The decay of soot surface growth reactivity and its importance in total soot formation

Abstract

The empirical soot surface growth kinetics of Haynes and Wagner are reconciled to the acetylene kinetics of Harris and Weiner by including the decay of the surface reactivity. The empirical rate constant measured by Haynes and Wagner is the decay rate of the surface growth reactivity, not the surface growth rate itself. This rate has a value of 50–400 s −1 and appears to depend only on temperature, but not pressure and flame composition. This description of surface growth with coagulation but without particle inception predicts the spherule size in soot chains and a near-constant value of the total soot surface area concentration. An analytic expression for the volume fraction history indicates small discrepancies with Haynes and Wagner's empirical form. When the initial number density is high (>10 11 cm −3), the highly nonlinear dependence of the final volume fraction f v ∗ on the initial “inception” volume fraction f v 0 is predicted to be f ∗ 1 3 = (f 0) 1 3 + (f sg ) 1 3 , where f sg is dependent on measured kinetic parameters and is of the order 2 × 10 −8. Using this kinetic description it should be possible to extrapolate late volume fractions backward to give either initial volume fractions or number densities. Given this sensitivity, it will be important to understand the systematic dependences of inception soot concentrations.