Subscriber access provided by UNIVERSITY OF TOLEDO LIBRARIES
Interfaces: Adsorption, Reactions, Films, Forces, Measurement Techniques, Charge Transfer, Electrochemistry, Electrocatalysis, Energy Production and Storage
Flow Regimes and Transition Criteria during Passage of Bubbles through a Liquid-Liquid Interface Travis S Emery, Pruthvik A Raghupathi, and Satish G. Kandlikar Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b01217 • Publication Date (Web): 21 May 2018 Downloaded from http://pubs.acs.org on May 24, 2018
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
Flow Regimes and Transition Criteria during Passage of Bubbles through a Liquid-Liquid Interface Travis S. Emery1, Pruthvik A. Raghupathi2, Satish G. Kandlikar 1,2,* 1
Microsystems Engineering Department, Rochester Institute of Technology, 76 Lomb Memorial
Dr., Rochester, NY 14623, U.S.A. 2
Mechanical Engineering Department, Rochester Institute of Technology, 76 Lomb Memorial
Dr., Rochester, NY 14623, U.S.A.
ACS Paragon Plus Environment
1
Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 32
Abstract
The passage of a single bubble or a stream of bubbles through a liquid-liquid interface is a highly dynamic process that can result in a number of different outcomes. Previous studies focused primarily on a single bubble and single flow regime, and very few investigations have considered bubble streams. In the present work, six different liquid combinations made up of water, ethanol, a perfluorocarbon liquid, PP1, and one of three different viscosity silicone oils are tested with air bubbles from 2-6 mm in diameter rising between 5-55 cm/s. Both single bubbles and bubble streams varying in frequency from 5-40 bubbles/s are tested. High-speed imaging is used to capture and classify the flow regimes associated with each flow type. Four different flow regimes are identified for single bubble passage and six are found for bubble stream passage. Based on theoretical considerations, non-dimensional numbers are developed for characterizing the flow regimes and maps are generated that distinguish them and define flow regime transitions.
ACS Paragon Plus Environment
2
Page 3 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
Introduction The passage of a single bubble or a bubble stream through a liquid-liquid interface is a highly dynamics process that has relevance in numerous industrial applications. Previous studies on this phenomenon focus on their importance in metallurgical processes1–9, chemical processes such as liquid-liquid extraction1,6,8–11, nuclear reactor safety2,3,6, biodiesel production12, and direct contact heat transfer8,10. Hollow metallic shells produced from this process also have many applications such as solid fuels, structural material, pharmaceuticals, explosives, etc13. Although bubble passage through a liquid-liquid interface has significant relevance to many industrial applications, it remains an understudied area in need of further exploration. A brief overview of bubble passage through a liquid-liquid interface is first presented in this section. Consider two immiscible liquids of different density in stratified layers with the heavier liquid as the bottom layer. When a bubble is introduced into the bottom liquid, it will rise due to the buoyancy force. It will continue to increase in rise velocity until the growing drag force balances out the buoyancy force. Eventually, the bubble will impact the horizontal interface between the liquid layers. When the bubble collides with the interface, interfacial tension resists the bubble passage and a thin liquid film is formed between the bubble and the interface. At this point, there are a number of possible outcomes which depend on the system parameters and properties of the two liquids and the liquid combination. Previous studies have shown that the bubble may become trapped at the interface or pass through with some of the bottom liquid entrained around and/or behind the bubble6. A similar process is seen in bubble coalescence in which the outcome is determined based on the thinning of the liquid film between the bubbles, and the expense of the kinetic energy to increase the free energy of the system via an increase in the bubbles surface area due to deformation14. For bubble passage through a
ACS Paragon Plus Environment
3
Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 4 of 32
liquid-liquid interface, the kinetic to free surface energy transfer would stem from bubble deformation and increased interfacial area between the liquids. The thinning rate of the liquid column entrained behind the bubble will also play a significant role in determining the outcome. A number of experimental and numerical studies have been performed on bubble passage through a liquid-liquid interface1–9,11,12,15–20. Many of these consider just an entrained volume of liquid, that is the volume of the bottom liquid carried over the interface by the bubble2–5,11,16,17. Greene et al.2,3 found that entrainment volume was inversely proportional to the density difference between the bottom and top liquid. Interfacial tension was shown to have relatively little effect on entrainment volume but did affect the onset of entrainment. The entrainment volume increased significantly when the viscosity of the bottom liquid decreased but was not nearly as sensitive to changes in the viscosity of the top liquid. Reiter and Schwerdtfeger4,5 documented the residence time of the bubble at the interface, the height of the column formed under the bubble, and characteristics of drops formed in the upper phase and correlated them using dimensionless parameters. Additional experimental studies have also been carried out to understand various fluidic phenomena associated with bubble passage through a liquid-liquid interface. Dietrich et al.11 studied the effects of bubble size and upper liquid viscosity on the velocity field around a bubble using a PIV system. Uemura et al.17 visualized film rupture as a bubble passed through an oilwater interface, and observed that the film retracted around the bubble and formed concentric ripples around the rupture point due to the variation in surface tension forces acting on either side of the film. Bonhomme et al.6 used the dimensionless Bond (buoynacy vs. surface tension) and Archimedes (buoyancy vs. viscous force) numbers to classify results found in experiment. They found small bubbles with low Bond numbers (~3) are seen to remain trapped at the interface for
ACS Paragon Plus Environment
4
Page 5 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
extended periods of time. As Bond number increased, interfacial tension was overcome by buoyancy and the bubble was able to pass through the interface without coming to a complete stop. As the Bond number reached ~30, the bubble began to take on a cap form as it rose. For these larger Bond number bubbles, if the Archimedes number was also very high (~8000 in these experiments) then the bubble took on a toroidal shape. Good agreement with a numerical model that employed a volume of fluid (VOF) approach based on the Navier-Stokes equation was observed. Hashimoto and Kawano’s group have conducted a number of studies on shell formation during bubble passage through a liquid-liquid interface and related features such as drag coefficient, velocity profile, and deformation of bubble shells10,18–22. More recently, Singh et al.9 experimentally found that bubbles with Reynolds number, Re, 190
