Danyal Rehman

Species transport models typically combine partial differential equations (PDEs) with relations from hindered transport theory to quantify electromigrative, convective, and diffusive transport through complex nanoporous systems; however, these formulations are frequently substantial simplifications of the governing dynamics, leading to the poor generalization performance of PDE-based models. Given the growing interest in deep learning methods for the physical sciences, we develop a machine learning-based approach to characterize ion transport across nanoporous membranes. Our proposed framework centers around attention-enhanced neural differential equations that incorporate electroneutrality-based inductive biases to improve generalization performance relative to conventional PDE-based methods. In addition, we study the role of the attention mechanism in illuminating physically-meaningful ion-pairing relationships across diverse mixture compositions. Further, we investigate the importance of pre-training on simulated data from PDE-based models, as well as the performance benefits from hard vs. soft inductive biases. Our results indicate that physics-informed deep learning solutions can outperform their classical PDE-based counterparts and provide promising avenues for modelling complex transport phenomena across diverse applications.

Membranes offer a scalable and cost-effective approach to ion separations for lithium recovery. In the case of salt-lake brines, however, the high feed salinity and low pH of the post-treated feed have an uncertain impact on nanofiltration's selectivity. Here, we adopt experimental and computational approaches to analyze the effect of pH and feed salinity and elucidate key selectivity mechanisms. Our data set comprises over 750 original ion rejection measurements, spanning five salinities and two pH levels, collected using brine solutions that model three salt-lake compositions. Our results demonstrate that the Li⁺/Mg²⁺ selectivity of polyamide membranes can be enhanced by 13 times with acid-pretreated feed solutions. This selectivity enhancement is attributed to the amplified Donnan potential from the ionization of carboxyl and amino moieties under low solution pH. As feed salinities increase from 10 to 250 g L^-1, the Li⁺/Mg²⁺ selectivity decreases by ∼43%, a consequence of weakening exclusion mechanisms. Further, our analysis accentuates the importance of measuring separation factors using representative solution compositions to replicate the ion-transport behaviors with salt-lake brine. Consequently, our results reveal that predictions of ion rejection and Li⁺/Mg²⁺ separation factors can be improved by up to 80% when feed solutions with the appropriate Cl^-/SO₄^2- molar ratios are used.

Selective capacitive deionization (SCDI) is a promising desalination process for preferentially removing specific ions from waters with complex compositions. Its selectivity towards certain species can be achieved through novel electrode materials with high affinities towards targeted ions. In this work, we studied the selective removal of fluoride ions from groundwater containing concentrated co-existing chloride ions. A carbon nanotube-CeO2 (CNT-CeO2) electrode was employed for electro-sorption of fluoride ions. When processing a F−/Cl− mixed solution containing 10 mg/L F− and 100 mg/L Cl−, the CNT-CeO2 electrode reduced the concentration of F− ions to 1.5 mg/L in 150 min, amounting to a 85% F− removal efficiency, while Cl− removal was below 2%. This corresponds to a separation factor of 4.16, which is 40x higher than that of conventional AC electrodes. The high affinity of CNT-CeO2 to fluoride could be attributed to the entrance of fluoride ions into the crystal lattice of the CeO2 and the subsequent substitution for lattice oxygen atoms. The addition of CNTs offers substantial improvements in conductivity of the electrode and restricts the aggregation of CeO2, accelerating ion diffusion and selective adsorption. In addition, a selective CDI adsorption-desorption transport model was developed to describe the defluoridation process.

Nanofiltration (NF) with high water flux and precise separation performance with high Li⁺/Mg²⁺ selectivity is ideal for lithium brine recovery. However, conventional polyamide-based commercial NF membranes are ineffective in lithium recovery processes due to their undesired Li⁺/Mg²⁺ selectivity. In addition, they are constrained by the water permeance selectivity trade-off, which means that a highly permeable membrane often has lower selectivity. In this study, we developed a novel nonpolyamide NF membrane based on metal-coordinated structure, which exhibits simultaneously improved water permeance and Li⁺/Mg²⁺ selectivity. Specifically, the optimized Cu–m-phenylenediamine (MPD) membrane demonstrated a high water permeance of 16.2 ± 2.7 LMH/bar and a high Li⁺/Mg²⁺ selectivity of 8.0 ± 1.0, which surpassed the trade-off of permeance selectivity. Meanwhile, the existence of copper in the Cu–MPD membrane further enhanced anti-biofouling property and the metal-coordinated nanofiltration membrane possesses a pH-responsive property. Finally, a transport model based on the Nernst–Planck equations has been developed to fit the water flux and rejection of uncharged solutes to the experiments conducted. The model had a deviation below 2% for all experiments performed and suggested an average pore radius of 1.25 nm with a porosity of 21% for the Cu–MPD membrane. Overall, our study provides an exciting approach for fabricating a nonpolyamide high-performance nanofiltration membrane in the context of lithium recovery.

The widely used van ’t Hoff linear relation for predicting the osmotic pressure of NaCl solutions may result in errors in the evaluation of key system parameters, which depend on osmotic pressure, in pressure-retarded osmosis and forward osmosis. In this paper, the linear van ’t Hoff approach is compared to the solutions using OLI Stream Analyzer, which gives the real osmotic pressure values. Various dilutions of NaCl solutions, including the lower solute concentrations typical of river water, are considered. Our results indicate that the disparity in the predicted osmotic pressure of the two considered methods can reach 30%, depending on the solute concentration, while that in the predicted power density can exceed over 50%. New experimental results are obtained for NanoH2O and Porifera membranes, and theoretical equations are also developed. Results show that discrepancies arise when using the van ’t Hoff equation, compared to the OLI method. At higher NaCl concentrations (C > 1.5 M), the deviation between the linear approach and the real values increases gradually, likely indicative of a larger error in van ’t Hoff predictions. The difference in structural parameter values predicted by the two evaluation methods is also significant; it can exceed the typical 50–70% range, depending on the operating conditions. We find that the external mass transfer coefficients should be considered in the evaluation of the structural parameter in order to avoid overestimating its value. Consequently, measured water flux and predicted structural parameter values from our own and literature measurements are recalculated with the OLI software to account for external mass transfer coefficients.