Numerical simulations of gas-dynamic conductivity of microchannels with allowance for their surface structure

Abstract

The effect of the microchannel surface structure on the free-molecular gas flow is studied by the testparticle method. Simulations are performed for channels whose surface either is obtained by means of statistical modeling or is reconstructed from the data of atomic-force microscopy of real surfaces. Dependences of monochromatic molecular beam scattering on the angle of incidence and the average height of microscopic roughness elements on the surface are considered. It is demonstrated that the method developed allows one to obtain the distribution function for particles reflected from a rough surface and to use it in the boundary conditions in problems of rarefied gas dynamics.Key words: rarefied gas flow in microchannels, Monte Carlo test-particle method, gas-surface interaction, scattering indicatrices, atomic-force microscopy.Introduction. In solving gas-dynamic problems associated with re-entry of flying vehicles into the upper atmospheric layers or with gas flows in microscale or nanoscale devices, one should take into account the parameters characterizing the structure and chemical composition of the surface. Numerous experimental studies show that the surface structure, its temperature, and other factors exert a significant effect on scattering of rarefied gas molecules and, as a consequence, on the gas-dynamic drag and heat transfer in the gas-solid system [1].One important component of the model of gas dynamics in external and internal flows are the boundary conditions for the Boltzmann equation, which imply that the distribution function of gas molecules reflected from the surface is available in an analytical form. This function depends on many characteristics of the gas and the surface, and also on thermodynamic parameters of the system as a whole. One factor exerting a significant effect on energy and momentum transfer in the gas-solid system is physical inhomogeneity (roughness) of the surface.Because of the lack of information about the surface structure and its role in gas-solid interaction, approaches with the use of absolutely smooth surfaces or extremely simple roughness models are usually used [2]. The influence of the surface structure on the free-molecular gas flow in cylindrical channels was studied in experiments [3,4].The development of methods of computer modeling and the use of new experimental technologies, in particular, scanning probe microscopy, allow certain progress to be achieved in numerical simulations of gas scattering on rough surfaces and in the description of rarefied gas flows in channels with the surface structure corresponding to conditions of physical experiments [5][6][7].The use of atomic force microscopy allows one to obtain high-resolution three-dimensional topograms. The thus-obtained digitized surface is an array whose elements contain the coordinates of each point of the surface of the examined sample. In the present work, we used the coordinates of 160 thousand points on the surface of a 20 × 20 μm silicon single crystal. In the course of studying the specified...

Gas Damping in Capacitive MEMS Transducers in the Free Molecular Flow Regime

“…In reality, however, the etched surfaces of a capacitive transducers will exhibit some amount of roughness and scalloping. Several analyses [20,21] suggest that these surface properties can slightly increase τ. When the scalloping profile that results from the fabrication process is known, it can be added to the simulation geometry to improve the accuracy of the estimates for τ at the cost of added model complexity.…”