Executive Summary
A first order model of the dynamics of pyrogenous fumes, based upon experimental and theoretical studies of the kinetics of particle growth and the structural rearrangements that occur following coagulation, suggests that the growth of nonagglomerated particles in aerosol reactors is best accomplished by dropping the temperature rapidly to quench coalescence before significant agglomeration occurs. Because of their larger collision cross sections, agglomerate particles coagulate more rapidly than do spheres of equal mass. As a result, once agglomerates begin to form, particle growth accelerates dramatically. Although agglomerate particles can be densified, the temperature would have to be increased significantly to do this, instead of decreasing continuously as occurs in most practical reactors.
Notably, the model predictions suggest that, for a given cooling rate, a high initial temperature will more effectively limit neck growth than will a lower one. The rate of decrease of the coalescence rate following the onset of agglomeration depends on the cooling rate and on the initial growth temperature. If the initial operating temperature is low enough that the coalescence time is comparable to the coagulation time, the coalescence time will increase only slightly fester than that for coagulation. Strong neck formation and hard agglomerates can then be expected. On the other hand, if the initial operating temperature is much higher so that coalescence is initially very rapid, the transition will occur much more abruptly. Neck growth within the first agglomerates to form will be reduced, and agglomerates will be more amenable to dispersion. These inferences require experimental testing. The proposed continuation of this project will focus on experimental definition of the bound between dense particle growth and agglomerate formation, and on quantifying the quench rate that is required to inhibit the formation of sintered agglomerates.
The classical model of neck development during sintering has been extended beyond the early stage of neck growth. Neck growth predicted using our model deviates significantly from that of the early- stage sintering model, raising serious questions about efforts to model the evolution of particle structure with sintering rates based on the classical model. Although this means that the model developed in this report can only be assumed to provide a qualitative picture of the transition, importance of the coupling of coagulation with coalescence is clear. Attempts at quantitative prediction of the structural evolution of pyrogenous fumes based upon the classical sintering time scales are, however, premature. Trace oxygen contamination of the silicon we have studied led to anomalous sintering behavior. Oxidation of the silicon surface would be expected to dramatically reduce the rate of surface diffusion. Neck growth predictions based upon the transport properties of pure silicon, but with surface diffusion eliminated, agree well with experimental observations. Thus, future work on the structural evolution of pyrogenous fumes must take the reaction atmosphere into account.
This report focuses on the theoretical interpretation of the results of our experimental program, and on defining the direction for future work. Experimental investigations aimed at obtaining quantitative measurements of the sintering of model agglomerates and at validating the models of the coagulation kinetics of agglomerate particles are near completion, and analysis of those experimental results is underway.