Absence of bulk electroconvective instability in concentration polarization

The problem of bulk electroconvective stability of quiescent electric conduction from an electrolyte solution into a charge-selective solid (ion-exchange membrane) has been revised. It is shown through a numerical solution of the linear stability problem that previously reported bulk electroconvective instability does not exist. This numerical result is supported by the short wave asymptotic analysis. Our comprehensive study confirms the result of an earlier, less detailed, report by Buchanan and Saville.

Figure 1

Comparison between the numerical solution (continuous line) and the short-wave asymptotic one (dashed line) in the boundary layer for different wave number $k$: curve 1, $k=3$; curve 2, $k=5$; curve 3, $k=10$.

Figure 2

Dependence of $\det \left(A\right)$ on $k$ for three values of $I∕I^{\lim }=0.9$ (continuous line), 0.99 (dashed line), and 0.999 (dashed-dot line).

Figure 3

Dependence of the largest eigenvalue $\lambda$ on $k$ for different currents $I$: continuous line, $I∕I^{\lim }=0.8$; dashed line, $I∕I^{\lim }=0.9$; dash-dot line, $I∕I^{\lim }=0.95$.