6.1 Matched asymptotics in electroosmotic flow [electroosmosis top]

Because the thin electrical double layer assumption implies scale separation between the electrical double layer and the bulk flowfield, we often find it useful to analyze electroosmotic flow in terms ofmatched asymptotics. In this case, we find two asymptotic solutions: (1) theinner solution, corresponding to the electrical double layer, in which we keep track of the details of the Coulomb forces and the resulting velocity gradients and vorticity, but we assume that the extrinsic electric field is uniform, and (2) theouter solution, where we assume that the fluid is electroneutral and irrotational, but allow the extrinsic electric field to vary spatially (Figure 6.2). The inner solution is valid in the electrical double layer, but gives incorrect results far from the wall if the extrinsic field varies with distance from the wall. The outer solution is valid outside the electrical double layer, but gives incorrect results near the wall and violates the no-slip condition.

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