Abstract
An analytic solution of counter-ion diffusion in a semi-infinite domain near a uniformly charged surface is obtained within the Smoluchowski-Poisson-Boltzmann treatment. The long-ranged Coulombic interaction results in a finite first-passage time to the charged surface, although higher moments of the first-passage time are infinite. This problem is directly related to an exactly solvable model of a lattice random walk with a position-dependent bias.
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Chan, D.Y.C., Hughes, B.D. Ion diffusion in a Coulombic field. J Stat Phys 52, 383–394 (1988). https://doi.org/10.1007/BF01016421
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DOI: https://doi.org/10.1007/BF01016421