With the bulk diffusion coefficient we still have

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Unformatted text preview: ⎤ υ x T L ⎛ dn ⎞ F= ×⎢ ×− ⎥= 2 1 −T ⎢ L 2 1 −T ⎜ dx ⎟ ⎝ ⎠ ⎥ ⎣ ⎦ This looks like Fick’s law ⎛ dn ⎞ F = − D ⎜ − ⎟ ⎝ dx ⎠ with + υx T L D= 2 1 −T Using λ T= , λ+L we find ⎛ dn ⎞ F = −D⎜ − ⎟ ⎝ dx ⎠ D= + υx λ , (viii) (ix) (x) (xi) (xii) 2 which is Fick’s Law with the bulk diffusion coefficient. We still have made no assumption that the region is long compared to the ballistic limit. Apparently, Fick’s Law holds all the way to the ballistic limit. 1b) Make a sketch of n ( x ) vs. x in the a) diffusive limit, b) in the ballistic limit, and c) in between. Solution: Use (iii) and (iv): + n ( 0 ) = ( 2 −T ) F + (0) υ x + n ( L ) =T F + (0) υ x ECE- 656 2 Fall 2013 Mark Lundstrom 10/19/13 a) diffusive limit: T → 0 + n ( 0 ) → 2 F + (0) υ x n ( L ) → 0 b) ballistic limit: T → 1 + n ( 0 ) → F + (0) υ x + n ( L ) → F + (0) υ x = n ( 0 ) c) in between: 0 <T < 1 + + F + (0) υ x <...
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This document was uploaded on 01/15/2014.

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