On the Solution of the Poisson-Boltzmann Equation with Application to the Theory of Thermal Explosions

Abstract

The theory of thermal explosions originally proposed by Frank‐Kamenetzky has been the subject of a number of investigations. The critical condition of inflammability requires the solution of the nonlinear Poisson‐Boltzmann differential equation. For the case of a reaction vessel of cylindrical or spherical shape the solution was obtained by previous investigators by numerical integration of the equation. It is shown, however, in the following that the solutions can be obtained in terms of known functions.