Interpretation of Optical Measurements of Flame Generated Particles

The dynamic equation for an aerosol undergoing simultaneous particle formation and coagulation is solved by the moment method. Solutions are obtained that quantify the evolution of the particle volume distribution function (PVDF) for both a size independent and a free molecular collision function. The solutions show that an equilibrium is rapidly established between the source and the coagulation terms and that the particle number concentration N is then proportional to the square root of the source strength. During the interval of equilibrium there is a widening of the PVDF, the moment ratio f(N) = D-3(3)/D-30(3), and other width parameters. These quantities may exceed the asymptotic values that apply in the absence of particle formation. The time evolution of the PVDF of soot particles in a laminar diffusion flame is derived using the profile of soot volume fraction that has been observed in recent in situ optical experiments. This analysis yields the evolution of f(N), which is necessary to determine the particle number concentration N from the optical data, and the geometric standard deviation sigma(g)(t) for the lognormal distribution function. The frequently used assumption that the soot aerosol is monodisperse (or possesses a constant value of sigma(g)) leads to highly distorted profiles of N vs t. We conclude that the optical experiment must be designed to provide a measure of f(N) (or sigma(g)) for the soot aerosol in flames if the values of N are to be derived with confidence.