Solution of inverse problems in population balances-II. Particle break-up

• Published in: Computers & chemical engineering Vol. 19; no. 4; pp. 437 - 451
• Main Authors: Sathyagal, A.N., Ramkrishna, D., Narsimhan, G.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 1995; Elsevier
• Subjects: Applications of mathematics to chemical engineering. Modeling. Simulation. Optimization; Applied sciences; Chemical engineering; Exact sciences and technology; Particle size; Similarity; Rupture; Numerical simulation; Liquid liquid; Grain size distribution; Modeling; Dispersion; Population balance; Drop; Inverse problem
• ISSN: 0098-1354; 1873-4375
• DOI: 10.1016/0098-1354(94)00062-S

A mathematical and computational procedure called the inverse problem is developed to extract quantitative information from transient particle size distribution measurements The population balance framework describes the evolution of these transient size distributions. This paper describes an inverse problem for the determination of the size specific breakage rates and daugher drop distributions from transient size distribution measurements when these distributions evolve to a “self-preserving” or similarity distribution. The experimental time scaled with respect to the timescale of breakage is used as the similarity variable. A test for the existence of similarity is developed. This test uses only the available transient size distribution data. The result of this test is also used to determine breakage rate information The determination of the daughter drop distribution is an ill-posed problem. The ill-posedness is overcome by using the property that the distribution is a monotone function. Analysis shows that the asymptotic behavior of the daughter drop distribution can be determined from the experimental similarity distribution. Incorporating this additional information into the solution strategy has resulted in significantly improved solutions of the inverse problem. The optimum solution is chosen such that the similarity distribution predicted using this solution has error of the same order of magnitude as the error in the experimental similarity distribution. Several examples of the inverse problem are outlined