An extended scattering kernel formalism for multi-scale gas-surface dynamics
Authors:
Sabin-Viorel Anton,
Bernardo Sousa Alves,
Christian Siemes,
Jose van den IJssel,
Pieter N. A. M. Visser
Abstract:
Gas-particle interactions with non-absorbing surfaces are commonly described using the scattering-kernel formalism. In this framework, an operator $\mathbf{K}$ maps incident velocity distributions to reflected velocity distributions. The operator is self-adjoint and has norm $\lVert \mathbf{K} \rVert = 1$ in an $L^2$ space weighted by the three-dimensional Maxwell-Boltzmann distribution, and must…
▽ More
Gas-particle interactions with non-absorbing surfaces are commonly described using the scattering-kernel formalism. In this framework, an operator $\mathbf{K}$ maps incident velocity distributions to reflected velocity distributions. The operator is self-adjoint and has norm $\lVert \mathbf{K} \rVert = 1$ in an $L^2$ space weighted by the three-dimensional Maxwell-Boltzmann distribution, and must satisfy non-negativity, normalisation, and reciprocity. In standard formulations, $\mathbf{K}$ represents the aggregate effect of all gas-surface interaction mechanisms through a single operator, without distinguishing the physical scales at which these mechanisms occur. For gas scattering from a rough surface, however, it is advantageous to separate geometric effects associated with distinct roughness scales from the underlying thermochemical processes occurring at the atomic scale. We therefore introduce a roughness-based extension of the scattering-kernel formalism, in which a local kernel is successively lifted to larger scales via single- and multi-reflection operators associated with statistically defined surface morphologies. We derive sufficient conditions under which the resulting global kernels preserve reciprocity, normalisation, and non-negativity whenever these properties hold for the smallest-scale kernel. We further show that these constructions define operators on the space of scattering kernels, and establish the associated multi-scale composition laws that allow independent roughness contributions to be combined recursively. The resulting framework provides a general basis for modelling gas-surface scattering on rough surfaces with arbitrary scale decompositions.
△ Less
Submitted 25 June, 2026; v1 submitted 29 May, 2026;
originally announced May 2026.
A Wave Scattering Approach to Modelling Surface Roughness in Orbital Aerodynamics
Authors:
Sabin Viorel Anton,
Bernardo Sousa Alves,
Christian Siemes,
Jose van den IJssel,
Pieter N. A. M. Visser
Abstract:
The increasing density of space objects in low-Earth orbit highlights the critical need for accurate orbit predictions to minimise operational disruptions. One significant challenge lies in accurately modelling the interaction of gas particles with the surfaces of these objects, as errors in aerodynamic coefficient modelling directly impact orbit prediction accuracy. Current approaches rely on emp…
▽ More
The increasing density of space objects in low-Earth orbit highlights the critical need for accurate orbit predictions to minimise operational disruptions. One significant challenge lies in accurately modelling the interaction of gas particles with the surfaces of these objects, as errors in aerodynamic coefficient modelling directly impact orbit prediction accuracy. Current approaches rely on empirical models, such as those by Sentman and Cercignani-Lampis-Lord, incorporating one or two adjustable parameters typically calibrated with orbital acceleration data. However, these models fall short in capturing essential gas-solid interaction processes, including multiple reflections, shadowing, and backscattering caused by surface roughness. We present a novel, physics-based gas-surface interaction model that utilises electromagnetic wave theory to account for macroscopic effects of surface roughness on gas particle scattering distributions. This approach not only offers a more accurate representation of gas-surface interactions but also allows parameter determination through a combination of ground-based surface roughness measurements and molecular dynamics simulations at the atomic scale. The model validity is tested across the entire parameter space using a test-particle Monte Carlo method on a simulated rough surface. Furthermore, it successfully reproduces experimental results from the literature on the scattering of Argon and Helium from smooth and rough Kapton and Aluminium surfaces. Finally, we demonstrate the model's impact on aerodynamic coefficients for simple geometric shapes, comparing the results with those from the Sentman and Cercignani-Lampis-Lord models. This comparison reveals that inconsistencies previously observed between these models and tracking data for spherical satellites can be attributed to surface roughness effects, which our model effectively accounts for.
△ Less
Submitted 16 November, 2024;
originally announced November 2024.