AN INVESTIGATION OF PARTICLE SIZE CORRELATIONS AND THE EFFECT OF LIMITED MIXING IN BROWNIAN COAGULATION
Abstract
A precise description of particulate agglomeration in aerosol and hydrosol systems requires knowledge of the particle size distribution along with the total number concentration. An integrodifferential kinetic equation, known as the population balance equation (PBE) has been used successfully in the past to predict the evolution of particle size distributions; however, assumptions concerning the number of available pairs of particles cause it to be inaccurate when it is applied to small populations. Monte Carlo simulations are used to model agglomerating Brownian particles. Preliminary simulation results, along with an analysis of the relative time scales of mixing and agglomeration indicate that only a small number of particles should be considered for the population to be "well-mixed." The number of particles in a "well-mixed" volume is shown to remain substantially constant, even as agglomeration proceeds, because the mixing volume increases in size. A second Monte Carlo routine demonstrates the inaccuracies of the PBE for small, constant-sized populations. Results are compared to a new solution to the PBE based on the Method of Weighted Residuals. Deviations from the PBE arise because of a statistical correlation effect known as particle size correlations. If such effects are to be included in the analysis, the PBE must be replaced by a hierarchy of equations, known as product density equations, which are not naturally closed. Rather than attempting a solution to the complete hierarchy, an approximate closure technique is sought to produce a readily solvable system of equations. A closure hypothesis is selected from several alternatives based upon its limiting behavior and a preliminary evaluation using Monte Carlo simulation. The closure hypothesis is substituted into the product density equations and a solution is generated for both the constant number and the constant volume cases, again using the Method of Weighted Residuals. The solution agrees closely with the simulation results and provides an accurate and precise estimate of the effects of particle size correlations. The results indicate that particle size correlations will lead to a significant decrease in the rate of production of large particles in systems with volume fractions higher than 10('-4).
Degree
Ph.D.
Subject Area
Chemical engineering
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