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Other geometries can be obtained by corrugating IEMs. Mass transfer in an electrochemical cell with corrugated electrodes (mimicking membranes) was analysed by measurements of ilim [293, 294], obtaining correlations for the Sherwood number. The use of actual corrugated membranes in ED was tested for the extraction of nickel and cobalt from their sulphate solutions [295], showing a significant increment of active area (60%) and a significant improvement of the current efficiency with respect to the use of flat membranes. The possibility of improving mass transfer by profiled membranes is reported also by Nikonenko et al. [192], who carried out measurements in overlimiting conditions. Also Larchet et al. [50] tested profiled membranes in overlimiting regimes, obtaining higher Sherwood numbers with respect to flat membranes and non-conducting spacers, along with high desalination rates in a large range of concentrations. In the last years, many research efforts have been devoted to the development and characterization of profiled membranes for reverse electrodialysis (see Section 6.6). In comparison with net spacers between flat membranes, simple profiled membranes created by either ridges or pillar profiles reduce pressure drop and Ohmic resistance, but, at least at the very low Re numbers typical of RED, are less effective in mass transfer [4, 259–261, 296]. Improved profile geometries, more similar to spacer filaments, lead to better trade-off between low pressure drops and good mixing, thus improving the stack performance [6, 292, 297]. Multi-physical modelling tools have been developed in order to investigate the potentials of profiled membranes by simulating simplified two-dimensional geometries for ED [187] and reverse electrodialysis [298] applications. Nowadays, profiled membranes represent a very attracting frontier for the development of ED systems and deserve further studies especially for process optimization perspectives. 4.4.3 Flow regimes in ED channels ED systems have been usually operated at a fluid velocity of ~2 to ~10 cm/s [10, 41, 46, 47, 49, 50], with higher values, even up to ~50 cm/s, in tortuous path configurations [10, 44, 45, 49]. Taking into account the typical channel thicknesses, the corresponding Reynolds number (calculated here by assuming as the equivalent diameter twice the channel thickness) ranges roughly from ~20 to ~400, with values up to ~2000 for tortuous paths (see also the Reynolds numbers reported in [39, 138, 185, 195, 199, 279]). In fact, tortuous path configurations are characterized by higher concentration polarization and lower pressure drop per unit length with respect to sheet flow channels with net 41PDF Image | Electrodialysis for water desalination
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