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# hw2 - BEH.430/2.795/6.561/10.539/HST.544 Homework Set 2...

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________________________________________________ BEH.430/2.795//6.561/10.539/HST.544 Homework Set 2 Handed out: Wednesday Sept. 22, 2004 Due: Wednesday, Sept 29 by 5pm ________________________________________________

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Problem 2.1: Transient Diffusion across Tissue Membrane (No Reaction) (a) This problem focuses on the use of Separation of Variables to solve for the evolution of the space-time concentration profile of IGF-1, c(x,t), inside a section of tissue having length L (i.e., 1-D profile). As stated in class, the boundary conditions are c(0,t) = c’; c(L,t) = c”; and the initial condition is c(x, 0) = 0. You are asked to carry through the details of the solution, and to derive in detail the coefficients of all the terms in the Fourier series, showing all the steps that yield the final analytical expression for c(x,t) written in lecture and on the overhead (posted with the lecture overheads). You can assume in part (a) that the partition coefficient valid at x = 0 and x = L is K = 1. (b) Suppose K 1 (e.g., for the case in class, K = 1.4). Will this affect the kinetics of the diffusion transient? State your reasoning. Write the answer given in (a) above but now including
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hw2 - BEH.430/2.795/6.561/10.539/HST.544 Homework Set 2...

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