PMID: 22587178May 17, 2012Paper

Numerical study on the bulk instability of constant-current conduction in cation-exchange membranes

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Y K Suh

Abstract

Numerical simulation of two-dimensional bulk instability of the one-dimensional conduction state in an electrolyte confined between a pair of cation-exchange membranes subjected to an external voltage is conducted under an assumption of constant current. By employing variable grids, we resolve the problem of sensitive dependence of the numerical solutions to the grid refinement in particular at a current close to the limiting value. In fact, the full range of parameters, i.e., Schmidt number, Peclet number, diffusivity ratio, and current, is considered in this study in obtaining the stability chart. It turns out that the Schmidt number exerts almost no influence on the results. From the neutral curves in the chart of the parameter space (current versus diffusivity ratio, i.e., cation diffusivity divided by anion diffusivity) we confirm that the system tends to be unstable at high Peclet numbers, high currents, and low diffusivity ratios. As the diffusivity ratio is increased the instability mode switches from the monotonic to the oscillatory type, and the critical diffusivity ratio for the switching is found to be decreased as the Peclet number decreases. At the switching, no jump in the neutral curves is found, contrary to the...Continue Reading

References

Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·I Rubinstein, B Zaltzman
Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Irina LermanBoris Zaltzman
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Isaak RubinsteinIrina Lerman
Feb 21, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tamara PundikBoris Zaltzman
Nov 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Brian D StoreyIsaak Rubinstein
Dec 31, 2008·Physical Review Letters·S M RubinsteinM Wessling
Jul 30, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P M BiesheuvelMartin Z Bazant

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Citations

Dec 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·H-C ChangV S Shelistov

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