Friction tensor for an ellipsoid enclosed in a rarefied gas

Abstract

This research renders calculations of rotranslational friction and diffusion tensors in a rarefied gas, considering both specular and diffuse reflection off ellipsoidal particles. Calculations were conducted in a spherical polar coordinate system, revealing the dynamic nature of these off-diagonal tensors. The tensor elements were determined analytically, intending to compute the surface integrals. All diagrams, and pictures of two-dimensional surfaces were obtained by the numerical integration process in MATLAB. Additionally, we performed calculations without using the time parameter and time derivatives in the relevant relations. Deviations from the state of spherical symmetry were observed in the results for an ellipsoid and show that the tensors are dynamic quantities. Therefore, it is necessary to provide average values. We established that the non-zero elements of the friction tensor for an ellipsoid represent the directions of linear momentum transfer. Also, the non-zero components of the diffusion tensor signify the extent of fluctuations in relevant momentum transfers in corresponding directions.