A device has been proposed that will serve as a blood oxygenator for a heartlung bypass machine,

A device has been proposed that will serve as a €œblood oxygenator€ for a heart€“lung bypass machine, as shown in the figure below. In this process, blood 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% O₂gas phase. Oxygen is soluble in blood, where the equilibrium solubility c_A* is function of the partial pressure of oxygen gas. In analyzing the mass transport of dissolved oxygen into the falling film, you may assume the following: (1) the process has a constant source of O₂(gas) and a constant sink (falling liquid film), and so is at steady state; (2) the process is dilute with respect to dissolved oxygen dissolved the fluid; (3) the falling liquid film has a flat velocity profile with velocity v_max; (4) the gas space always contains 100% oxygen; (5) the width of the liquid film, W, is much larger than the length of the liquid film, L.

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

b. Provide one simplified differential equation in terms of the oxygen concentration c_A.

c. Provide boundary conditions associated with the oxygen mass-transfer process.

Transcribed Image Text:

Blood containing no dissolved oxygen (blood) SIDE VIEW Inlet blood ehamber for O2 gas Falling liquid film .z = L Inert solid surface 100% O2 gas Vm 100% P2 gas 1.0 átm, 25°Ç Exiting oxygenated blood Z=L X = 6 x= 0 Exiting oxygenated blood, 40°C Falling liquid film N.