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Figure 19. Unit cell for CFD simulations solving the convection-diffusion equation: (a) overlapped and (b) woven spacer [281], (c) square and (d) circular pillar profiled membrane [296], (e) chevron profiled membrane [297], (f) overlapped crossed filaments profiled membrane [6]. Moreover, CFD simulations of narrow channels have general validity for various membrane processes, as reverse osmosis, nanofiltration and others [198, 200, 230, 266, 271–274]; through the heat/mass analogy, the same applies even for simulations of temperature driven processes [269, 275]. Therefore, mass transfer correlations for a large number of channel geometries are available in the literature and are suitable for assessing the effects of concentration polarization in ED modules. For example, CFD results have been used for the calculation of the DBL effects in [6, 141, 297]; in addition, CFD results concerning pressure drops can be used in order to calculate the pumping power consumption, as will be discussed in the next section. Other models have used experimental data on mass transfer [174, 199, 254]. Among the non-Ohmic effects of the DBL, often only the concentration overpotential is taken into account [6, 141, 254, 297], but in other cases also the diffusion potential is considered [174, 199]. In regard to the mathematical expression for ionic fluxes through the IEMs, a more rigorous (but also more complex) description can be provided by the phenomenological approach of Irreversible Thermodynamics (IT) and its derivations such as the Kedem-Katchalsky equations [354–356]. This 61PDF Image | Electrodialysis for water desalination
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