Fig. 7: Effect of polarization phenomena on productivity.
Considered feed stream: a, b 4 M LiCl-based aqueous solution; c, d 154 mM NaCl-based aqueous solution. In detail, panels (a) and (c) quantify the relative water vapor flux loss due to polarization defined as \(\frac{{J}_{{{{\rm{w}}}},{{{\rm{ideal}}}}}-{J}_{{{{\rm{w}}}}}}{{J}_{{{{\rm{w}}}},{{{\rm{ideal}}}}}}\), where Jw,ideal was obtained imposing θT and θs equal to 1. Panels (b) and (d) quantify, through the parameter − 1 ≤ R ≤ 1, the partial linearized contribution of temperature (i.e., θs equal to 1) and concentration (i.e., θT equal to 1) polarization phenomena to the full polarization loss. This parameter is defined as \(R=\frac{\left({J}_{{\theta }_{T} = 1}-{J}_{{{{\rm{w}}}}}\right)-\left({J}_{{\theta }_{{{{\rm{s}}}}} = 1}-{J}_{{{{\rm{w}}}}}\right)}{\left({J}_{{{{\rm{w}}}},{{{\rm{ideal}}}}}-{J}_{{{{\rm{w}}}}}\right)}\). The results were obtained by considering a CaCl2 aqueous solution as draw at bulk temperature of 20 °C. The membrane characteristics used for the calculations were those of the PTFE membrane deployed in the experiments. See Supplementary Note 1 for detailed trends of the polarization coefficients, the temperature difference across the hydrophobic membrane (ΔTm), and the ideal (Jw,ideal) and effective (Jw) yields, in the two considered case studies.
