Coalescence of Bubble Clusters Rising Freely in Low-Viscosity Liquids

MODELING COALESCENCE OF BUBBLE CLUSTERS RISING FREELY IN LOW-VISCOSITY LIQUIDS 

The mechanisms by which freely rising bubbles interact with each other in relatively low-viscosity liquids and, specifically, how they approach, contact, and coalesce or break up are important aspects of multi-phase flow. Coalescence and breakup can control the interfacial area and mass transfer rate in bubble columns and gas-sparged chemical and biological reactors. Bubble interaction is fundamental in two-phase flow instability that plagues boilers and oil and gas wells. But bubble interaction remains a relatively mysterious area. 

Good models for bubble swarm dynamics, coalescence and breakup rates, interfacial area transport, and bubble size distributions must be based on real physical phenomena. Bubbly flow instability, for example, has typically been treated as a 

The density and viscosity of the gas can be neglected in favor of the liquid properties, and the dynamic behavior of a single bubble can be correlated with three independent, dimensionless groups commonly defined as the Reynolds number, Eotvos number, and Morton number (Grace et ai, [1]). These are given, respectively, by 

Bubble shape can be correlated with some precision on a map of Re vs. Ed with M as a parameter [I]. Changes in bubble behavior and shape transitions in liquids of differing viscosities lead to the classification of liquids as high-M or low-M. The boundary between low-M and high-M liquids is approximately M = 4(10 ), where a local maximum in terminal velocity begins to appear as M increases [2]. 

---