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The governing nonlinear steady equations for oxygen transport in a microfluidic channel are solved analytically. The Lagrange inversion theorem is used which admits complete integrable solutions in the channel. Considering a cell-rich and cell free region with RBCs and blood plasma, we obtain results showing clearly that there is a significant decrease in oxygen tension in the vicinity of an oxygen permeable membrane placed on the upper channel/tube wall and to the right side of it in the downstream field. The purpose of the membrane is to cause a rapid change in oxygen saturation as RBC’s flow through channel/tube. To the right of the membrane downstream the greatest amount of ATP is released. The method of solution is compared to numerical results. The analytical results obtained could prove useful for the corresponding time dependent problem in future studies.
Two solutions are presented : 1) A mathematical / Analytical solution, 2) Numerical solution, and a comparison is made for blood flow and ATP release in microfluidic channel.