Molecular dynamics modelling of gas-surface interactions

Abstract

The advancement of engineering fluid flow systems operating at the micro/nanoscale, alongside the exploration of ultra-low vacuum environments, presents unprecedented challenges and opportunities in the field of rarefied gas dynamics. In such scenarios, gas flows are no longer in quasi-thermodynamic equilibrium, necessitating a shift to a modelling approach that goes beyond standard continuum fluid dynamics. The fluid behaviour must then be modelled using the Boltzmann equation or a kinetic model equation, supplemented by boundary conditions that model gas–surface interactions (GSIs). It is to these GSIs that one can trace the origin of the drag and lift exerted by gas on bodies and the heat transfer between gas and walls.

Accordingly, GSIs determine the velocity slip and temperature jump at the surface, which are macroscopic manifestations of fluid non-equilibrium conditions and significantly influence the overall flow field. Furthermore, GSIs may be regarded as a bridge between the kinetic theory of gases and solid-state physics, accounting for the fluid flow inhomogeneity introduced by solid wall atoms. Despite this, the study of GSIs within the kinetic theory often needs a more direct connection with the properties of real walls. This thesis aims to bridge this gap, offering a detailed exploration of GSIs by considering the effects of surface characteristics like porosity, physisorption, and nanoscale roughness on gas scattering and transport phenomena. The use of soft, continuous Lennard-Jones fluids in molecular dynamics (MD) simulations enables the capture of the essential physics of real-world systems, providing a detailed insight into the complex interplay of gas and surface interactions.

The transport of gas inside organic/inorganic matter in underground geological reservoirs, important to shale extraction, introduces factors like porosity, adsorption, roughness, low-speed flows, elevated pressures and temperatures, differing significantly from the controllable metal surfaces typically investigated in GSI studies. This thesis begins with a systematic investigation of the scattering and transport process for methane molecules within a pore slit confined by two parallel walls composed of the organic matter called kerogen, found in shale. It is demonstrated that tight matrix porosities have a negligible effect on the timescale and lengthscale of the scattering process, consistent with the assumptions of conventional scattering kernels (SKs). Subsequently, the effectiveness of commonly used scattering models is evaluated by examining reflected velocity distributions. These evaluations indicate that although these models do not fully capture the scattering intricacies, especially at higher incident molecular speeds, the Maxwell model captures the observed scattered angular beam pattern and overall reflected velocity distribution most accurately. These aspects are more crucial for transport studies than merely modelling individual velocity component fluxes. Furthermore, a Maxwell model adjusted with a tangential momentum accommodation coefficient (TMAC) — nearing unity with increased surface roughness up to approximately 2 nm—sufficiently predicts velocity profiles and mass flow rates in moderately confined kerogen mesopores. Discrepancies between the Maxwell model and MD simulations are noted only in cases of highly rarefied transport, which are outside the typical scope of shale reservoir applications.

Although it is widely recognised that there is a layer of physically adsorbed gas adjacent to surfaces, the development of scattering models that incorporate adsorption has received relatively little attention. Neglecting the presence of adsorbed molecules oversimplifies the complexity of scattering dynamics since impinging gas molecules interact not only with wall atoms, but also with other gas molecules next to the surface. To address this problem, a new SK has been developed that considers the influence of physisorption, which results from van der Waals interactions, on the dynamics of molecules impinging on solid, smooth surfaces. This SK is a linear combination of the Cercignani–Lampis (CL) and Maxwell fully diffuse models, with the Langmuir adsorption isotherm serving as a weighting factor. The rationale behind this model is that the CL component is designed to account for the scattering process from a clean, smooth surface in thermal equilibrium, while the fully diffuse component accurately describes gas–gas interactions within an adsorbed gas layer. This proposed scattering model successfully replicates observed molecular scattering patterns, along with the prediction of momentum and energy accommodation coefficients (ACs) in the entire range of explored conditions.

Another elusive aspect of GSIs originates from nanoscale surface roughness or irregularities, attributed to the height variation of wall atoms on the order of a few nanometres. Significant research efforts have been devoted to understanding how these irregularities impact scattering dynamics and rarefied gas transport, but the emphasis has been predominantly on oversimplified geometrical constructions and is thus not general. To include more detailed surface irregularities, a SK for surfaces possessing random roughness has been developed, using a similar technique as the adsorption SK. Here, a linear combination of the CL and Maxwell fully diffuse models is proposed. The weighting coefficient is derived by making an analogy between wave scattering near surfaces and gas–surface scattering, conceptualising random roughness as wave-like distortions on flat surfaces. The resulting SK enables a quantitative relationship between ACs, the gas scattering patterns and random surface roughness, revealing how the thermal motion of wall atoms and nanoscale roughness influence complex fluid behaviour in GSIs. The accuracy of various SKs has been evaluated through high-fidelity MD simulations. It is demonstrated that the newly proposed SK achieves the best agreement with benchmark MD simulations across the range of tested systems with varied roughness, temperature, and gas–surface combinations.

Altogether, these results provide a physically grounded understanding of GSIs as the boundary condition in kinetic theory. They have significant implications for modern technological applications, such as designing micro/nanofluidic devices, engineering systems in low vacuum environments, and CO₂ sequestration or hydrogen storage in underground reservoirs.