On evaporation of a spherical particle at arbitrary Knudsen numbers

Abstract

The description of drop growth in certain devices or under natural conditions (e.g., in clouds), as well as of thermophoresis and diffusiophoresis phenomena, needs a quantitative theory capable of treating the gas flow around a particle immersed in gas aerosol in a wide range of Knudsen numbers. This theory must be based on solving the Boltzmann kinetic equation. To date, there exists a number of approaches related to solving the Boltzmann equation for arbitrary Knudsen numbers. Among them, we note the Lees method [1, 2] with certain modifications [3, 4] and a method based on solving integro-moment equations by the variational Bubnov–Galerkin method [5–7]. Each of these methods have advantages and shortcomings. For example, the Lees method describes gas flows at large Knudsen numbers (Kn @ 1) well but fails at small Knudsen numbers (Kn ! 1). In the intermediate range of Knudsen numbers (Kn ~ 1), the accuracy of the method is, generally speaking, unknown. The integro-moment Bubnov–Galerkin method is variational and makes it impossible to find the distribution function. In this study, we use the method proposed previously in [8] for solving the Boltzmann equation at arbitrary Knudsen numbers. This method can be considered a natural generalization of the method of half-space moments with allowance for the ideas applied in the Lees method [1, 2]. The essence of the method is the following. A gas flow is described by a distribution function that has a discontinuity in the velocity space (as in the method of half-space moments [9]). However, as in the Lees method, the discontinuity takes place in the influence cone (Fig. 1) rather than in the half-plane vn = 0 (vn is the molecule velocity component normal to the particle surface). The procedure of constructing a system of moment equations is similar to the method of halfspace moments [9]. Thus, the method proposed com-