Evgeny A. Demekhin (Kuban State University, Russian Federation)
24 octobre 2014
Study of the space charge in the electric double layer near ion-selective surfaces is a fundamental problem of modern physics first addressed by Helmholtz. Experiments show that volt-current (VC)-characteristic for a ion-selective surface has 3 distinguishable regions : I – for a small voltage it obeys a linear Ohmic relation (under-limiting currents) ; II – saturation region with a limiting plateau (limiting currents) ; III – region with further increasing of current (over-limiting currents). Deviation from the Ohmic law was explained by Rubinsten and Shtilman (1979). It was theoretically predicted by Rubinstein and Zaltzman (2000), that a physical mechanism responsible for the arising of the over-limiting currents is electro-convective instability. In our work electro-convective instability and nonlinear evolution to the over- limiting regimes are considered from the view-point of hydrodynamic stability and bifurcation theory. Direct numerical simulation of the full Nernst-Planck-Poisson- Stokes system is fulfilled. Galerkin pseudo-spectral method is applied. Periodic domain along the membrane surface allows us to utilize Fourier series in this direction. Chebyshev polynomials are applied in the transverse direction. Accumulation of zeros of these polynomials near the walls allows us to properly resolve in thin space charge region. Two types of initial conditions are superimposed on the initial equilibrium : a) ”forced”, sinusoidal of finite amplitude, with some wave number n ; b) ”natural”, small amplitude random noise. The main stages of evolution are clarified. Numerically found VC – characteristics quantitatively coincide with experimental ones.
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