The Monte Carlo and Molecular Dynamics Simulation of Gas-Surface Interaction

A testing procedure and a program product for modeling gas-surface scattering process have been developed. Using the developed product the numerical simulation of the thermal transpiration phenomenon at free molecular conditions of the gas flow in channels with the use of different scattering kernels has been carried out. The surface structure influence on energy and momentum exchange in a gas-surface system has been studied by the use of Molecular Dynamics method. 1 Thermal Transpiration Phenomenon Study by Monte Carlo Method Realized for Different Gas-Surface Scattering Kernels The most well-known diffuse-specular scheme of the boundary conditions to the heat and mass transfer equations of rarefied gas dynamics developed by Maxwell is successfully used for the majority of practical calculations (see, for instance, [1]). But some experimental data and corresponding theoretical calculations based on this scheme come into conflict with each other. As an example, one of the results of such calculations affirms that the thermal transpiration phenomenon (or “thermo molecular pressure difference effect” as it appears in scientific papers) does not depend on the kind of the gas and the surface state [2]. Such result contradicts the rather reliable experiments, for instance [3]. Apparently, the diffuse-specular scheme is not suitable for the correct description of the gas-surface scattering process at the non-isothermal rarefied gas flow, the striking example of which is the thermal transpiration phenomenon. The use of the diffuse-specular scheme does not provide the dependence of scattering process on the gas molecule state that leads to contradiction between the theory and the experiment especially for non-isothermal gas flow. To eliminate such contradiction the boundary conditions that include certain data about the state of gas molecules interacting with the surface must be applied. Nowadays, besides the diffuse-specular scheme other boundary conditions based on scattering kernels developed by Epstein [4] and Cercignani-Lampis [5,6] are widely recognized. The mathematical forms of these kernels contain certain expressions where the velocity of a gas molecules incident on the surface and the surface temperature are included. The Cercignani-Lampis and the Epstein scattering kernels are based on a certain physical ground and they satisfy all the requirements established for a scattering kernel [7]. 144 S. Borisov, O. Sazhin, and O. Gerasimova To test the correctness of modeling the gas-surface scattering the program product that provides simulating the behavior of non-interacting molecules in finite space while changing the shape of the limited surface as well as the modeling method of the scattering process, the surface temperature distribution and the initial gas state has been developed. The free molecular version of the Monte Carlo direct simulation method [8] has been realized. The efficiency of the program product has been demonstrated on the example of reaching the equilibrium state of the gas in the bulbs of various forms at the temperature perturbation of the surface. On the base of this product the results that do not contradict the principal postulates of the gas kinetic theory have been achieved. This fact has initiated our interest to apply the developed approach for studying the thermal transpiration phenomenon in rarefied gas at nonisothermal conditions that meets the problem in description while using the scheme of boundary conditions based on the Maxwell scattering kernel. To understand the problem let us consider the free molecular stationary gas flow in cylindrical channel connecting two bulbs where the gas is in the equilibrium with the “hot” and the “cold” bulb at the temperature Тh and Тc accordingly. The main equation for the gas pressure reached in each bulb is