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16 Nov 2019

W25.12 A device has been proposed that will serve as a “blood oxygenator” for a heart-lung bypass machine. In this process, blood (which is mostly water, species B) containing no dissolved oxygen (O2 species A) enters the top of the chamber and then falls vertically down as a liquid film of uniform thickness, along a surface designed to appropriately wet blood. Contacting the liquid surface is a 100% O2 gas phase. Oxygen is soluble in blood, with the equilibrium solubility described by Henry’s law, , where is the partial pressure of oxygen (atm), is the Henry’s law constant, and is the solubility concentration limit of oxygen dissolved in blood (mmol/L) at . In analyzing the mass transport of dissolved oxygen into the falling film, you may assume the following: (1) the process is dilute with respect to dissolved oxygen in the fluid; (2) the falling liquid film has a flat velocity profile with velocity ; (3) the gas space always contains 100% oxygen; (4) the width of the liquid film, W, is much larger than the length of the liquid film, L.

Simplify the general differential equation for O2 transfer. If your analysis suggests more than one dimension for flux, provide a simplified flux equation for each coordinate of interest.

Provide one simplified differential equation in terms of the fluxes and another simplified differential equation in terms of the oxygen concentration .

List boundary conditions associated with the oxygen mass transfer process.

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