Theory of the Spherical Diffusion Flame : The Effect of Atmosphere Depletion

A major uncertainty in the interpretation of data from spherical diffusion flame methods of measuring reaction rates has lain in the difficulty of estimating the effect of depletion of the atmosphere reactant. It is known that the exact treatment of this problem, assuming spherical, purely diffusive flow, leads to a nonlinear ordinary differential equation of the second order. An analytical solution of this equation is presented in a form conveniently applicable to experimental data. The correction is shown to depend on a parameter which is usually small. The solution is applied to the method of temperature pattern measurements, and a modified method of calculating rate constants from experimental data is proposed. The correction to the reaction rate constants previously determined by this method is shown to be small. The use of a wider range of experimental variables than heretofore is made possible.