Question

Problem 4 - Steady-state Diffusion with Chemical Reaction. (20 pts) One of the most studied bioarticificial organ systems is the encapsulation of islets of Langerhans cells to produce insulin in diabetic patients. They consist of islets encapsulated in a spherical gel bead. The spheres are kept at 310K, are 150 microns in diameter, and the islets consume oxygen at a rate of 25.9 UM/s. The diffusivity of oxygen into the system is 1.67 x 10-9 cm/sec. The average partial pressure of oxygen at the capsule boundary is 68 mmHg. Henry's constant is 0.74 mmHg/uM. a) Derive the equation that describes the concentration at a radial position r in the gel bead in the absence of bulk flow (analytical solution only). b) What is the oxygen flux at the surface of the spherical gel r= R? c) What is the oxygen concentration half the total radius from the center? d) If the Michaelis-Menton constant Km for the oxygen uptake is 1 MM, does the zeroth order reaction still hold? e) What is the maximum consumption rate without the presence of necrotic region?

Answer 1

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NA-Dandal dolor No-Doolen (26) Lory (26) Peale 6 DAB IRER NAS NDAR 3 DAR NA= 25.9x10b 10 3 NA 1.995 mis WR 3. x 150x164 cu moderni CAC = Pa = 60 91-4891 NM:- Н. 6.74 CA=-No2+ Cro+ WR² GDAO 6Dao 8=R 1 CA=oWR² Cro & WR² 24 DAB 60m CA = Cao + WR² 6Dm14 CA= Cact WR² 103 -1073 CAz 91.8918156 25-5215*Cisoxlo") 10% &x 1067x09 Saz qlo1891 V1O3; 50450-6X10 91.891.*10?+ 49:64x153 1- x16 381 Co UM 44-20 3 V- Amex C с. = Vmer 1200 order) Since, Kon=lunch Co give

using given data and mass balance we can find the concnetration. WHile using ficks law we have omitted negative sign as flux is in decreasing r direction making over all term positive

as per guidelines only first four parts are to be solved

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