A porous €˜water vapor barrier€ is placed over the tissue implant shown in the figure in the next column. The purpose of the porous €œwater vapor barrier€ is to allow O₂gas direct access to the tissue while minimizing the diffusion-limited rate of evaporation of water from the tissue. Both the vapor barrier and the tissue implant possess €œslab€ geometry. The process is slightly pressurized and operates at 37°C and 1.2 atm total system pressure (P). The O₂gas stream contains water vapor at 20% relative humidity at 37°C. The vapor barrier material is a random micro porous polymer with mean pore size of 50 nm (1 × nm = 1.0 cm) and void fraction (ε) of 0.40. The tissue approximates the properties of liquid water. At 37°C, the vapor pressure of liquid water is 47 mm Hg (1.0 atm = 760 mm Hg), and the Henry€™s law constant (H) for the dissolution of O₂gas in water is 800 L · atm/gmole. Let A = H₂O, B = O₂. 

a. Making use of the Fuller€”Schettler€”Giddings correlation in the calculations, what is the effective diffusion coefficient (D_Ae) of H₂O vapor in the randomly micro porous water vapor barrier? 

b. What is the thickness of the vapor barrier (L) required to limit the rate of water evaporation from the tissue to 0.180 g H₂O/cm² · day? State all assumptions for your analysis. 

c. What is the concentration of dissolved oxygen in the tissue (CBL *, gmole O₂/L tissue) at the interface between the tissue and the porous vapor barrier (z = 0)?

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O2 gas + H20 vapor (20% relative humidity) T= 37°C, P = 1.2 atm "H,O vapor barrier" random microporous layer ɛ = 0.40, 50 nm pore size z = 0 1 Tissue implant layer (liquid water + dissolved O,) Inert surface