| Abstract: |
| Filtration systems play a fundamental role in a wide range of industrial and biomedical applications, where fluid transport through porous media is predominantly driven by pressure gradients. This study presents an analytical investigation of three-dimensional filtration flow under both linear and oscillatory pressure conditions, with the aim of advancing the theoretical understanding of such systems. The governing continuity and Navier-Stokes equations, describing momentum and pressure variations, are solved using Lie symmetry analysis to obtain closed-form expressions for the velocity and pressure fields within the filter chamber. These analytical solutions are subsequently utilised to examine the behaviour of momentum and pressure distributions throughout the system. The results demonstrate that linear pressure gradients generate stable and predictable flow patterns, while oscillatory pressure gradients mitigate clogging effects and enhance filtration efficiency. Overall, the findings provide valuable theoretical insights for optimising outflow and improving the performance of filtration systems. |
|