Transfer matrices and solution of the heat-mass transfer problem for aerosol clusters in a rarefied gas medium by the Monte Carlo method

Abstract

The form of the decomposition of summands in Neumann series and the general solution to a linear integral equation based on separation of variables are considered under some assumptions on the properties of the integral transform. It is shown that one can reduce the order of the problem. Special transfer matrices are proposed for estimation of functionals. Based on weighted Monte Carlo methods and the use of transfer matrices, an algorithm for the calculation of molecular heat-mass transfer in an aerosol cluster is constructed in the approximation of free molecular gas kinetics. The cluster exists in a rarefied gas medium and, in the general case, absorbs radiation in the visible and infrared wave ranges. The algorithm allows one to compute the molecular heat transfer, photophoretic forces and their momenta, the four tensors describing the viscous forces and their momenta, and also the relationship between the translatory and rotatory motion of the cluster under an approximation linear with respect to the translatory and rotatory velocities of the system. The results of the application of the developed algorithms to the analysis of the influence of gravito-photophoresis on aerosol stratification in the stratosphere and mesosphere of the Earth are discussed as well.