An approximate analytical solution to the ultra-filtration profile in a hemodialysis process between parallel porous plates

In a hemodialysis process, the blood that runs through straight channels exchanges substances with the dialysate through a semi-permeable membrane. The waste products, such as urea and creatinine, are therefore removed from the plasma by the membrane. In the analysis of this process, determination of the ultra-filtration profile along the porous membrane surface remains a difficult problem. In this work, an analytical solution to the derivation of such a profile was detailed, and the feasibility of this solution was discussed. The ultra-filtration profile was found to be in a cosine shape.