Schematic of the problem in a particle-fixed frame. The boundary conditions apply at the effective boundary (dashed circle), essentially the outer-edge of the electrical double-layer.
Decomposition of the fluid domain into two asymptotic regions: an inner near-particle region where salt diffusion dominates advection, and an outer far-field region where the two mechanisms are comparable.
The nonlinear electrophoretic speed , as given by (5.9) , plotted as a function of Du = Bi(1 + 2α−) for α = 0 (thin) and α = 0.3 (thick), with . Each α-value is illustrated by three curves, corresponding to ζ0 = 4, 6, and 8. For comparison, expression (7.1) suggested by Shilov et al., 29 in which is interpreted as Du, is also shown (dashed curve). It is evident from the inset that an approximate agreement is realized only when advection is disregarded (α = 0) and Du is exceedingly small.
The dependence of on the counter-ion drag coefficient α− for Bi = 0.5 and ζ0 = 6. The three curves correspond to α+ = α, α+ = 2α−, and α+ = α−/2. The value , corresponding to the absence of convection, is indicated by the horizontal dashed line.
Comparison of the weakly nonlinear theory with numerical simulations for Du = 0.5, , ζ0 = 6, and the indicated α values. The dashed lines depict the analytically calculated velocity correction . The symbols represent its numerical equivalent, namely the difference between the computed velocity and the linear approximation .
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