Impact of viscosity on creeping viscous fluid flow through a permeable slit: a study for the artificial kidneys

The idea of this study is to present the mathematical model of two-dimensional biofluid flow having variable viscosity along the height of the channel (proximal renal tube of artificial kidney). This research describes that flow resistance is dependent on the height of the channel (proximal renal tube of artificial kidney) which makes the high flow near the centre and slow near the wall. The goal of this research is to provide the formulas to find the flow speed, average pressure, outflow flux and filtration rate of the viscous fluid having variable viscosity. The complex mathematical problem is solved by the Inverse method and results for axial velocity are plotted at the opening, central and departure region of the conduit. The numerical values for constant reabsorption and mean pressure are calculated against the filtration rate for the constant and variable viscosity. The numerical results of pressure rise show that when the viscosity of biofluid varies from centre to the boundary, then high change in pressure is required as compared with the biofluid having constant viscosity along the height of the slit. These mathematical formulas are very useful for the bioengineers to design the portable artificial kidney which works as a mechanical tool to filter the biofluid.