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Figure 18. Schematic representation of the transport phenomena involved along the channels and through the membranes of an ED cell pair. Most semi-empirical models are based on the segmentation modelling approach (see Section 4.3), which, in turn, can be supported either by experiments or by simulations providing Sherwood numbers (Section 5.2.1). Phenomenological expressions of the mass fluxes can thus be written and can be linked to the mass balance equations for the simulation of the whole cell pair length (Section 5.2.2). In particular, when fluid dynamics and mass transfer are simulated at small scale (channel repetitive unit, or unit cell) and the results are transferred to the higher scale at which mass balances and fluxes across the membranes apply (channel-scale, or meso-scale), a multi-scale model is obtained. This represents an integrated simulation tool, built on a hierarchical structure of scales, which can effectively address the full simulation problem [201]. 5.2.1 Voltage drop over the cell pair by the segmentation modelling approach As illustrated in Section 4.3, the total voltage drop over a multi-layer system of solutions and membranes can be assessed as the sum of the various contributions provided by elements in series. For a cell pair, eq. (15) can be rewritten in a more compact form as ∆𝑉 = 𝜂 + 𝑟𝐼 (28) where 𝜂 is the overall non-Ohmic voltage drop occurring in DBLs and IEMs (eqs. (19)-(20)), 𝐼 is the electrical current and 𝑅 is the overall Ohmic resistance. The non-Ohmic term becomes more important when the activity gradient increases, thus generally representing the main contribution on potential drop at the stack outlet when drinking water is obtained. Moreover, the effect of mass transport from bulk to interface, also contributing to the non- Ohmic losses, can be described at different scales of complexity. The simplest approaches adopt the definition of limiting current density, often experimentally determined and empirically correlated to the process conditions. On the other side, several studies have adopted CFD-based or experimental 56PDF Image | Electrodialysis for water desalination
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