Thanks for your reply. I have attached the pdf as per your
request. I will try to address your email in a enumerated list to
make my points clear.
1) \omega^\infty seems to have the wrong units. It is because
"h_rate" has the units of length/time (Please correct me if I am
wrong). Specifically, I am referring to lines: "omega[i] +=
0.5*h_rate; ..." which subtracts h_rate from omega. In case
"h_rate" has the right units of 1/time, I am confused about the
units of Ef (E^\infty) which should be the rate of strain tensor.
2) The results given in Chapter 9 of Ref. (1) are slightly
misleading, because they cite Jeffrey and Onishi's work (doi:
10.1017/S0022112084000355) before giving the final formulae for
the forces, and torques. In the original work by Jefferey and
Onishi, the gap distance is non-dimensionalised by (radi+radj)/2.
3) Eqs. 9.26, and 9.27 in Ref. (1) are the solutions for force
and torques for shearing of two surfaces only due to rotation. Why
does the pump term account only for the torque? I don't think the
current formulation of the force considers the shearing of two
surfaces only due to rotation correctly. (Please see Sec. IV of
the attached document).
4) a.The squeeze term in lubricate/poly is taken from the force
given in Eq. 9. 33 of Ref. (1). According to the resistance matrix
formulation, the first term in Eq. 9. 33 should be multiplied by a
prefactor of "2/(1+\beta)" , and the second term by "\beta"
(apologies for the mistake in my previous email). One simple way
to see that is that the magnitude of the leading order terms given
in Sec. 11.2.2 should be twice of Eq. 9. 33, which is not the case
in the textbook.
4) b. The squeeze or the shearing terms should be independent of
the particle velocities and rotations, so Chapters 9 and 11 of Kim
and Karilla should be consistent with each other. In case they are
not, I have tried to refer to the original research articles and
verify the same.
5) I don't think we need to bring in volume fraction dependencies
at the moment, because the issues that I have raised can be
tracked down using just two particles of unequal sizes.
The general solution of the problem of two unequal spheres in a
fluid is given in Chapter 11 of Kim and Karilla, or originally in
Jeffrey's research article (doi:10.1063/1.858494). In the attached
pdf, I have mainly relied on Kim and Karilla as the reference. The
results that you are referring to in Chapter 9 of Kim and Karilla
can be derived as cases of the general result in Chapter 11 (as
shown in Section IV of the attached pdf). As you rightly mention the
grand (shear) resistance matrix formulation is slightly more
involved to implement efficiently. However, one can get simplified
expressions for forces and torques that are easier to implement in
LAMMPS by considering only the first two leading order terms as
shown in the attached document (Eqs. 12, or 13, and 23, or 24).
On 28/06/17 14:51, Heine, David R
didn’t get the attached pdf when the message was forwarded,
so maybe sending it directly to me will help me understand
the issue better.
general, I followed the equations in Chapter 9 to
incorporate polydispersity into pair_lubricate. As I was
discussing with Tim Najuch, the text assumes you have
particle A approaching another particle B, so being
consistent with them, the separation distance is scaled by
the radius of particle A. In the lubricate implementation,
the forces on A and B are calculated separately, hence the
requirement that “newton” is set to off. The grand
resistance matrix approach in Chapter 11 that Tim was
working on assumes the particles are approaching each other
at the same speed, which may be a better approximation, but
I don’t have a sense of how big the difference is when
modeling things like highly filled systems as opposed to
semi-dilute solutions. If you haven’t already talked to Tim
about the grand resistance matrix implementation, maybe that
will address some of your issues.
don’t see the issues about specific terms you mention below,
but again, maybe I need the pdf attachment to see your
explanation. If you have a means of making this more
generally applicable than what is provided in Kim and
Karilla, then I am all in favor of it.
Steve Plimpton [mailto:sjplimp@...24...]
Sent: Wednesday, June 21, 2017 10:23 AM
To: Ranga Radhakrishnan; Heine, David R;
Bolintineanu, Dan Stefan (-EXP)
Subject: Re: [lammps-users] Errors in lubricate/poly
I'm CCing Dan Bolintineanu and Dave
Heine who can likely
On Wed, Jun 21, 2017 at 4:54 AM, Ranga
I think that I have a few issues with the lubricate/poly
implementation in LAMMPS based on my reading of
Microhydrodynamics book by Kim and Karilla .
1) The gap-distance (h_sep) between the particles should
be scaled by (radi+radj)/2 and not as radi, where radi,
radj are the radii of the two particles.
2) The first term in the squeeze force seems to be missing
a prefactor of 2.
3) \omega^\infty seems to have the wrong units. It is
because "h_rate" has the units of length.
4) The pump term is also incorrect for particles of
different sizes. Briefly, specific cases of calculation of
torques in Ref.  cannot be used to write down a
Please look at the attached pdf for a more detailed
explanation on why I raised these concerns, and how to
implement a "corrected" lubrication force if you agree
with my concerns. Just to be clear, I have looked at
previous messages in the mailing list before I send this
message, and I don't think any of the previous messages
have answered my concerns.
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