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Time Dependent & 2D Component Transfer
Applications of isothermal equation of continuity of components
•
Steady state gas absorption by diffusion into a falling liquid film
 Assumption: constant diffusivity, diffusion is negligible in z
 Nonzero components: u
z
, dc
A
/dz, dc
A
/dx, dc
B
/dz, dc
B
/dx
 Balance for component A
Recall that
2
max
1
z
x
uu
δ
⎡
⎤
⎛⎞
=−
⎢
⎥
⎜⎟
⎝⎠
⎢
⎥
⎣
⎦
2
*
2
A
A
z
cc
uD
z
x
∂∂
=
∂
∂
2
2
max
2
1
A
A
x
z
x
⎡⎤
⇒−
=
⎢⎥
∂
∂
⎣⎦
with boundary conditions
0
00
0
0
A
AA
A
A
A
zx
x
c
c
N
D
x
==
=
∂
=
−
=
∂
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View Full Document Time Dependent & 2D Component Transfer
Applications of isothermal equation of continuity of components
•
Steady state gas absorption by diffusion into a falling liquid film
This equation could be solved using the method of variable combination
0
max
1
4/
A
A
c
xx
erf
erfc
c
Dz u
=−
=
The local flux of gas at a given z position on the gasliquid interface
0
0
0
A
AA
x
x
uD
c
ND
c
x
z
π
=
=
∂
⎛⎞
=
⎜⎟
∂
⎝⎠
called
penetration model
Total flux over the interface can also be calculated
*
.
x
x
Dx
t
α
∂
⎡⎤
+
∇=
∇
⎣⎦
∂
u
Time Dependent & 2D Component Transfer
Applications of isothermal equation of continuity of components
•
Dissolution and diffusion from solid surface into a falling liquid film
 Assumption: constant diffusivity, diffusion is negligible in z
 Nonzero components: u
z
, dc
A
/dz, dc
A
/dx, dc
B
/dz, dc
B
/dx
 Balance for component A for a short exposure time
Due to the coordinate change
2
2
2
2
z
gy
y
xy
u
ρδ
δ
μδ
⎡
⎤
⎛⎞
=−
⇒
=
−
⎢
⎥
⎜⎟
⎝⎠
⎢
⎥
⎣
⎦
2
2
AA
cc
ay
D
zy
g
a
μ
∂∂
=
=
⇒
For the region very close to the surface
()
2
2
2
z
yy
u
a
y
δδ
>>
⇒
=
=
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This note was uploaded on 09/01/2011 for the course PGE 312 taught by Professor Peters during the Fall '08 term at University of Texas at Austin.
 Fall '08
 Peters

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