Nonequilibrium nonclassical phenomena in regions with membrane boundaries

Abstract

In the present paper, we consider a number of problems related to nonclassical transport phenomena in gas flows in regions with membranes. Our simulations focus on complex flows that might be of interest given the current trends in developing new membrane technologies. The methodological basis of this study is numerical modeling within the framework of solving the Boltzmann equation by various methods. Comparison between direct methods for solving the Boltzmann equation and the direct Monte Carlo modeling makes the assessment of the potential of both methods and better estimation of the accuracy of calculations possible. Flows through one or two consecutive membranes are considered for the classes of one-dimensional (1D) and two-dimensional (2D) problems. Several approaches to modeling thin membranes are discussed. Supersonic 2D flows in rectangular regions are considered. The results obtained confirm the assumptions of the 1D model of the membrane with additional explanation. The effects of nonclassical transfer are shown in 1D and 2D cases.