InterPore2025

Probabilistic learning of gas wall interaction from molecular Dynamics simulations and applications to gas transport problems in nano micropores

22 May 2025, 14:45

15m

Oral Presentation (MS11) Microfluidics and nanofluidics in porous systems MS11

Speaker

Quy Dong To

Description

Modeling and characterizing gas-wall interactions at the atomic scale are crucial for understanding transport behavior in micro- and nanopores and for accurately simulating gas flows in porous materials. It is well known that gas displacement in extremely tight channels is complex and significantly influenced by adsorption/desorption physics and surface diffusion mechanisms at the boundary walls. In this work, the collisions of helium atoms with graphite plates in thermal equilibrium are simulated using Molecular Dynamics methods at various temperatures [1]. It is observed that at temperatures as high as 200 K, gas atoms reflect almost instantaneously, and pre- and post-collision velocities are strongly correlated. However, at lower temperatures, a significant proportion of gas atoms are adsorbed and move randomly on the surface before being desorbed. The velocity correlations are also weaker and reduced with temperature. A detailed analysis of the Potential Energy Surface (PES) and Mean Square Displacement (MSD) reveals a two-stage ballistic-diffusive behavior under weak energy barriers and low friction conditions. The velocity correlation coefficient, which is directly related to the tangential momentum accommodation coefficient (TMAC), is also determined, and an empirical relation between TMAC and temperature $T$ is proposed.

From the collision data, including particles' velocity, residence time, and surface displacement, a surrogate stochastic wall model is constructed using probabilistic learning approaches [2]. The model is designed to replace atomic walls by predicting the probability distribution of residence time $\tau$, surface displacements ${\mathrm{\Delta }}_x,{\mathrm{\Delta }}_y$, and post-collision velocities $v_x,v_y,v_z$ for a given pre-collision velocity $v_x^{\prime },v_y^{\prime },v_z^{\prime }$ in the form:
$(v_x,v_y,v_z,{\mathrm{\Delta }}_x,{\mathrm{\Delta }}_y,\tau )=f(v_x^{\prime },v_y^{\prime },v_z^{\prime },U)$
The latent gaussian variables $U$ are reduced unknowns representing the microstate of the solid walls at temperature $T$. The function $f$ is composed of orthogonal polynomials of random variables, whose parameters are determined by minimizing probalistic distance. Since the data is generated under equilibrium conditions, special attention is given to ensuring the equilibrium distribution of classical particle velocities and respecting the principle of time reciprocity. An example of a Monte Carlo simulation of Knudsen diffusion for gas particles traveling between two parallel walls using the stochastic wall model is presented.

[1] Magnico P., To Q.D. (2023) Collisions and diffusion of Helium gas in nanometric graphitic channel. International Journal of Heat and Mass Transfer, 214, pp.124371.
[2] Soize C., To Q.D. (2024) Polynomial-chaos-based conditional statistics for probabilistic learning with heterogeneous data applied to atomic collisions of Helium on graphite substrate. Journal of Computational Physics, 496, pp.112582.