Gas-surface scattering models for particle fluid dynamics: a comparison between analytical approximate models and molecular dynamics calculations

Thermal Energy Transfer between Helium Gas and Graphene Surface According to Molecular Dynamics Simulations and the Monte Carlo Method

The scattering of gases on solid surfaces plays a vital role in many advanced technologies. In this study, the scattering behavior of helium on graphene surfaces was investigated, including the thermal accommodation coefficient (TAC), outgoing zenith angle of helium, bounce number, and interaction time. First, we performed molecular dynamics simulations to describe the incident angle-resolved behaviors, and showed that the scattering is highly dependent on the zenith angle of incident helium but insensitive to the azimuthal angle. The contribution of the normal velocity component of the incident helium dominated the energy transfer. The nonlinear relationship of the parameters to the zenith angle of the incident helium could be suppressed by increasing the graphene temperature or decreasing the speed of the incident helium. Subsequently, the scattering performance considering all gas molecules in the hemispherical space was evaluated using the Monte Carlo method with angle-resolved results. The result showed that the TAC, its nominal components, and the zenith angle of the scattered helium increased with higher speeds of incident helium and lower temperatures of graphene. This study should provide a fundamental understanding of energy transfer between gas and two-dimensional materials and guidelines to tune the scattering behavior between them.

Theoretical derivation of slip boundary conditions for single-species gas and binary gas mixture

A theoretical derivation of slip boundary conditions for single-species gas and binary gas mixture based on two typical gas-surface scattering kernels is presented. If the Maxwell model is assumed, then the derived slip boundary conditions are consistent with the previous conclusions. Considering the limitation of the Maxwell model in describing the complexity of gas-surface scattering behavior, we further perform theoretical analyses based on the Cercignani-Lampis-Lord (CLL) model, where separate accommodation coefficients in the tangential and normal directions are defined. Our results demonstrate that for both single-species gas and binary gas mixture, the velocity slip predicted by the CLL model is only dependent on the tangential accommodation coefficient, while the temperature jump determined by the CLL model is related to the accommodation coefficients in both tangential and normal directions. To account for the collision effect in the Knudsen layer, we propose to add correction terms to the theoretical models, and the corrected slip coefficients agree well with the previous numerical results obtained by solving Boltzmann equation for single-species gas. Moreover, the slip boundary conditions for binary gas mixture based on the CLL model are determined theoretically for the first time. Since at most situations the tangential and normal accommodation coefficients are not equal, the temperature jump boundary condition based on the CLL model is expected to give more accurate predictions about temperature distribution and heat flux at the boundaries, particularly for hypersonic gas flows with strong nonequilibrium effect.

Modeling rarefied gas-solid surface interactions for Couette flow with different wall temperatures using an unsupervised machine learning technique

In rarefied gas flows, discontinuity phenomena such as velocity slip and temperature jump commonly appear in the gas layer adjacent to a solid boundary. Due to the physical complexity of the interactions at the gas-solid interface, particularly in the case of systems with local nonequilibrium state, boundary models with limited number of parameters cannot completely describe the reflection of gas molecules at the boundary. In this work, the Gaussian mixture (GM) model, which is an unsupervised machine learning technique, is employed to construct a statistical gas-solid surface scattering model based on the collisional data obtained from molecular dynamics (MD) simulations. The GM model is applied to study Couette flow for different inert gases (Ar and He) confined between two parallel infinite gold walls at different temperatures. A direct comparison between the results obtained from the GM model and the Cercignani-Lampis-Lord (CLL) scattering kernel against the MD collisional data in terms of the distribution of the predicted postcollisional velocities, and accommodation coefficients has shown that the results from the GM model are an excellent match with the MD results outperforming the CLL scattering kernel. As an example, for He gas, while the predicted energy accommodation coefficient by the CLL model is more than two times higher than the MD predictions, the value computed by the GM model is in excellent agreement with the MD results. This superior performance of the GM model confirms its high potential to derive a generalized boundary condition in systems encountered with highly nonequilibrium and complex gas flow conditions.

Kinetic model of adsorption on crystal surfaces

A kinetic theory model describing physisorption and chemisorption of gas particles on a crystal surface is introduced. A single kinetic equation is used to model gas and physisorbed particles interacting with a crystal potential and colliding with phonons. The phonons are assumed to be at equilibrium and the physisorbate-gas equation is coupled to similar kinetic equations describing chemisorbed particles and crystal atoms on the surface. A kinetic entropy is introduced for the coupled system and the H theorem is established. Using the Chapman-Enskog method with a fluid scaling, the asymptotic structure of the adsorbate is investigated and fluid boundary conditions are derived from the kinetic model.

Performance evaluation of Maxwell and Cercignani-Lampis gas-wall interaction models in the modeling of thermally driven rarefied gas transport

A systematic study on the performance of two empirical gas-wall interaction models, the Maxwell model and the Cercignani-Lampis (CL) model, in the entire Knudsen range is conducted. The models are evaluated by examining the accuracy of key macroscopic quantities such as temperature, density, and pressure, in three benchmark thermal problems, namely the Fourier thermal problem, the Knudsen force problem, and the thermal transpiration problem. The reference solutions are obtained from a validated hybrid DSMC-MD algorithm developed in-house. It has been found that while both models predict temperature and density reasonably well in the Fourier thermal problem, the pressure profile obtained from Maxwell model exhibits a trend that opposes that from the reference solution. As a consequence, the Maxwell model is unable to predict the orientation change of the Knudsen force acting on a cold cylinder embedded in a hot cylindrical enclosure at a certain Knudsen number. In the simulation of the thermal transpiration coefficient, although all three models overestimate the coefficient, the coefficient obtained from CL model is the closest to the reference solution. The Maxwell model performs the worst. The cause of the overestimated coefficient is investigated and its link to the overly constrained correlation between the tangential momentum accommodation coefficient and the tangential energy accommodation coefficient inherent in the models is pointed out. Directions for further improvement of models are suggested.

Computation of accommodation coefficients and the use of velocity correlation profiles in molecular dynamics simulations

For understanding the behavior of a gas close to a channel wall it is important to model the gas-wall interactions as detailed as possible. When using molecular dynamics simulations these interactions can be modeled explicitly, but the computations are time consuming. Replacing the explicit wall with a wall model reduces the computational time but the same characteristics should still remain. Elaborate wall models, such as the Maxwell-Yamamoto model or the Cercignani-Lampis model need a phenomenological parameter (the accommodation coefficient) for the description of the gas-wall interaction as an input. Therefore, computing these accommodation coefficients in a reliable way is very important. In this paper, two systems (platinum walls with either argon or xenon gas confined between them) are investigated and are used for comparison of the accommodation coefficients for the wall models and the explicit molecular dynamics simulations. Velocity correlations between incoming and outgoing particles colliding with the wall have been used to compare explicit simulations and wall models even further. Furthermore, based on these velocity correlations, a method to compute the accommodation coefficients is presented, and these newly computed accommodation coefficients are used to show improved correlation behavior for the wall models.