Final Report Summary - COTRAPHEN (Coupled Ion- and Volume-Transfer Phenomena in Heterogeneous Systems: Modeling, Experiment and Applications in Clean Energy, Micro-Analysis and Water Treatment) In general terms, the CoTraPhen project has revealed clear benefits of a close interdisciplinary collaboration between mathematicians, physicists, chemists, chemical engineers and electrical engineers. The systems involved in this R&D effort are quite complex. Accordingly, the model formulation implies finding a delicate balance between the model rigorousness and feasibility. Elaboration of this kind of subtleties in the equations and boundary/initial conditions and planning of experiments requires extensive face-to-face interactions that cannot, yet, be effectively substituted by long-distance communication.Within the scope of WP 1, in view of the technological challenges presented by the conventional electrophoretic deposition with externally-applied high-voltage electric fields, we have additionally studied a novel process of current-less electrophoretic deposition. In both processes (current-driven and current-less) most important phenomena occur when the colloidal dispersion of nanoparticles becomes non-dilute and collective phenomena get very important. For the description of such systems we developed a modelling approach based on the combination of Irreversible Thermodynamic and Standard Electrokinetic Model. By making an appropriate choice of reference system, the developed theory can be applied to both fluid suspensions and stationary porous media, which is very useful for the description of electrophoretic deposition.By using this approach, we obtained expressions for a complete set of kinetic coefficients that provide full description of transport of all the system components (solid and liquid phases, ions) for arbitrary mixed electrolyte solution. The obtained results generalize the classical Smoluchowski theory for the cases where ion concentration gradients are either imposed externally or arise spontaneously.In a parallel experimental effort, Membrane-Electrode Assemblies for High-Temperature Polymer-Electrolyte Membrane Fuel Cells were fabricated via classical (current-driven) Electrophoretic Deposition. Stability measurements of the EPD MEAs with PTFE and Nafion ionomer in the Catalyst Layers showed that both MEAs reached stable current densities after ~48 hours of activation followed by negligible decrease in current densities over the duration of stability tests.Within the scope of WP 2, we have developed a “basic” model of over-limiting current transfer in Electrodialysis that uses only first-principles laws and does not contain any adjustable parameters. Mathematically, the model involves the fully coupled Nernst-Planck-Poisson - Navier-Stokes equations, which are solved numerically. The calculated current-voltage curve of an ED flow-through cell shows a linear region, a sloped plateau that surpasses the “limiting” current and a rapidly rising region characterized by increasing current oscillations.In parallel, we carried out more experimental work on the electrochemical behaviour of Ion-Exchange Membranes (IEMs) affected by water splitting. These studies have revealed that at least two methods of surface treatment are available to reduce the water splitting: 1. chemical treatment with a strong polyelectrolyte solution to transform the catalytically active fixed ion-exchange sites into groups with low catalytic activity; 2. homogenization of membrane surface, for example, via casting a homogeneous conducting film. In experiments, it was found that the water splitting rate was reduced by ca.2 times, and the over-limiting mass transfer rate was increased up to 3.5 times due to the electro-convection.The theoretical predictions by Dukhin and Mishchuk and Rubinstein and Zaltzman on the enhancement of electro-convection due to undulated membrane surfaces were confirmed by using numerical solution of fully coupled Nernst-Planck-Poisson-Navier-Stokes equations. For the first time, the increase in the over-limiting mass-transfer rate near undulated membrane surface was explored quantitatively. Also for the first time, a theoretical optimization of membrane surface heterogeneity has been carried out.It was demonstrated both experimentally and theoretically that pulsed-current mode is advantageous for electrodialysis and optimal (under-limiting) pulse frequency as well as duty cycle were identified. At over-limiting currents the optimal parameters were found to be different. The mass-transfer enhancement in pulsed over-limiting mode essentially depends on electro-convection. As an inertial process, it needs some time to develop, which explains the different time scale. Finally, it has been shown experimentally that over-limiting pulsed currents not only increase the mass transfer rate, but also mitigate membrane fouling.Within the scope of WP 3, it was shown theoretically that the occurrence of limiting currents at micro-/nano-interfaces critically depends on the ratio of nano-channel height (nano-pore size) and the Debye screening length. If this ratio is sufficiently large, the limiting-current phenomenon is suppressed due to the electroosmotic transfer of salt towards the polarized micro-/nano-interface. Therefore, not too narrow nano-channels behave like micro-channels in the limiting-current terms. It has been shown that some recent experimental findings on the concentration polarization of joined micro-/nano-fluidic systems can be explained by using this criterion.We have also considered theoretically the problem of dynamics of current-induced concentration polarization of interfaces between ideally perm-selective and non-ideally perm-selective ion-exchange media. In contrast to the previous studies, the analysis has been systematically carried out in terms of local thermodynamic equilibrium. The results were formulated in terms of phenomenological properties like ion transport numbers, diffusion permeability to salt and specific chemical capacity. An easy-to-solve numerically 1D PDE has also been formulated in the same terms.In the problem of coupled concentration-polarization and electrokinetic phenomena close to micro-nano-interfaces, a posteriori analysis has revealed that the primary cause of inapplicability of Taylor-Aris approach is the failure of approximation of slow processes. Accordingly, we developed a 2D model within the scope of approximation of local electric neutrality and binary electrolyte. This model has been used to show that in the stationary transport of non-electrolyte molecules in straight long channels under conditions of electroosmotic circulation in a major part of the channel there is a linear dependence of concentration on the coordinate with the exception of boundary layers close to the edges. Such linearity corresponds to the solute transfer with a constant dispersion coefficient, which is in agreement with the Taylor and Aris dispersion model.In the problem of transport of an electrolyte due to a stationary concentration difference in straight long channels under conditions of electroosmotic circulation the Taylor-Aris Dispersion (TAD) theory has been demonstrated to be approximately applicable locally within an inner part of the channel for a wide range of Péclet numbers and concentration differences. The breakdown of TAD theory occurs within relatively narrow boundary regions near the channel ends.The project findings are important for researchers and practitioners in the fields of environmental technology, clean energy and micro-analysis.Contact: Dr. Andriy Yaroshchuk, project coordinator, ICREA and Polytechnic University of Catalonia – BarcelonaTech, andriy.yaroshchuk@upc.edu
