FORMULAS FOR TEMPERATURE AND CONCENTRATION PROFILES AROUND TWO IDENTICAL EVAPORATING DROPS HEATED BY ELECTROMAGNETIC RADIATION

Abstract

Aim. We derive formulas by operator methods for the temperature and concentration profiles around two interacting identical aerosol drops heated by radiation and evaporating in the diffusion regime. Methodology. The temperature and concentration fields are represented as standard expansions in spherical functions, and the undefined coefficients of these expansions are considered as coordinates of vectors of an infinite-dimensional linear normed space. The search for the undefined coefficients is reduced to finding infinite-dimensional vectors from the boundary conditions by means of linear operators. Scalar quantities are represented as linear functionals defined on the infinite-dimensional linear normed space mentioned above. Results. Formulas for temperature and concentration profiles around two identical drops are obtained and corresponding graphs are presented. These graphs are compared with the graphs obtained by the method using the bipolar coordinate system. Research implications. Simple formulas are obtained for temperature and concentration profiles. When solving specific problems, calculation algorithms based on these formulas can be easily implemented in Excel.

Keywords

• aerosol drops
• evaporation of drops
• interacting drops