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You work in a pharmaceutical company which has recently discovered a new drug to treat certain skin diseases. The drug is to be applied in the form of a dermal patch directly over the affected area of the skin. The company would like to study the concentration profile of the drug as a function of time to determine if the release rate is suitable for the human body. You have been assigned the lead engineer for this project. A meeting was convened to brief you on the properties of this drug. You were given the following information: 1) The drug is uniformly dissolved in a gel at an initial concentration of C = 1.5 concentration unit. 2) Once applied on the skin, the drug will then diffuse through the gel and into the skin. 3) The dosing time is to be 24 h (i.e. the patch should be replaced every 24 hours). Your task is to determine the optimal diffusivity that so that 1) Att=12 h after the application of the patch, 60% of the drug in the patch needs to have been absorbed by the skin. This is to prevent over-dose or under-dose of the drug. The parameter you can change is: 1) The diffusivity of the drug in the gel. The diagram below shows the cross-section (not to scale) of the dermal patch. Patch containing drug skin x=0 x=1 For simplicity, the thickness of the patch is 1 (0o ax2 C(x,0) = 1.5 0 0 C(1,t) = 0 t> 0 You will need to solve this problem numerically using Excel with the procedure discussed in the lectures. Use a grid of x= 19 interior nodes for your calculations. At any time t, the total amount A of the drug left in the patch is given by this formula: n-1 AX 22c +cm i=1 Co + 2 2 where Co and C are the concentration values at the 2 boundary nodes, and C.Ca......-1 are the interior nodes. At t=0, A = 1.5. Answer the following questions: a) For At = 0.02 h and D=0.04, numerically evaluate the concentration profile C(x, t) for 0 o ax2 C(x,0) = 1.5 0 0 C(1,t) = 0 t> 0 You will need to solve this problem numerically using Excel with the procedure discussed in the lectures. Use a grid of x= 19 interior nodes for your calculations. At any time t, the total amount A of the drug left in the patch is given by this formula: n-1 AX 22c +cm i=1 Co + 2 2 where Co and C are the concentration values at the 2 boundary nodes, and C.Ca......-1 are the interior nodes. At t=0, A = 1.5. Answer the following questions: a) For At = 0.02 h and D=0.04, numerically evaluate the concentration profile C(x, t) for 0

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