Mathematical modeling of two-dimensional unsteady-state mass transfer of ions in desalination chamber of chemical photosynthetic desalination cells

Abstract

In this study, we have developed a two-dimensional (2D), time-dependent mathematical model focusing on the desalination chamber (DC) of CPDCs. The model simulates ion transport mechanisms, including diffusion and migration, under laminar flow with recirculation between the DC and a well-mixed recirculation tank (RT). Governing equations for mass transfer were solved numerically in MATLAB, and the model was validated against lab-scale experimental data, demonstrating good agreement. The model enables detailed analysis of ion concentration profiles and salinity reduction within the DC, offering predictive insights into system optimization and scale-up. Key operational parameters, such as brackish water flow rate, cell height, intermembrane spacing, and electric potential difference (EPD), were systematically investigated through sensitivity analysis. The results highlight the nonlinear effects of design and operating conditions on desalination efficiency and help define optimal ranges for system configuration. Furthermore, by calculating ion-specific mass transfer coefficient, Sherwood–Reynolds (Sh–Re) correlations were derived for Na⁺ and Cl⁻. These correlations serve as engineering tools for scaling up CPDC modules and optimizing design without full-scale experimentation. In overall, this modeling framework serves as a foundation for future expansion to multi-chamber, fully coupled models that can capture bioelectrochemical dynamics and power generation, ultimately enabling integrated and scalable design of next-generation CPDC systems. © 2025 Elsevier Ltd.