Geodesic
Self-similar solution to the problem of electrokinetic instability in semipermeable membranes
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2014), pp. 62-65

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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. 
@article{VMUMM_2014_5_a11,
     author = {V. S. Shelistov and E. A. Demekhin and G. S. Ganchenko},
     title = {Self-similar solution to the problem of electrokinetic instability in semipermeable membranes},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {62--65},
     publisher = {mathdoc},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2014_5_a11/}
}
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V. S. Shelistov; E. A. Demekhin; G. S. Ganchenko. Self-similar solution to the problem of electrokinetic instability in semipermeable membranes. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2014), pp. 62-65. http://geodesic.mathdoc.fr/item/VMUMM_2014_5_a11/