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Lattice Boltzmann simulation of the rise and dissolution of two-dimensional immiscible droplets

Phys. Fluids 21, 103301 (2009); doi:10.1063/1.3253385

Published 22 October 2009

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Cheng Chen and Dongxiao Zhang
The Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, California 90089, USA
We used a coupled multiphase lattice Boltzmann (LB) model to simulate the dissolution of immiscible liquid droplets in another liquid during the rising process resulting from buoyancy. It was found that there existed a terminal rise velocity for each droplet, and there was a power law relationship between the Eötvös (Eo) number and the terminal Reynolds (Re) number. Our simulation results were in agreement with the empirical correlation derived for predicting bubble rise. When more than two identical droplets rose simultaneously in a close proximity, the average terminal rise velocity was lower than that of a single droplet with the same size because of the mutual resistant interactions. The droplet trajectories at the noncentral positions were not straight because of the nonzero net horizontal forces acting on the droplets. The Damkohler (Da) and Peclet (Pe) numbers were varied to investigate the coupling between droplet size, flow field, dissolution at the interface, and solute transport. For a given Pe, increasing Da led to a higher dissolution rate. For a given Da, increasing Pe led to a higher dissolution rate. For a large Da and a small Pe, the process near the interface was diffusion limited, and the advective flow relative to the droplet resulting from droplet rise was unable to move the accumulated solute away from the interface quickly. In this case, it was favorable to split the single droplet into as many small ones as possible in order to increase the interface area per unit mass and consequently enhance the whole dissolution process. For a small Da and a large Pe, the process was dissolution limited near the interface. The mass of accumulated solute near the interface was little, so the advective flow at the top side of the droplet was able to clean the solute quickly. In this case it was favorable to keep the droplet as a single one in order to obtain a high rise velocity and consequently enhance the whole dissolution process. By studying the coupling between Da and Pe, we qualitatively proposed to construct a Da-Pe phase plane and found the interface dividing the plane into regions 1 and 2. Region 1 was the collection of points where it was favorable to break down the droplet into as many small ones as possible in order to accelerate dissolution, while region 2 was the collection of points where it was favorable to keep the droplet in a single one for the same purpose. Based on our LB simulations, we found that the interface was an increasing function of Pe. Region 1 was the portion above the interface, while region 2 was the portion below it. In real applications, if both Pe and Da are obtained, it will be easy to judge whether it is favorable to break down the droplet or not in order to accelerate dissolution by checking whether (Pe, Da) falls in region 1 or 2. ©2009 American Institute of Physics
History: Received 20 June 2009; accepted 30 September 2009; published 22 October 2009
Permalink: http://link.aip.org/link/?PHFLE6/21/103301/1
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1070-6631 (print)   1089-7666 (online)
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