Interdisciplinary Applied Mathematics

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Hence, the contribution of Fek can be evaluated as





Therefore, the additional drag force due to the electrokinetic effects can be calculated in the postprocessing stage, under the approximation of decoupling between the directions of the electroosmotic and external electric fields. This approach is valid for XD/h ^ 1 and XD/R ^ 1. The primary advantage is that we do not need to resolve the flow and the corresponding electroosmotic body forces in the EDL region. Hence, there is no need to solve for the Poisson-Boltzmann equation, and the numerical stiffness in the momentum equation is reduced.

7.4-6 Joule Heating


Large electric fields utilized in electrokinetic flows often result in Joule heating, due to the electrical current and the resistivity of the electrolyte. Using Ohm’s law, Joule heating can be characterized as a volumetric heat source

12


q = —,

a


where a is the electric conductivity, and I is the electric current density. In absence of fluid flow, I = a||E||, and hence q = a||E21|. However, in the presence    of fluid    flow,    current    density    should    also    include    the    charge


convection effects (Tang et al., 2004a). Therefore, for electroosmotic flows,


I = PeUEO + a||E||,


where pe is the charge density, and uEO is the axial electroosmotic flow velocity. We must note that the (peuEO) term can be substantial for thick/over-lapping EDL situations. However, for thin EDL cases, electric current density variations are confined to a very thin region, since the net charge density (pe) vanishes outside the EDL region. Therefore, we can assume q « ct||E2|| in the entire channel domain. Analysis of Joule heating in electroosmotic flows and dielectrophoresis can be found in (Tang et al., 2004a; Tang et al., 2004b; Sinton and Li, 2003), and (Morgan et al., 1999).

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