Chronopotentiometric Response of an Electrically Heterogeneous Permselective Surface: 3D Modeling of Transition Time and Experiment

Abstract

Understanding of the current density distribution over an electrically heterogeneous surface and its effect on ion transport represents an important issue in electrochemistry, composite materials, geophysics, and some other domains. We report an approach for three-dimensional (3D) modeling (with cylindrical symmetry) of transient ion transfer across a surface composed of conductive and nonconductive areas. In the model formulation and solution we use the electrical current stream function. It allows setting the integral boundary condition for electric current at a heterogeneous surface without any restrictions on the local current density distribution. A very good agreement is found between the numerical solution and the experimental transition time determined from chronopotentiograms. The use of a specially designed membrane allows computation without fitted parameters. We show that the application of specific simplifications for the current density distribution over the surface (uniform distribution throughout all the surface or its conductive area, neglect of tangential current density) results in essential deviations from experimental transition time.

Prospects of Membrane Science Development

“…A significant number of studies [166][167][168][169] show that a substantial gain in current density above the value i lim (overlimiting transport) can be achieved if the membrane surface has a certain electric and geometric nonuniformity. In this case, the tangential transport of ions [170], which initiates the electroosmotic slip of the solution on the membrane surface (electroconvective transport), is essential [166][167][168][169]. Surfaces that spontaneously induce the stirring of the solution in an applied external electric field are promising for overlimiting transport.…”

Modelling of Ion Transport in Electromembrane Systems: Impacts of Membrane Bulk and Surface Heterogeneity

“…However, this condition was not verified using another approach. The use of the electric current stream function [303] seems promising for the solution of this kind of problems, since this approach does not require any assumption about the character of current density distribution. Stream functions are widely used in fluid mechanics [304].…”

“…Later on, this approach was applied for simulation of electric current density distribution in semiconductors [307], in superconductors [308], in thin circuits [309], on the earth's surface [310], in electromagnetic devices [311] and other systems. In membrane systems, this method was applied by Pismensky et al [312] and Mareev et al [303]. 3D modelling in Ref.…”

“…3D modelling in Ref. [303] was used for describing the chronopotentiograms of a heterogeneous IEM; the results of computations were compared with experiment and with other known theories, namely, that by Sand [284], Choi and Moon [291] and Rubinstein et al [274].…”

“…The geometry used in Ref. [303] is shown in Figure 15. A hexagonal distribution of conductive areas (the open circles in Figure 15) over the membrane surface is assumed.…”