Size effects of rarefied gas flows in nanochannels by simulations based on statistical surrogate model for atomistic collisions

In this paper, the problem of helium gas transport in graphene nanochannels is investigated by a multilevel approach coupling surrogate modeling and Monte Carlo simulations. Under the rarefaction condition, the Knudsen diffusion is the dominant gas flow regime, characterized by gas-wall collisions. Furthermore, at low temperatures, helium gas atoms can be adsorbed on the surface and move like Brownian particles. To address the problem, the collision data between gas atoms and wall surfaces in equilibrium state are first generated by molecular dynamics simulations. A general statistical surrogate model based on polynomial chaos expansion accounting for adsorption and surface diffusion is constructed. The model exploits the Langevin dynamics analogy to satisfy physical constraints on the velocity distribution, the decaying time-dependent velocity correlation, and time-dependent displacement behavior. The trained model is then used in Monte Carlo simulations to compute various transport quantities in long nanochannels. Numerical results from the Monte Carlo study show that the approach can capture the size effect on the diffusion coefficient and transmission probability. Without being limited to helium and graphene, the developed method can be applied to any gas and solid couple and the problem of construction of kinetic boundary conditions.