Anisotropic scattering kernel and temperature jump at the wall

Dadzie, K. and Meolans, J.G. (2004) Anisotropic scattering kernel and temperature jump at the wall. In: 24th International Symposium on Rarefied Gas Dynamics, Bari, Italy, 1900-01-01. (

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We present a model of scattering kernel for the boundary conditions of the Boltzmann equation for unstructured molecules. The proposed scattering kernel is based on an anisotropic accommodation argument. Three parameters are used to characterize the influence of each direction. Contrary to the previous models of scattering kernel using arbitrary constant, the three parameters involved in this model are shown to be the real accommodation coefficients of the three momentum components. First, in order to clarify the physical consistency of the new approach, the new scattering kernel is derived from a phenomenological criticism of the first form of the scattering kernel proposed by Maxwell; then the same result is established from an analytic approach based on the spectral nature of the linear integral operator associated to the scattering kernel problem. As a result, the model provides a correct form of scattering kernel to describe an anisotropic surface. Finally using this surface modelling we establish a temperature jump at the wall which involves influence of the surface anisotropy and of the gas viscous heating at the wall in novel terms. These additional terms should exert a significant influence in some rarefied gas phenomena occurring in micro channel flows or in atmospheric re-entries of spatial engines.