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Electrodialysis for water desalination

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Electrodialysis for water desalination ( electrodialysis-water-desalination )

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approaches to determine the values of Sherwood number and link it to the main process variables, thus providing a more complex tool for characterising these phenomena (Section 5.2.3). In several models, the Ohmic resistance of compartments has been calculated based on the solutions’ bulk concentration [6, 141, 174, 254]. Therefore, the Ohmic cell pair resistance can be expressed as 𝑟􏰖􏰲􏰔 = 𝑟􏰶􏰾􏰿 + 𝑟􏱀􏰾􏰿 +𝑟􏰶 + 𝑟􏰏 (29) where 𝑟􏰶􏰾􏰿 and 𝑟􏱀􏰾􏰿 are the resistances of the IEMs, while 𝑟􏰶 and 𝑟􏰏 are the resistances of concentrate and dilute compartments, respectively, which can easily be evaluated as [226] 𝑟=𝐹 h􏰶 (30) 􏰶 􏰕 𝜆􏰶 𝐶􏰶 𝑟 =𝐹 h􏰏 (31) 􏰏 􏰕 𝜆􏰏 𝐶􏰏 where 𝐹􏰕 is a factor accounting for the shadow effect due to spacer filaments or membrane profiles (see below), h is the compartment thickness, 𝜆 is the equivalent conductivity, C is the bulk concentration of electrolyte. Membrane resistance represents the most difficult term to estimate. Fidaleo et al. [199] derived the membrane resistance and the effective membrane area from measurements on a stack built with only CEMs or AEMs. Often, a constant value is used for the membrane resistance [174, 254, 297]. However, it has been widely shown that the resistance is strongly affected by the solution concentration, steeply increasing as the solution concentration decreases [75, 142]. Therefore, some models take into account the effect of solutions concentration [6, 141, 247]. Since it is difficult to estimate the actual behaviour of an IEM inside an operating stack, a theoretical approach could represent an effective solution. In this context, Berezina et al. [60] proposed a theoretical method for the estimation of conductivity based on the structure of the IEM itself. In particular, membrane conductivity was correlated to the conductivity of individual phases, the volume fraction of each phase and a correction factor accounting for the arrangement of phases inside the material. However, there is still no common approach in experimental methods for membrane resistance measurement and models interpreting the membrane behaviour [76]. The presence of non-conducting net spacers causes an increase of channel Ohmic resistance, referred to as “shadow effect”. This aspect has been taken into account in several models by a correction factor defined in different ways, e.g. as the reciprocal of the spacer open area [141], or as the reciprocal of the square of the channel porosity [254]. Pawlowski et al. [297] used the reciprocal of the channel porosity but took into account also the increment of the membrane resistance due to the coverage effect of spacers. Clearly, the real effect of spacers depends on their actual geometry. Therefore, more 57

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