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hydrodynamics and mass transport, also affect other aspects that may be critical, such as the Ohmic voltage drop. Finally, pressure drop in the manifolds, voltage losses caused by a non-uniform flow distribution among and in the channels, internal leakages due to pressure gradients across the membrane are additional phenomena depending on the stack hydrodynamics. Clearly, the optimization of ED (or EDR, or other electromembrane processes) units is based on a very delicate equilibrium among the stack features (including the membranes properties) and the operating conditions. The following sections will examine in detail the fundamentals of hydrodynamics and mass transport in ED and the way these affect the operation of ED and related processes, together with more recent strategies for the improvement of hydrodynamics performances and novel experimental techniques for their characterisation. 4.1 Concentration polarization phenomena In membrane separation processes, concentration polarization is a well-known phenomenon which manifests itself as a concentration gradient within the solution and perpendicular to the membrane surface. In the case of IEMs-based processes, the electrical current is carried roughly in the same amount by cations and anions migrating through the solution in opposite directions. On the contrary, inside the membrane current is carried mainly by counter-ions, while co-ions are (ideally) excluded. As a consequence, at the solution-membrane interface the migrative flux of co-ions (typically directed from the interface to the bulk of the solution) has to be counterbalanced by a diffusive flux in the opposite direction, intrinsically accompanied by a concentration gradient able to generate such diffusive flux according to Fick’s law [10, 168–170]. Concentration polarization and transport phenomena near interfaces have commonly been analysed by the Nernst film model [171, 172]. The basic assumption of this theory is the existence of a “Nernst diffusion layer” between the membrane-solution interface and the fluid bulk with uniform composition. This is also known as “diffusion boundary layer” (DBL) and can be considered as a thin stagnant layer where no convection occurs and mass transfer is controlled by diffusion-migration, resulting in a linear concentration profile (Figure 6 (a)). The Nernstian idealization was improved by Levich [172], showing that the presence of convective transport within the DBL results in a smooth monotone concentration profile asymptotically approaching the bulk concentration. Mass transport in IEMs and electrolyte solutions has been widely studied by the theoretical description given by the Nernst–Planck formalism [62, 171], which can also lead to a more rigorous 23PDF Image | Electrodialysis for water desalination
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