Using maximum entropy, Gamma, Inverse Gaussian and Weibull approach for prediction of drop size distribution in a liquid–liquid extraction column

Abstract

In this study, drop size distribution and Sauter mean drop diameters were measured and correlated under operating variables and physical properties of the systems using a 113mm diameter Kühni column. Three systems including toluene-water, n-butyl acetate-water and n-butanol-water were experimented in this column. The countercurrent flow pattern of the liquid phases was characterized regarding the Sauter mean drop diameter and drop size distribution; a photographic method was used to assess drop sizes. The following operating variables were studied: rotor speed, flow rate of both liquid phases and interfacial tension. The drop size distribution and Sauter mean drop diameter were found to depend largely on the rotor speed and interfacial tension, albeit, only partially dependent on the phase velocities. The maximum entropy principle and the conventional probability distribution functions (Gamma, Inverse Gaussian, Weibull) have already been applied to estimate the drop size distribution. Experimental results show that the maximum entropy function describes the drop size distribution better than the conventional probability distribution functions for three systems in a Kühni column extractor. An empirical correlation is proposed for the estimation of the Sauter mean drop diameter. The acquired information would be useful in design of liquid–liquid extraction columns.