Counter-current flow in channels separated by a membrane has been studied by several scientists and researchers. The current study aims to analytically simulate and describe the distribution of pressure, volumetric flow rate, and velocity in square channels separated by a membrane. Consequently, the study was conducted using one-dimensional (1D) analytical solutions to achieve several objectives: avoiding the execution of experimental tests, reducing the effort required for expensive and time-consuming module design, and enabling easy observation of variations in pressure, volumetric flow rate, and velocity. The 1D analytical solution directly simulates flow in square channels separated by a membrane by solving the continuity equation and Darcy’s law, through which pressure, volumetric flow rate, and velocity are calculated. Experimental results were used to validate the 1D analytical solutions. The results of the current study indicate that pressure decreases from the inlet to the outlet of the channel, while the horizontal velocity decreases from the inlet to the midpoint of the channel length and then increases toward the outlet. The 1D analytical solutions show acceptable accuracy when compared with experimental results. Consequently, these solutions can be used to explore and illustrate the distributions of pressure, volumetric flow rate, and velocity in square channels separated by a membrane, enabling the evaluation of hemodialysis prototype module performance and efficiency prior to fabrication.
Abdullah et al. (2026) studied this question.