it looks like you have done your homework. Tim submitted a
GRM version of pair_lubricate based on Chapter 11, but maybe
we are better off using the equations you highlighted here.
Do you have this implemented in LAMMPS? It would be
interesting to compare the behavior of two near-contact
spheres with the three versions of pair_lubricate we now
Ranga Radhakrishnan [mailto:r.radhakrishnan@...652...]
Sent: Wednesday, June 28, 2017 12:53 PM
To: Heine, David R; Steve Plimpton; Bolintineanu,
Dan Stefan (-EXP)
Subject: Re: [lammps-users] Errors in
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
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
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
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
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 wrote:
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
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
I'm CCing Dan Bolintineanu and Dave
Heine who can likely
On Wed, Jun 21, 2017 at 4:54 AM,
Ranga Radhakrishnan <r.radhakrishnan@...652...>
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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