Self-similar solution to the problem on electro-kinetic instability in semipermeable membranes / G. S. Ganchenko, E. A. Demekhin, V. S. Shelistov. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2014. № 5. P. 62-65 [Moscow Univ. Math. Bulletin. Vol. 69, N 5, 2014.].
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°, whereas, in the 3D case, it is equal to 76,78°. 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.