# diffusion coefficient suspension non-equilibrium

Hello everyone,

I have a liquid that interacts with a Lennard-Jones potential . In this liquid suspended colloidal particles are larger . The colloid - colloid and solvent - colloid interaction is performed with the potential colloid ( Hamaker ) .

I’m inducing a temperature gradient using the heat fix command, as shown in an example of lammps . The configuration is such that the gradient is almost linear .

My question is : How can I calculate the diffusion coefficient of colloidal particles (big ) in the liquid when the system is out of thermal equilibrium , and in each layer of the system temperature is different ?.

Any help is welcome me .

Hello everyone,

I have a liquid that interacts with a Lennard-Jones potential . In this
liquid suspended colloidal particles are larger . The colloid - colloid and
solvent - colloid interaction is performed with the potential colloid (
Hamaker ) .

I'm inducing a temperature gradient using the heat fix command, as shown
in an example of lammps . The configuration is such that the gradient is
almost linear .

My question is : How can I calculate the diffusion coefficient of
colloidal particles (big ) in the liquid when the system is out of thermal
equilibrium , and in each layer of the system temperature is different ?.

​the question you should rather ask (yourself) is: how would a
(self-)diffusion coefficient be defined at all for such a system?

axel​

of course, it makes no sense really. Rather should analyze the diffusion in each of the layers of the system and considering each layer in equilibrium but at different temperatures . For example, if the temperature gradient is applied in the z axis would have to bins in the z axis.

In each bin could calculate the diffusion coefficient using traditional methods : msd or VACF .

It refers to that Dr. Axel ?.

My intention is to see how the mass flow of the large particles in a system of these characteristics . So I’m interested in the diffusion coefficient associated with the large particles ( in all directions) . I understand that should observe a Soret effect on the gradient direction , but I’m interested to see what happens in the other directions when the temperature profile is slightly disturbed about linear profile .

of course, it makes no sense really. Rather should analyze the diffusion
in each of the layers of the system and considering each layer in
equilibrium but at different temperatures . For example, if the temperature
gradient is applied in the z axis would have to bins in the z axis.

In each bin could calculate the diffusion coefficient using traditional
methods : msd or VACF .

​how?​

It refers to that Dr. Axel ?.

​it is an ill-defined problem. for example, how large should the slices be?
that will affect the results.
or how do you plan to handle atoms that ​travel from one slice to another?
if you keep atoms that only stay in the same slice all the time, you have a
bias towards slower atoms. do you "tag" atoms where they start, or where
they finish? and how are these results affected by correlation length.

My intention is to see how the mass flow of the large particles in a
system of these characteristics . So I'm interested in the diffusion
coefficient associated with the large particles ( in all directions) . I
understand that should observe a Soret effect on the gradient direction ,
but I'm interested to see what happens in the other directions when the
temperature profile is slightly disturbed about linear profile .

​like i said, before even thinking about how to do it in LAMMPS, you have
to find a well defined parameter that can give you the kind of insight you
want. this is really more of a question of how to do your research than how
to use LAMMPS.

axel.​

Thanks Dr. Axel , their responses and questions are spot on.

I debated posting this here, since it is very non-LAMMPS. But… I’ve seen questions of inhomogeneous diffusion problems come up multiple times; and its always met with the response: that’s ill-defined and do your own research.

But rest assured, there are methods to estimate inhomogeneous drifts and diffusions, and avoid small time-scale sampling (non-markovian) biases used by other Time projection/Markov matrix methods. Here’s one I’m working with (D.T. Crommelin, J. Statist. Phys. (2012), Vol. 149, pages 220-233). This method (may be many others) is far beyond MSD and VACF. It doesn’t provide a diffusion coefficient but rather an equation of motion. It requires tinkering (selection of “good” basis functions). For all those reasons, methods like this will likely never be implemented in LAMMPS, and you will have to do some of your own work. But at least now people can find some glimmer of hope in the archives.

Hope it can been of some help.

I debated posting this here, since it is very non-LAMMPS. But... I've
seen questions of inhomogeneous diffusion problems come up multiple times;
and its always met with the response: that's ill-defined and do your own
research.

