Professor Ruth E. Baltus
Dept of Chemical and Biomolecular Engineering
Clarkson University
Potsdam, NY 13699-5705
315/268-2368 voice
315/268-6654 fax
Email: baltus@clarkson.edu
February 9, 2016
Dr. Michael P. Harold, Editor
AIChE Journal
Department of Chemical and Biomolecular Engineering
University of Houston
Houston, TX
Dear Dr. Harold:
Enclosed is a revised manuscript titled “Membrane Rejection of Non-spherical Particles: Modeling and
Experiment ” . This manuscript was originally submitted for publication in the AIChE Journal last July
and a revised manuscript was submitted in December.
We thank the reviewers for their comments and suggestions. We have made the following changes in
response to the comments:
Comment 1:
I still don’t understand how the velocity profile remains parabolic (eq. A3) when the particle
takes up significant cross-sectional area in the pore, say for gamma>0.5. Can the authors
justify this? The authors show an example of the fluid velocity using a color scale in Fig. S2,
but this does not really demonstrate how the ALE algorithm adjusts the velocity field to the
presence of a large particle, particularly when gamma > 0.5. And if the velocity field adjusts,
how is this reflected in eq. 2 which seems to presume a parabolic velocity profile?
The velocity profile in the cylindrical channel is influenced by the presence of the particle; the
fluid-particle interactions are captured in the ALE algorithm. When the particle attains a steady
state velocity in the pore, the fluid on the particle surface has velocity equal to the particle
velocity. We have changed Figure S2 to now show sequential snapshots of the particle position in
the pore from time = 0 to time = 0.94 (close to steady state). This revised figure illustrates that at
time = 0, the fluid velocity on the particle surface = 0. As time increases, the fluid velocity on the
particle surface increases until the particle achieves a steady state. The velocity field in Equation
2 (and A3) is defined when the particle is excluded from the cylindrical pore and hence it is
parabolic. For a detailed derivation of these equations, we refer to reader to Anderson (reference
11 in the manuscript).
Comment 2:
The point above is further confused by the statement on p. 9 that “the fluid flowing through the
channel …follows Poiseuille flow in advance of the particle.” What does this mean? In front
of the particle or initially before the particle is placed in the pore? By the way, this is not a
channel (usually considered to be flow with a Cartesian geometry not a cylindrical geometry).
We have changed this sentence to clarify that the fluid follows Poiseuille flow before the particle
is placed in the pore.
Comment 3:
Where are the results for silica? Apparently, they are Fig. S4 in the supplementary material.
Why not include this in the manuscript? It is quite compelling that the approach works.
Figure S4 has been moved to the main document – now Figure 7.
Comment 4:
Figure 3 indicates that the centerline fluid velocity 0.25*u_c, where u_c is the average velocity
in the pore, according to p. 9. This does not quite make sense to me. For Poiseuille flow in a
pore, the centerline velocity should be 2*u_c. What am I missing?
We have revised our non-dimensionalization of the Navier-Stokes equation; the centerline fluid
velocity is now used for velocity scaling. Hence, the dimensionless centerline velocity is now
̅𝑚 = 𝑢⁄𝑢𝑚 = 1 (previously it was 𝑈
̅𝑚 = 𝑢⁄𝑢𝑚 = 0.25). These changes are reflected in the
𝑈
revised Figure 3. When examining the calculations, we discovered an error which has a small
impact on G for the larger aspect ratio particles, but did not have any appreciable impact on σ.
Hence, the results presented in Figure 4 for ε = 4 are slightly different than results presented in
the earlier drafts of the paper.
Comment 5:
Figure S3 provides convincing evidence that the author’s simulations are correct. It should be
included in the paper
Figure S3 is now included in the manuscript as Figure 6, although we are not opposed to leaving
it in the Supplementary Information.
Comment 6:
Figure 6 is redundant with Fig. 7 and should be omitted.
While the experimental results presented Figures 6 and 7 (now Figures 8 and 9) are the same, we
feel that both figures contribute to the discussion of the results. Figure 8 demonstrates that σ
increases as particle aspect ratio increases for particles with the same volume (i.e., the same λ) , a
conclusion that is difficult to draw from Figure 9 alone. Figure 9 illustrates the good agreement
between experimental results and our model predictions.
Again, we appreciate the thorough reviews provided to us. Please contact me at baltus@clarkson.edu if I
can provide additional information. I look forward to hearing from you.
Sincerely,
Ruth E. Baltus
Professor
Department of Chemical and Biomolecular Engineering