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Unformatted text preview: IV. Transport Phenomena Lecture 19: Transient Di ff usion MIT Student In this lecture we show how to use simple scaling arguments to approx imate the solution to transient di ff usion problems, which arise in electro chemical energy systems. In each case, we will also briey mention the related results from exact solutions to the di ff usion equation to show how well the scaling analysis works. For further reading, see Bard & Faulkner, Electrochemical Methods . 1 Response to a Current Step 1.1 Sands Time Suppose we have a cell and we turn on the current at time t = 0, I ( t ) = I ( t ), where ( t ) is the Heaviside step function, and I is above the limiting current, we observe the concentration profiles indicated in Fig. 1. This current can be sustained for an amount known as Sands time, which occurs when c ( x = 0) 0 and V 0. This is solved in 2009 previous notes and in Bard & Faulkner, Electro chemical Methods . Here we give a simple scaling analysis for t sand : Ft Since x Dt and the A Ft x c , and thus c Dt = c at t sand ....
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.
- Spring '03