HW 8 - SP2 - Estimating the Time Required for Vaccine Ultrafiltration - 5 pts
We want to filter 840 L of a solution containing 0.061 wt% of a protein used as a vaccine for herpes. This protein has a MW of 16,900 and a diffusivity of 1.1 x 10-6 cm2/sec. We want to raise the concentration to 2.0 wt%. The ultrafilter we hope to use has eight hollow fiber cartridges., each of which has a surface area of 1.2 m2. The solution is chilled to 4oC. When a pressure drop of 31 atm is used, the membrane in the cartridges gives an initial volume flux of 5.7 x 10-5 cm/s (that is just over 1 gal/ft2/day). Assume the density of the solution is essentially the same as that of water (1000 g/L). Also, assume that the boundary layer is 0.01 cm thick.
a.) Assuming that concentration polarization is negligible, estimate the timerquired to filter the entire solution using all eight cartridges in paralel.
b.) Test whether concentration polarization is significant.
a.) Assuming that concentration polarization is negligible, estimate the timerquired to filter the entire solution using all eight cartridges in paralel.
b.) Test whether concentration polarization is significant.
posted by Dr. B at 8:20 AM
9 Comments:
Assume the density of the solution is essentially the same as that of water (1000 g/L). Also, assume that the boundary layer is 0.01 cm thick.
I'm getting a huge value for t. I think I might've went wrong in finding Vr. Vro is given right (840L) and Vr can be found by doing a balance on Protein. You can assume no Protein leaves => it would be a balance to get Vr because you know the solute has to be at 2%. Does this sound right? What do I do with the initial volume flux?
bill:
Yes, Vr0 = 840 L. Yes, you can find VR by a protein material balance. I got about 25 L.
Since you are assuming no CP effect, the volume flux is always the same...the initial value ! This allows you to calculate the value of the ratio of the permeance to the membrane thickness. See slide 20 of the PPT from Friday.
You are in good shape.
on slide 21, there is a square instead of an inequality. should it be < 1 or > 1 for CP to be insignificant?
is NH2O = the initial volume flux?
blah:
This is a font problem. It happens most often when the PPT is opened on a Mac. The equation should be: D*density/(lmem*Nw*MWw) >> 1 for the CP layer to be significant.
blah2:
NH2O is the molar flx of water. But, NH2O*MW/density is the volume flux of water.
basil:
NH2O is the molar flux of water through the membrane. check out my last comment for more info.
basil 4:53 PM:
Good point. I sent out an email telling everyone that there was a typo in the eqn. Where there was just "b" on the RHS, there should have been"1/b".
The other source of unit problems is that NH2O in this equation is the MOLAAR flux of water while the problem statement gives you the volume flux of water. The relationship is: the volume flux of water = (NH2O*MW/density).
I hope this helps and maybe is not too late.
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