On the Breakage of Liquid−Liquid Dispersions in Turbulent Pipe Flow:  Spatial Patterns of Breakage Intensity

Abstract

The breakage of droplets in turbulent pipe flow is a subject of great technological interest. The purpose of this work is to take advantage of state-of the-art theoretical developments and obtain quantitative predictions enhancing our physical understanding of this problem. From this perspective, the subject of the “exact” solutions to an appropriate mathematical model, being recently an issue in the literature, is clarified. Furthermore, the simplest possible mathematical model of the breakage process is derived that retains the complete process parameter dependencies. To implement the model, an appropriate algebraic approach is proposed for the prediction of the radial profiles of key turbulent flow field parameters. This mathematical model adequately relates the breakage pattern in the pipe with the operating process parameters. The results suggest that droplet breakage occurs almost exclusively in an annular region at the periphery of the pipe. Droplets larger than a certain critical size initially have a tendency to break quite rapidly in that region, whereas turbulent diffusion seems to be comparatively slow and cannot spread the fragments into the bulk. This interplay of breakage and diffusion mechanisms seems to lead to initially nonuniform lateral droplet number concentration profiles with rather strong axial (or equivalent time) dependence, over distances of practical significance for process plants. This work clearly suggests that the often-made assumption of uniform conditions in the pipe cross section, regarding size distribution of the droplets that are undergoing breakage, should be reconsidered.

A CFD-based simulation study of a large scale flocculation tank for potable water treatment

“…That is, the g particle size is about 280 m (measured particles at the outlet of flocculation tank) whereas the f particle size is in most cases smaller than 100 m (estimated from the simulations). Employing the simplest of the methods of moments, the so-called monodisperse approximation (which have been proved useful for engineering calculations [25]) the function f can be approximated as f(x) = Nı(x − x o ) where ı is the Dirac delta function, N is the total fresh particles number concentration, x o is the average volume of these particles defined as =M f /N where M f is their total volume concentration (volume fraction). The corresponding volume fraction of the mud particles is denoted M g and it is the only needed quantity related to g(x).…”

Topics in Multiphase and Multicomponent Systems

“…Rozentsvaig (1981) pointed out that the contribution of viscous shear may be significant to droplet breakage in pipe flows, and he modified the model in an attempt to reconcile it with the published experimental data. It has been observed by a number of investigators, including Kostoglou and Karableas (2007) that a "stable" droplet size may not really exist. Recall that the Kolmogorov microscale is given by η = (ν 3 /ε) 1/4 and the corresponding velocity scale is v(η) = (εν) 1/4 .…”