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lecture6

# lecture6 - Square Root Relationship For infinite or...

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Square Root Relationship For infinite or semi-infinite systems with constant surface concentration, the solution involves only the single dimensionless parameter Dt x 2 1. The distance of penetration of any given concentration is proportional to the square root of time 2. The time required for any point to reach a given concentration is proportional to the square of the its distance from the surface and varies inversely as the diffusion coefficient 3. The amount of diffusing substance entering the medium through unit area of its surface as the square root of time. Infinite vs. Finite Systems or Short vs. Long Time h c x c s ( ) = h dx t x c M , Error of assuming a semi-infinite system, ( ) ( ) = = 0 , , error dx t x c dx t x c Q M h Dt h 4 ~ 01 . 0 error If Dt h 4 ~ the system can be considered as infinite, and the corresponding solution is called “short-time” solution

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Finite Systems A straightforward way is to use reflection and superposition h h c x +
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