Fundamental Studies of Particle Growth and Structure During Powder Synthesis

Publication Reference: 
20-03
Author Last Name: 
Flagan
Authors: 
R C Flagan
Report Type: 
FRR
Research Area: 
Particle Formation
Publication Year: 
1993
Publication Month: 
05
Country: 
United States

Executive Summary

The primary objective of the Caltech program supported by IFPRI is to understand the dynamics of particles which do not coalesce immediately upon coagulation and, through that understanding, to guide the development of processes for production of particles with particular properties. Theoretical and experimental investigations of the dynamics of aggregate aerosols have been undertaken with IFPRI support. Following on our studies of the properties of agglomerate particles, we have developed models to describe the kinetics of agglomeration. The kinetics of agglomeration are determined by the mobilities of the agglomerate particles and by their collision cross sections. The lower density of agglomerates has competing effects on the coagulation kinetics &s compared with dense particles of equal mass: (i) the aerodynamic drag on the particles is increased due to the larger size of the particle of the same mass; (ii) the low density tends to increase the collision cross section of the agglomerate over that of the dense sphere. We have used fractal scaling concepts to evaluate the relationship between these measures of particle size and the particle structure.

The dynamics of aerosol formation and growth is well documented for particles that remain as dense spheres throughout their growth. We have generalized those models to account for aggregate structure, and have developed the first model for the collision frequency function that spans the entire range of particle Knudsen numbers and fractal dimensions. The particle size distribution is shown to approach an asymptotic form when the primary growth mechanism is coagulation, This asymptotic form is the so-called self-preseting particle size distribution. A dynamic exponent is defined that describes the rate of growth of the mean particle size. The dynamic exponent is shown to pass through a minimum in the transition regime, behavior that has not previously been described. Essential features of this asymptotic solution are observed experimentally, although direct comparison between experiment and theory is complicated by the transition between coalescing coagulation and agglomer&ion that took place in our experiments at about the same particle size as the transition between the free molecular and continuum size regimes.

A more complete description of aerosol agglomeration was made in numerical solutions to the coagulation equation using a modified sectional code. Comparison of the collision frequency functions of spheres and agglomerate particles reveals that the predominant effect is the increased collision cross section of the agglomerate, leading to a dramatic increase in the collision frequency of agglomerates as compared to dense particles of the same mass. Simulations that assume that particles coalesce completely up to a limiting size and do not coalesce at all beyond that size exhibit a broadening of the size distribution at that transitional size. Experimental evidence of that broadening is provided. The comparisons at this point can be considered only provisional in as much as direct experimental validation of the collision frequency function is still lacking.

Experimental studies have been conducted to explore a number of aspects of the evolution of aggregate aerosols. The structure-drag relationship has been explored by image analysis of transmission electron micrographs of mobility classified aggregate particles. For the low fractal dimensions of the aggregates studied (Df N 1.8), the drag on the particle scales well with the projected area. This result holds through most of the transition regime even though it is expected to be strictly valid only for particles much smaller than the mean free path of the gas molecules.

Structural rearrangements during sintering of aggregates have been explored by heat treating aggregate particles while they are still entrained in the carrier gas. Particles are observed to retain the appearance of fractal clusters of smaller primary particles throughout coalescence that leads to many primary particles from the original particle being incorporated into a single primary particle in the sintered agglomerate. This observation raises serious questions about the inference of mechanisms of particle growth from structure measurements alone.