{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Week9HWSolutions

# With the bulk diffusion coefficient we still have

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 <...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online