asymptotic scheme collapses. Surface-charge advection is accordingly absent in the macroscale description. Owing to the inevitable presence of (screened) net charge on the genuine interface, the drop also undergoes electrophoretic motion. The associated flow, however, is asymptotically smaller than that corresponding to the Taylor–Melcher circulation. Our successful matching procedure contrasts the analysis of Baygents & Saville, who considered more general electrolytes and were unable to directly match the inner and outer regions. We discuss this difference in detail.