- Notes on the juice concentration problem
- This page
contains solutions of 1) flavor mass balance equation
for the fed-batch concentrator (derived in class)
and 2) flavor mass balance equation for the simple
batch concentrator (not derived in class). Comparison
of solutions shows that the concentration of juice
in the recycling tank of the fed-batch system is always
higher than in the batch system. Thus, Cf will be
higher and more flavor will be lost to the filtrate
in the fed-batch system. Qualitatively, the result
can be understood if you think about the concentrate
being diluted by a much larger volume of non-concentrated
juice in the simple batch system (compare V0=10,000
L of initial juice volume with Vrt=500 L, which is
the recycling tank volume in the fed-batch system.)
- At one point in the solution for the batch system,
the following approximation is made: 1/(1-x) =~ 1+x.
You can show, by the Taylor expansion of 1/(1+x),
that the approximation is true for x->0, which
is the case in our example, where x=Qt/V0.
- Lecture 24 (Hemodialysis) slides are posted. See Contents
- Lecture 24 slides are posted. See Contents
- HW#5 is posted.
Due by 12:40pm on Wednesday, Apr 25
- Handout on the Carman-Kozeny equation can be downloaded
- Solutions to HW#3 are posteddocs/Lecture19.ppt
- Materials are posted for lecture 24 (MBR). See Contents
- Comments on HW#4:
- Problem #1:
- Cp, rejection, and recovery for the entire element
can be easily determined based on Ms and Qp values
for the element, which can be calculated by summing
up corresponding values for 10 increments.
- To solve the system of two equations with two
unkowns (jw, beta) in Part 3 of problem #1, consider
using Goal Seek (Data Tools -> What-If-Analysis
-> Goal Seek)
- Problem #3:
- See this paper
for linearized versions of integrated forms of
blocking laws for complete blocking and intermediate
- Materials are posted for lecture 23 (MF & UF):
- Papers discussed in class (lectures 21 and 22):
- Achilli, A., Cath, T. Y., A. E. Childress. Power
generation with pressure retarded osmosis: An experimental
and theoretical investigation. J. Membr. Sci.
343 (2009) 42-52
- Cath, T. Y., Childress, A. E., M. Elimelech. Forward
osmosis: Principles, applications, and recent developments.
J. Membr. Sci. 281 (2006) 70-87
- Achilli, A., Cath, T. Y., Marchand, E. A., A. E.
MBR and pressure-retarded osmosis MBR for wastewater
treatment. Presented at ICOM 2008, Honolulu, Hawaii,
- A broken link to the paper by Ho and Zydney (see 03/26
entry) has been fixed
- To provide you with more up-to-date number on the state
of the desalination market, see this Water
Desalination Report (March 12, 2012 issue.) Note the
recent double-dip recession and projected gradually recovery
of the seawater desal segment.
03/26 (2nd post)
- HW#4 is posted.
Due by 12:40pm on Monday, Apr 9
- materials are posted for
- lectures 16-18 (concentration polarization and fouling)
- lectures 19-20 (NF/RO)
- lectures schedule is adjusted to reflect that
- blocking laws and concentration polarization topics
were covered over 2 (and not 1, as initially planned)
- there will be no term paper presentations at the
end of the class
- papers discussed in class:
- Ho, C.-C., A. L. Zydney. A
combined pore blockage and cake filtration model for
protein fouling during microfiltration. J. Colloid
Interface Sci. 232 (2000) 389-399
- Bellona, C., Drewes, J. E., Xu, P., G. Amy. Factors
affecting the rejection of organic solutes during
NF/RO treatment—a literature review. Water
Res. 38 (2004) 2795 - 2809
- Nghiem, L. D., Schäfer, A. I., M. Elimelech.
Retention of emerging
water and wastewater pollutants in nanofiltration,
IMSTEC, November 11-13, 2003, Australia, Sydney
03/15 (2nd post)
- Information on term projects is posted
- Clarifications on HW#3:
- In problem 2, assume the length of the membrane
channel L is equal to 1 m
- In problem 1, assume that the flux values reported
on Sterlitech's website were obtained at room temperature.
- Solutions to HW#1 and HW#2 are posted.
Your graded HW1, HW2, and quiz 3 can be picked up from
Mrs. Mary Mroz in the CEE office (3546 Engineering Building)
- HW#3 is posted.
Due by 12:40pm on Monday, Mar 19
- This file contains
an example of how a simple ODE (ordinary differential
equation) can be solved using Excel.
- The file contains solution of the equation dY/dX
= -Y^2 with the following initial condition: Y(X=0)=1
- The numerical solution is obtained for 3 different
values of deltaX
- The analytical solution is 1/(1+x) is plotted on
the same graph with the numerical solutions to illustrate
the effect of deltaX on the numerical error.
- 3 sets of board notes for lectures on the theory of
membrane processes are uploaded (see Contents)
- 2 sets of board notes for Lectures 13 and 14 are uploaded
- Papers on the solution-diffusion model:
- In HW#2, problem V-18:
- assume that the membrane area in the experiment
#2 is the same as that in the experiment #1
- there is a typo in problem formulation in the textbook.
The decrease in sucrose concentration should be 1.6%,
- HW#2 is posted.
Due by 12:40pm on Wednesday, Feb 29
- Two sets of slides on the "Membrane preparation
methods " topic are uploaded (see Contents)
- Lecture schedule is adjusted to reflect where we are
in the class
- Office hours on Monday, Jan 29 are rescheduled for 3:30-5pm
- HW#1 is posted.
Due by 12:40pm on Wednesday, Feb 8
Uploads (see Contents):
- A set of slides for the "Membrane materials"
- Uploads (see Contents):
- 2 sets of slides for the introductory module of
- Uploads (see Contents):
- a set of slides for lecture 2
- the website is password-protected now
- Please download a "New
course questionnaire " form, fill it out, and send
it to me by email
- Uploads (see Contents):
- two sets of slides for lecture 1
- solution to the example problem
- Required reading
- Recommended reading on historic developments in membrane