## 7 Conclusions  
In conclusion, we once again emphasize that the heterogeneity of both membrane bulk and surface plays an important role in conditioning membrane properties and enhancing their performance in electroseparation and energy production applications. The recent research shows that design of the membrane bulk affects such membrane properties as conductivity, diffusion permeability and permselectivity (mainly as related to the selective transport of ions of a certain sign of charge). An important example is the immobilization of inorganic nanoparticles in the membrane bulk, which increases membrane conductivity and permselectivity, especially at low relative humidity. Modification of membrane surface exerts a strong impact on the properties related to mass exchange between the  
Figure 18: Dependence of the \(\tau/\tau_{Sand}\) ratio on the \(i/i_{\text{lim}}\) ratio for the M1 (the conductive surface area fraction \(\gamma=0.077\), red circles) and M2 (\(\gamma=0.318\), triangles) membranes (both are lab-made on the basis of track-etched membranes) (**a**) and for a anion-exchange heterogeneous MA-41 membrane (\(\gamma=0.2\)) (**b**). The horizontal dashed line shows the \(\tau_{Sand}\) value. The solid curves present the results of calculation of \(\tau\) using the 3D model [303]: curve 1 relates to a hypothetical homogeneous membrane, curves 2 and 3, to the M1 and M2 heterogeneous membranes, respectively. Reproduced with permission from [314], Elsevier, 2018.  
solution and membrane surface. The use of membranes with tailored surface heterogeneity allows a significant increase of the limiting current density and overlimiting ion transport rate. It possible to talk about the formation of surfaces, self-inducing the mixing of the adjacent solution. Mathematical modelling brings a new insight into complicated transport phenomena occurring in heterogeneous systems. This deeper understanding may be very useful for the development of high-performance membranes and membrane devices. In particular, the modelling suggests that the very important factors affecting the intensity of electroconvection mixing are the size and surface fraction of the conductive/non-conductive surface regions. Numerical computations can give optimum values of these parameters. However, there is no good accordance between the computations made in different laboratories. Besides, the role of charge density and degree of hydrophilicity of surface is not yet well understood, while these parameters are also important. Although there is a strong progress in understanding of the response of membrane performance on certain modifications of their bulk and surface, some important knowledge gaps remain. Most experiments and theoretical calculations are made for NaCl solutions and in conditions proper for laboratory tests. There are no studies on the effects of these modifications on the performance of real ED, no estimations of how these effects depend on solution concentration and forced flow velocity, what is the influence of the cell geometry, intermembrane distance, geometric shape of surface patterns, the presence of intermembrane spacers. Even more questions remain as to the effect of modification on the membrane antifouling behaviour. The understanding of the relationships between the surface properties and antifouling resistance is rather poor. No mathematical modelling of these effects is available. The problem here is complicated by complexity of coupling between mass transport and chemical reactions, especially when the rate of these reactions is quite low. A similar situation occurs with respect to the relationship between membrane properties and the characteristics of competing transfer of ions having the same charge sign but different valence. However, given the importance of these problems for the sustainable development of society, we can expect rapid progress in this area. Writing--original draft preparation, S.M. ; computations, A.N., A.K. and M.U. ; writing--review and editing, V.N. and G.P. ; funding acquisition, V.N.