## 6 Effect of Surface Heterogeneity on the Transient Behaviour of IEMs
### Phenomenon of Two Transition Times of Chronopotentiograms for Membranes with Heterogeneous Surface  
When an electric current is applied to an IEM with electrically heterogeneous surface, the current lines are concentrated within the conductive regions. With the passage of time, the electrolyte concentration decreases first near the conductive surface regions, then the concentration changes propagate to the solution domains near the non-conducting regions (Figure 17). Tangential diffusion, which enhances the delivery of electrolyte to the surface of conductive regions occurs in this system. The contribution of tangential diffusion is detected by appearance of two transition times in chronopotentiometry, as it was observed by [PERSON] et al. [314]. The first transition time, \(\tau_{1}\), is attained, when the electrolyte concentration at the conductive regions of the surface becomes sufficiently low to give rise current-induced convection developed locally at the boundaries between the conductive and non-conductive regions. The second transition time, \(\tau_{2}\), is reached when a critically small concentration is attained at the whole membrane surface, including the conductive and non-conductive regions [314]. As the 3D model [303] predicts, when there is no current-induced convection, the electrolyte concentration remains rather elevated at the non-conductive regions, while it reaches very small values at the conductive regions (Figure 17). According to this model, only one transition time \(\tau_{1}<\tau_{Sand}\) can occur in a heterogeneous membrane  
Figure 17: Distribution of electrolyte concentration in the DBL at a heterogeneous membrane surface, calculated using the 3D model [303] at \(i=1.25\text{i}_{\text{lim}}\) in moments of time 0.2, 0.8, 1.4 \(\dots\) 5.6 s. The parameters used in simulation relate to a membrane with randomly distributed conductive areas with the radius of 12.95 \(\upmu\)m, the fraction of the conductive surface area \(\gamma=0.077\), the DBL thickness \(\delta=260\)\(\upmu\)m. The centre of the conductive area refers to \(r=0\), the boundary between the conductive and non-conductive regions is shown with the dashed line. Reproduced with permission from [314], Elsevier, 2018.  
system if the ions in the depleted DBL are transferred by electrodiffusion solely. The decrease of concentration near the non-conductive regions may be caused by the current-induced convection, apparently electroconvection occurring as electroosmosis of the first kind [314]. Electroconvection enhances the exchange between the solution domains, which are located near the conductive and non-conductive surface regions. The onset of this enhancement (occurring at \(t=\tau_{1}<\tau_{Sand}\)) reduces the rate of the PD growth, which gives the first inflection point on the chronopotentiogram. The appearance of larger electroconvective vortices, when the concentration reaches a critically small value on the entire membrane surface (\(t=\tau_{2}\approx\tau_{Sand}\)), gives the second inflection point. \(\tau_{2}\) is close to \(\tau_{Sand}\), since the latter event occurs also at homogeneous membrane surface. However, electroconvection occurring when the near-surface concentration is small everywhere can enhance mass transfer and slows down the rate of concentration decrease resulting in increasing \(\tau_{2}\) higher than \(\tau_{Sand}\). This case is shown in Figure 18 for the M1 and M2 membranes. The experimental values of \(\tau_{2}\) are essentially higher than the results of calculations for these membranes using the 3D model [303], which takes into account the electrical heterogeneity of the surface but not account for electroconvection. Note that the increase in the values of \(\tau_{2}\) with decreasing the \(i/i_{\text{lim}}\) ratio is due to the effect of the finite length of DBL described in Section 6.1. The behaviour of the MA-41 membrane is similar: at \(i/i_{\text{lim}}\leq 1.25\), there are two transition times.