# Nanoscale roughness effect on Maxwell-like boundary conditions for the Boltzmann equation

## Abstract

It is well known that the roughness of the wall has an effect on microscale gas flows. This effect can be shown for large Knudsen numbers by using a numerical solution of the Boltzmann equation. However, when the wall is rough at a nanometric scale, it is necessary to use a very small mesh size which is much too expansive. An alternative approach is to incorporate the roughness effect in the scattering kernel of the boundary condition, such as the Maxwell-like kernel introduced by the authors in a previous paper. Here, we explain how this boundary condition can be implemented in a discrete velocity approximation of the Boltzmann equation. Moreover, the influence of the roughness is shown by computing the structure scattering pattern of mono-energetic beams of the incident gas molecules. The effect of the angle of incidence of these molecules, of their mass, and of the morphology of the wall is investigated and discussed in a simplified two-dimensional configuration. The effect of the azimuthal angle of the incident beams is shown for a three-dimensional configuration. Finally, the case of non-elastic scattering is considered. All these results suggest that our approach is a promising way to incorporate enough physics ofmore »

- Authors:

- University of Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400 Talence (France)

- Publication Date:

- OSTI Identifier:
- 22598911

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Fluids; Journal Volume: 28; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 42 ENGINEERING; ACCIDENTS; APPROXIMATIONS; BEAMS; BOLTZMANN EQUATION; BOUNDARY CONDITIONS; CONFIGURATION; ELASTIC SCATTERING; GAS FLOW; INCIDENCE ANGLE; KERNELS; MORPHOLOGY; NANOSTRUCTURES; NUMERICAL SOLUTION; ROUGHNESS; THREE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS; WALLS

### Citation Formats

```
Brull, S., E-mail: Stephane.Brull@math.u-bordeaux.fr, Charrier, P., E-mail: Pierre.Charrier@math.u-bordeaux.fr, and Mieussens, L., E-mail: Luc.Mieussens@math.u-bordeaux.fr.
```*Nanoscale roughness effect on Maxwell-like boundary conditions for the Boltzmann equation*. United States: N. p., 2016.
Web. doi:10.1063/1.4960024.

```
Brull, S., E-mail: Stephane.Brull@math.u-bordeaux.fr, Charrier, P., E-mail: Pierre.Charrier@math.u-bordeaux.fr, & Mieussens, L., E-mail: Luc.Mieussens@math.u-bordeaux.fr.
```*Nanoscale roughness effect on Maxwell-like boundary conditions for the Boltzmann equation*. United States. doi:10.1063/1.4960024.

```
Brull, S., E-mail: Stephane.Brull@math.u-bordeaux.fr, Charrier, P., E-mail: Pierre.Charrier@math.u-bordeaux.fr, and Mieussens, L., E-mail: Luc.Mieussens@math.u-bordeaux.fr. Mon .
"Nanoscale roughness effect on Maxwell-like boundary conditions for the Boltzmann equation". United States.
doi:10.1063/1.4960024.
```

```
@article{osti_22598911,
```

title = {Nanoscale roughness effect on Maxwell-like boundary conditions for the Boltzmann equation},

author = {Brull, S., E-mail: Stephane.Brull@math.u-bordeaux.fr and Charrier, P., E-mail: Pierre.Charrier@math.u-bordeaux.fr and Mieussens, L., E-mail: Luc.Mieussens@math.u-bordeaux.fr},

abstractNote = {It is well known that the roughness of the wall has an effect on microscale gas flows. This effect can be shown for large Knudsen numbers by using a numerical solution of the Boltzmann equation. However, when the wall is rough at a nanometric scale, it is necessary to use a very small mesh size which is much too expansive. An alternative approach is to incorporate the roughness effect in the scattering kernel of the boundary condition, such as the Maxwell-like kernel introduced by the authors in a previous paper. Here, we explain how this boundary condition can be implemented in a discrete velocity approximation of the Boltzmann equation. Moreover, the influence of the roughness is shown by computing the structure scattering pattern of mono-energetic beams of the incident gas molecules. The effect of the angle of incidence of these molecules, of their mass, and of the morphology of the wall is investigated and discussed in a simplified two-dimensional configuration. The effect of the azimuthal angle of the incident beams is shown for a three-dimensional configuration. Finally, the case of non-elastic scattering is considered. All these results suggest that our approach is a promising way to incorporate enough physics of gas-surface interaction, at a reasonable computing cost, to improve kinetic simulations of micro- and nano-flows.},

doi = {10.1063/1.4960024},

journal = {Physics of Fluids},

number = 8,

volume = 28,

place = {United States},

year = {Mon Aug 15 00:00:00 EDT 2016},

month = {Mon Aug 15 00:00:00 EDT 2016}

}