Analytical Relation between Temperature Polarization Intensity and Effective Ratio of Mass Transfer Coefficient in Membrane Distillation

Abstract

Temperature polarization is a fundamental phenomenon that limits the efficiency of membrane distillation by reducing the effective temperature difference across the membrane. This study establishes a mathematical formulation that connects temperature polarization intensity with the effective ratio of mass transfer coefficient under practical operating conditions. By analyzing typical membrane distillation scenarios, we derive a theoretical framework that quantitatively relates near-membrane temperature polarization factors to the effective ratio of the mass transfer coefficient. Through dimensional analysis and empirical fitting, a functional correlation is proposed and validated using experimental data obtained from precisely controlled temperature measurements in the boundary layer adjacent to the membrane surface. The results demonstrate that the effective ratio is closely dependent on the intensity of hot-side temperature polarization, with an empirical relationship proposed to describe this correlation. This work provides a direct mathematical interpretation of how thermal boundary layer behavior affects transmembrane mass transfer. It provides a physically meaningful and practical tool to evaluating process performance.