Inverse problems in agglomeration

Harold Arthur Wright, Purdue University

Abstract

Dispersed phase systems are common in science and engineering. Aerosols, dispersions, and emulsions are common examples. Such systems undergo two characteristic processes; breakup and agglomeration of dispersed phase particles. This thesis deals with agglomeration. An integrodifferential kinetic equation, known as the population balance equation (PBE) has been used previously to describe the transient behavior of agglomerating systems. The key input to the population balance equation is the agglomeration frequency. The agglomeration frequency is the probability per unit time that particles of two specific sizes agglomerate given that they are in the same unit volume. A mathematical and computational technique called the inverse problem is developed to extract the agglomeration frequency from measurements of the transient particle size distribution. This technique relies on a similarity transformation of the transient particle size distributions. An assumption about the number of particle pairs available for agglomeration, called the first order closure hypothesis, allows the population balance equation to be closed. The inverse problem procedure is able to determine if the first order closure hypothesis is a valid assumption. The conditions for the validity of the closure hypothesis are investigated. The inverse problem is applied to two agglomerating systems where physical models for the agglomeration frequency have been elusive. The first system is diffusion limited cluster cluster aggregatian (DLCCA). Computer simulations have been performed for DLCCA in two and three diminsions. It was found via the inverse problem that the agglomeration frequency increased for increases in the collision cross-section available for agglomeration in both cases. Liquid-liquid dispersions are commonly used for separations and/or reaction systems because the added interfacial area due to dispersion aids in mass transfer and chemical reaction rates. Transient coalesence experiments have been performed over a wide range of dispersed phase fractions and for two different impeller speeds. A similarity transformation of the experimental data is possible for most of the experiments performed. The coalescence frequency is obtained via the inverse problem. The coalescence frequency increases with the size of the drop pair, the dispersed phase fraction, and the impeller speed. The results are compared with previous models for the coalescence frequency.

Degree

Ph.D.

Advisors

Ramkrishna, Purdue University.

Subject Area

Chemical engineering

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