# exprobs - 10.302 Fall 2004 EXAMPLE PROBLEMS Problem 1...

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10.302 Fall 2004 EXAMPLE PROBLEMS Problem 1 Transdermal drug delivery devices (such as the nicotine patch) typically consist of a reservoir of drug sealed onto the surface of a polymer membrane as shown in the figure. The device is manufactured by injecting a drug solution into the reservoir (labeled “drug” in the figure) and sealing the reservoir shut. The polymer membrane does not contain any of the drug initially. During use, the bottom of the polymer membrane is attached to the surface of the skin and drug diffuses from the reservoir down through the membrane into the skin. The drug essentially remains at a constant concentration c in the reservoir during use. L drug c Polymer membrane (diffusion barrier) a) How long after the device is manufactured will it take for drug to penetrate to the exterior (bottom) surface of the polymer membrane? b) How long after manufacture before the membrane is saturated with drug? You may assume saturation has been obtained if the concentration in the membrane has reached 99% of its final value. Data: L = 1 mm c D = = 100 mg/ml 5 x 10 -8 cm 2 /s (diffusion coefficient of drug in membrane) S = 0.01 (concentration of drug in membrane/concentration of drug in reservoir fluid)

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Problem 2 Mammalian tissue is to be grown in the annular space between a tube of (poly) dimethyl siloxane (PDMS) and an impermeable outer shell (see figure). Oxygen will flow through the interior of the tubing. In order to meet the metabolic demands of the tissue, the oxygen will diffuse through the tubing wall and then into the tissue. For this problem, it may be assumed that any resistance to mass transport associated with the tubing may be neglected. Thus, the appropriate boundary condition at r = R 1 is ° = C O 2 r @ = R 1 C O 2 It is assumed that the O 2 reacts with the tissue in accordance with N o 2 = constant = 7x10 - 5 - mol/ m 3 s Furthermore, the diffusivity of O 2 in tissue is known to be about 2 x 10 -5 cm 2 /s. In o addition, the value of is about 1.4 mol/m 3 . Convective transport of O 2 may be C O 2 neglected. i. What is the expression for ( r )? C o 2 ii. There is a critical value of R 2 at which C o 2 = R at 0 2 . What is the expression for this critical radius? For the parameters given above, show that R crit <4R 1 if R 1 = 0.25 cm. DATA In cylindrical coordinates 1 F z F = r r (rF r ) + 1 F θ + r θ z 2 f = 1 ∂  f 1 2 f 2 f r + r r r + r 2 θ 2 z 2 Tissue R 2 R 2 R 1 r R 2
Problem 3 A wetted wall column is to be used to study the absorption of CO 2 into water. The column is supplied with solute-free water at the top and air containing 5 mole percent CO 2 is supplied at the bottom. The air flow rate is such that the change in gas composition may be neglected. The gas phase resistance to mass transfer is negligible. The situation is as depicted in Sketch A.

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exprobs - 10.302 Fall 2004 EXAMPLE PROBLEMS Problem 1...

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