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Induced-charge electrokinetic flows about polarizable nano-particles: the thick-Debye-layer limit


Using the standard weak-field approximation, we analyse the steady-state electrokinetic flow about an uncharged ideally polarizable spherical particle for the case of a Debye thickness which is large compared with the particle size. The dimensionless problem is governed by two parameters: β, the applied field magnitude (normalized with the thermal scale), and λ, the Debye thickness (normalized with particle size). The double limit β ≪ 1 and λ ≫ 1 is singular, and the resolution of the flow field requires the use of inner–outer asymptotic expansions in the spirit of Proudman & Pearson (J. Fluid Mech., vol. 2, 1957, p. 237). Two asymptotic limits are identified: the ‘moderately thick’ limit βλ ≪ 1, in which the outer domain is characterized by the Debye thickness, and the ‘super-thick’ limit βλ ≫ 1, in which the outer domain represents the emergence of electro-migration in the leading-order ionic-transport process. The singularity is stronger in the comparable two-dimensional flow about a circular cylinder, where a switchback mechanism in the moderately thick limit modifies the familiar O2) leading-order flow to O2 ln λ).

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