# Poiseuille flow by LAMMPS

## Summary:

I try to model Poiseuille flow of Argon gas confined between two parallel Platinum plates. However, I am not able to obtain the density of Ar at the end of my simulation. So, probably, I am doing something wrong and I need help to calculate lattice parameter.

## Main Question or Discussion Point

Hello everyone. I am newbie at MD. I started with Poiseuille flow.

I try to model 3D Poiseuille flow of Argon gas confined between two parallel Platinum plates by using LAMMPS. I have one reference paper, as given in  below. I built my Platinum structure correctly and I placed Ar atoms and run my simulation. At the end of simulation, I checked the density and it was totally wrong. I suspect that, I am not able to build sufficient number of atoms in my model. I try to use equations given below to obtain number of atoms but I couldn't decide the number of Ar atoms in my model, still. So, I need your help.

In the paper, they obtain the number of atoms by using Knudsen number. So, from the definition of Knudsen,

$$Kn = {\lambda \over D}$$

and

$$\lambda = {1 \over \sqrt{2} \Pi d^2 {n_0}}$$

where ## {n_0} ## is bulk number density. The two things that I know are D, which is 103 Angstrom and the bulk density of Argon, which is 1.6 ## kg \over {m^3} ## .

I want to build Ar atoms using lattice fcc command of Lammps and for that, I need lattice parameter. How can I calculate it and match the number of atoms that I expect and that I get from Lammps?

I would be very happy if you can help me which means a lot for me as I am stuck at this point.

The reference that I use:

 https://doi.org/10.1080/15567265.2016.1215364

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anuttarasammyak
Gold Member
Usual formula for mean free path is
$$\ell ={\frac {k_{\text{B}}T}{{\sqrt {2}}\pi d^{2}p}},$$
where ##k_B## is the Boltzmann constant. Comparing it with your fomula it seems
$$n_0=\frac{p}{k_B T}=\frac{N}{V}$$
Does it meet your "bulk density" though its dimension is ##L^{-3}## number density not ##ML^{-3}## mass density?

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