Applying BEM to modelling of uptaking pollutants in clouds or fog drops

A one-dimensional coupled diffusion and chemical reaction steady-state problem in spherical geometry has been considered. This type of problem is often encountered in atmospheric chemistry when dealing with uptaking of gaseous pollutants in cloud or fog drops. A closed form fundamental solution of the governing equation has been obtained. Making use of this solution and following the standard BEM approach, the boundary value problem under consideration has been transformed into a nonlinear integral equation. The discretization of this equation resulted in a set of nonlinear algebraic equations solved by the Newton-Raphson solver. For specific, linear cases the results obtained have been compared with analytical solutions available in the literature. Good accuracy has been observed. Numerical examples dealing with two coupled nonlinear equations describing diffusion with chemical reaction of two species have been included.