​in fact, i agree it is mostly a problem of asking a right question. most
of it comes from the fact, that people have a tendency to using a known
term to describe something that is in reality something different
(sometimes only by a small amount).

so why diffusion is indeed ill-defined in an inhomogeneous environment,
properties like particle or mass transport or momentum transport are not,
and can be determined in a rather straightforward fashion with LAMMPS using
existing facilities. However, which of those is a good descriptor depends
on the system under investigation and the overall goal of the research.
that is what i mean, when i ask people to look for other, more suitable
parameters. while people may colloquially also describe this as diffusion
processes, they are not "the" diffusion as it is understood in the context
of MD. one could say, that is a rather nitpicky, but you also have to
understand that one can quite easily lead people down the wrong path when
using this kind of "casual" nomenclature. i would claim that people asking
about how to use MSD across a density or temperature gradient is exactly
the reason for people being casual rather than precise. to me this serves
as a warning to be not too casual about domain specific terms, and with
this statement, i think i've been making the discussion rather on- than
off-topic.

But rest assured, there are methods to estimate inhomogeneous drifts and
diffusions, and avoid small time-scale sampling (non-markovian) biases used
by other Time projection/Markov matrix methods. Here's one I'm working
with (D.T. Crommelin, *J. Statist. Phys.* (2012), Vol. 149, pages 220-233).
This method (may be many others) is far beyond MSD and VACF. It doesn't
provide a diffusion coefficient but rather an equation of motion. It
requires tinkering (selection of "good" basis functions). For all those
reasons, methods like this will likely never be implemented in LAMMPS, and
you will have to do some of your own work. But at least now people can
find some glimmer of hope in the archives.

​i would also look into the coupling of MD to continuum models​, as it
*requires* these kinds of transport parameters.

axel.

Agreed throughout, and I certainly have no problem with the nitpicky. I am particularly prone to cringing at oft repeated questions about using measures that only have meaning in statistically stationary and homogeneous problems, where that is clearly not the case. (RDF’s come to mind) The response in my head is always the tounge in cheek “you can always compute something”. But I think at times there needs to be the candid “look somewhere else, possibly here” response, even if it is entirely LAMMPS unrelated. If not just to have somewhere to point in the archives when a misunderstanding is inevitably brought up again.

As for staying on-topic, I have been trying to follow your (and Steve’s) example, with some stumbles e.g. ^. Cheers!

Just to chip in along similar lines - thermophoresis (movement of molecules along temperature gradients) is a bit tricky, and isn’t terribly well understood. This is quite a nice review: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1750914/ , and it introduces some of the ways people typically characterise the motion of objects experiencing a temperature gradient.

Niall Jackson
PhD Student, Bresme Group (Computational Chemical Physics Section)
Department of Chemistry, Imperial College London

Two words from someone who’s in and out this forum periodically but is not a developer in any way. I celebrate Eric’s post on providing his expertise/comments to discuss a topic that marginally touches the main objective of the forum; i.e, lammps machinery functionality. I have witnessed some past posts where physical intuition has been key to identify subtle bugs in the code. I actually believe that posts like Eric’s above or Nail’s, have actually helped to make lammps even more popular. This is a community where people not only come to report bugs but to look for answers to scientific issues as well. Axel is probably the most committed person I’ve ever seen that promptly answers questions coming from all flanks. I do understand that under certain circumstances he or Steve or Aidan like to wave the “this is not a lammps Q” flag, yet, I would hope for this not to discourage people from sharing some of their expertise here at times, especially those who regularly do their best to participate and keep the ball running.
Carlos

Thanks for the information Eric and Niall.

I share a doctoral thesis ( D. Lüsebrink ) setting out in detail, how to simulate colloidal systems under a temperature gradient using a mesoscopic method . Although my intention is to make a simulation using an atomic solvent, this thesis suggests several important to consider , especially for calculating the coefficient of soret and it helps me get closer to answers some of the questions posed at the beginning of the thread Axel .

I share this information in case anyone has the same concern. http://kups.ub.uni-koeln.de/4410/1/thesis_published.pdf

the article:

http://iopscience.iop.org/0953-8984/24/28/284132

Cheers

I second this. Any post that educates, whether it’s directly LAMMPS-related

or not, is good. It’s also fine if someone posts, try this other MD code,

it can do that better.

Steve