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Self-similar solution to the problem of electrokinetic instability in semipermeable membranes

V. S. Shelistov, E. A. Demekhin, G. S. Ganchenko

Kuban State University, Krasnodar

Abstract: Numerical solution of the Nernst–Planck–Poisson–Stokes system near a charge-selective surface shows the creation of coherent structures which have a form of spikes. In these structures liquid is pumped out of a space charge region into an electroneutral region from these spikes. In this work the analytic self-similar solution of the full system is found in a vicinity of the spike tip. In the 2D case, the opening angle of the spikes is equal to $110{,}23^{\circ}$, whereas, in the 3D case, it is equal to $76{,}78^{\circ}$. The values of the opening angles are in good agreement with the numerical results.

Key words: Nernst–Plank–Poisson–Stokes system, electrokinetic instability, self-similar solution, space charge equation, coherent structures, charge-selective surface, electrolyte.

UDC: 511

Received: 03.12.2012

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2014, 69:5, 119–122

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