Self-similarity in drop break-up phenomena in liquid-liquid dispersions: Identification of break-up functions by inverse problem approach

Arun Nagaraju Sathyagal, Purdue University

Abstract

Two phase liquid dispersions are used in many engineering operations such as liquid-liquid extraction and multiphase reactions. Good control of the drop size distribution is required to optimize these operations. To achieve this control requires a good understanding of the underlying breakage and coalescence phenomena. This work focuses on the process of drop breakage and uses the population balance framework to describe the evolution of transient size distributions undergoing breakage. A mathematical and computational procedure called the inverse problem is developed to extract quantitative information on breakage rates and daughter drop distributions from transient size distribution measurements when these distributions evolve to a similarity distribution. The experimental time scaled with respect to the timescale of breakage is used as the similarity variable. Since the experimental data are not known a priori to be self-similar, a test for the existence of similarity is developed using only the available experimental data. The result of this test is also used to determine the breakage rate. The determination of the daughter drop distribution is an ill-posed problem. The ill-posedness is overcome by using the monotonicity property of the distribution. Analysis shows that the asymptotic behavior of the daughter drop distribution can be determined from the similarity distribution. Incorporating this additional information into the solution strategy has resulted in significantly improved solutions of the inverse problem. Transient breakage drop size distributions in stirred dispersions have been experimentally measured. The transient distributions show self-similar behavior, enabling the determination of the breakage functions via the inverse problem approach. The results show that the breakage rate is not a power law function of drop size. The breakage rate increases with drop size and stirrer speed while decreasing with interfacial tension and dispersed phase viscosity, though the dependence on viscosity is weaker than on the other variables. The daughter drop distribution is relatively insensitive to stirrer speed and interfacial tension. However, as the drop viscosity increases, the breakage becomes more erosive, leading to a broader size distribution of daughter drops. Generalized correlations for the breakage functions have been developed. Models for the breakage functions are compared with the results from this study.

Degree

Ph.D.

Advisors

Ramkrishna, Purdue University.

Subject Area

Chemical engineering

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