CHEN 6603 MIDTERM EXAMINATION 2 Problem 1 (10 pts)

CHEN 6603 MIDTERM EXAMINATION 2
Problem 1 (10 pts)
We have discussed diffusion barrier, reverse diffusion and osmotic diffusion. When we first introduced these effects,
we had (∇x) as the only diffusion driving force, and we concluded that these were uniquely multicomponent effects
which could not occur in a binary system. In light of what we have learned about the full driving force for diffusion,
answer the questions below.
d i =
(
n−1
∑ Γ ij ∇x j + 1
c
j=1
t RT (φ i − ω i )∇p − ω iρ
c t RT
f i −
n
∑
k=1
ω k f k
)
1. (5 pts) Can osmotic diffusion exist in a binary system In other words, can J 1 ̸= 0 even when ∇x 1 = 0 Be
specific about what conditions may cause this.
,
2. (5 pts) Can a diffusion barrier occur in a binary system In other words, can J 1 = 0 even when ∇x 1 ̸= 0 Be
specific about what conditions may cause this.
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Problem 2 (14 pts)
Recall the two-bulb problem that we discussed in class and that you solved in your homework (isothermal, isobaric,
nonreacting ideal gases).
1. (4 pts) Show that the species mole balance on a bulb can be written as c t V dx i
dt
the bulb and A is the area of the tube.
= −J i A, where V is the volume of
2. (4 pts) Show that the species profiles in the tube can be written as x i = xL i −x0 i
L
z + xi 0, where x0 i
is the composition
in the bulb at z = 0, and xi L is the composition in the bulb at z = L. Indicate assumptions you make.
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3. (6 pts) Below is a figure showing the composition in each bulb as a function of time. Using this information,
indicate evidence of multicomponent effects. Be as specific as you can in your arguments, including identification
of reverse diffusion, osmotic diffusion, and diffusion barrier if they exist. This will likely require you to
justify how you will obtain quantities such as J i and ∂x i
∂z
from the plots below.
(a) Bulb 1 at z = 0. (b) Bulb 2 at z = L.
Figure 1: Composition histories, x i (t).
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Problem 3 (15 pts)
1. (3 pts) Does linearized theory require the assumption that [D] is constant Why or why not Be specific.
2. (3 pts) Does effective diffusivity require the assumption that [D] is constant Why or why not
3. (4 pts) Assuming that you solved a problem using an effective diffusivity approach to obtain x i (z, t), how might
you determine if you need to revise your solution to include multicomponent effects
4. (5 pts) Recall for the two-bulb problem we obtained the solution for the species profiles in the tube:
x i = xL i
− x 0 i
L
z + x 0 i , (1)
where x 0 i
is the composition in the bulb at z = 0, and x L i
is the composition in the bulb at z = L.
If we wanted to use a mass-transfer coefficient approach to obtain (J) within the tube, define [k • ] , [k] (low-flux
mass transfer coefficient) and [Ξ] (the correction factor matrix).
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