Comment on “On the flow field about an electrophoretic particle” [Phys. Fluids 24, 102001 (2012)]

Electrodiffusiophoresis of a large-zeta-potential particle in weak fields

“…Since λ l / is assumed asymptotically small, the perturbation is small for finite f . Accordingly, as duly pointed out by other authors [7], boundary condition (25) becomes practically equivalent to ( )…”

“…In the small-ζ ˜ and thin-DL limits, and if the sole driving force is an externally applied electric field, then the diffusioosmotic contribution is actually negligible as compared to the electroosmotic one and use of equations ( 4) and ( 5) to express velocity in the DL is permissible [1,15]. However, as shown in section 2.5 by simple scaling arguments, the two contributions are of same order in the concerned case of large ζ ˜; thus, equations ( 6) and (7) should respectively be used in the place of equations ( 4) and ( 5). Here, it is worthwhile mentioning that equations ( 6) and ( 7) do allow for variable ζ and λ over the surface (resulting from non-uniform c b ), despite no terms involving the surface gradients of λ and ζ appears in those equations.…”

“…is a non-dimensional parameter, termed ion-drag coefficient, which is inherently O(1) [7]. In the absence of an externally applied concentration field, concentration gradients arise solely as a consequence of an electric field and, in view of equation (14), their magnitude can be no larger than that of ( ) ∇ Ψ zec k T / B :…”

“…It is important to stress that the analysis in [1] is valid only for sufficiently weak applied fields (specifically, ζ l / ) and zeta potential much smaller than the thermal voltage: ζ k T ze / B (k B , T, z and e denoting Boltzmann constant, absolute temperature, anion/cation valence and elementary charge, respectively), wherein the perturbations to salt concentration produced by surface current are negligible in comparison with the perturbations to the electric field [6]. However, it was noted that in such a small-ζ regime the deviations from the classical Smoluchowski behavior are also necessarily small [7].…”

Response to “Comment on ‘On the flow field about an electrophoretic particle’” [Phys. Fluids 25, 049102 (2013)]

“…(2-R) S.&Y. 2 observe that, according to (A26), 1 the salt perturbation would be O(λζ E) in the limitλ 1,ζ 1. Then, they notice an inconsistency in that the electric-field perturbation, of orderλζ 3 E, to the slip velocity would actually be comparable with (or perhaps smaller than) the perturbation produced by the salt gradient, which had been neglected.…”