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We characterize the dynamics of a z − z electrolyte embedded in a varying-section channel. In the linear response regime, by means of suitable approximations, we derive the Onsager matrix associated to externally enforced gradients in electrostatic potential, chemical potential, and pressure, for both dielectric and conducting channel walls. We show here that the linear transport coefficients are particularly sensitive to the geometry and the conductive properties of the channel walls when the Debye length is comparable to the channel width.In this regime, we found that one pair of off-diagonal Onsager matrix elements increases with the corrugation of the channel transport, in contrast to all other elements which are either unaffected by or decrease with increasing corrugation. Our results have a possible impact on the design of blue-energy devices as well as on the understanding of biological ion channels through membranes

We propose a model to show the formation of Liesegang rings under non-isothermal conditions. The model formulates reaction-diffusion equations for all components intervening in the process together with an evolution equation for the temperature. The reactive parts in these equations follow from the analysis of the non-equilibrium self-assembly (NESA) process undergone by the meso-particles which make up the patterns. The solution of these equations enables us to know the concentration of each component, the spherical structures diameter, and the system temperature as a function of time and radial position. The values found for the structures diameter and the rings position are in agreement with the experiments. The results for the system temperature with peaks at the rings positions suggest that heat accumulates at these positions as a consequence of the dissipation inherent to the NESA process. Our model enables us to rationalize how from non-homogeneous initial conditions a transient self-organization process involving formation of self-assembled structures may produce macroscopic patterns. It can, in general, be used to analyze pattern formation due to diffusion-reaction-precipitation processes with potential applications in the design of advanced materials.