Interfacial Area Transport Equation for Bubble Coalescence and Breakup: Developments and Comparisons

Bubble coalescence and breakup play important roles in physical-chemical processes and bubbles are treated in two groups in the interfacial area transport equation (IATE). This paper presents a review of IATE for bubble coalescence and breakup to model five bubble interaction mechanisms: bubble coalescence due to random collision, bubble coalescence due to wake entrainment, bubble breakup due to turbulent impact, bubble breakup due to shearing-off, and bubble breakup due to surface instability. In bubble coalescence, bubble size, velocity and collision frequency are dominant. In bubble breakup, the influence of viscous shear, shearing-off, and surface instability are neglected, and their corresponding theory and modelling are rare in the literature. Furthermore, combining turbulent kinetic energy and inertial force together is the best choice for the bubble breakup criterion. The reviewed one-group constitutive models include the one developed by Wu et al., Ishii and Kim, Hibiki and Ishii, Yao and Morel, and Nguyen et al. To extend the IATE prediction capability beyond bubbly flow, two-group IATE is needed and its performance is strongly dependent on the channel size and geometry. Therefore, constitutive models for two-group IATE in a three-type channel (i.e., narrow confined channel, round pipe and relatively larger pipe) are summarized. Although great progress in extending the IATE beyond churn-turbulent flow to churn-annual flow was made, there are still some issues in their modelling and experiments due to the highly distorted interface measurement. Regarded as the challenges to be addressed in the further study, some limitations of IATE general applicability and the directions for future development are highlighted.

[1]  J. Lasheras,et al.  A review of statistical models for the break-up of an immiscible fluid immersed into a fully developed turbulent flow , 2002 .

[2]  Theodore Stanley Worosz.  Interfacial Area Transport Equation for Bubbly to Cap-bubbly Transition Flows , 2015 .

[3]  V. Cristini,et al.  Scalings for fragments produced from drop breakup in shear flow with inertia , 2001 .

[4]  Lawrence L. Tavlarides,et al.  Description of interaction processes in agitated liquid-liquid dispersions , 1977 .

[5]  Benjamin Doup.  Methodology Development of a Gas-Liquid Dynamic Flow Regime Transition Model , 2014 .

[6]  M. Ishii,et al.  Investigation of one-dimensional interfacial area transport for vertical upward air–water two-phase flow in an annular channel at elevated pressures , 2013 .

[7]  Xiaodong Sun.  Two-group interfacial area transport equation for a confined test section , 2001 .

[8]  A. Vignes.  Extractive Metallurgy 2: Metallurgical Reaction Processes , 2011 .

[9]  Nanoemulsions obtained via bubble-bursting at a compound interface , 2013, 1312.3369.

[10]  Jinfu Wang,et al.  Population Balance Model for Gas−Liquid Flows: Influence of Bubble Coalescence and Breakup Models , 2005 .

[11]  Xia Wang.  Simulations of Two-phase Flows Using Interfacial Area Transport Equation , 2010 .

[12]  J. Buchanan,et al.  Characterization of horizontal air–water two-phase flow in a round pipe part I: Flow visualization , 2015 .

[13]  Seungjin Kim,et al.  Characterization of horizontal air–water two-phase flow , 2017 .

[14]  D. Mewes,et al.  Bubble‐Size distributions and flow fields in bubble columns , 2002 .

[15]  Mamoru Ishii,et al.  Foundation of the interfacial area transport equation and its closure relations , 1995 .

[16]  Juan C. Lasheras,et al.  On the breakup of an air bubble injected into a fully developed turbulent flow. Part 1. Breakup frequency , 1999, Journal of Fluid Mechanics.

[17]  Seungjin Kim,et al.  Development of One-Group and Two-Group Interfacial Area Transport Equation , 2004 .

[18]  Costas Kiparissides,et al.  Generalized model for prediction of the steady-state drop size distributions in batch stirred vessels , 1989 .

[20]  H. Svendsen,et al.  Theoretical model for drop and bubble breakup in turbulent dispersions , 1996 .

[21]  N. Zuber,et al.  Drag coefficient and relative velocity in bubbly, droplet or particulate flows , 1979 .

[22]  L. Erickson,et al.  DYNAMICS OF BUBBLE SIZE DISTRIBUTION IN TURBULENT GAS-LIQUID DISPERSIONS , 1987 .

[23]  S. Qiao,et al.  Air-water two-phase bubbly flow across 90° vertical elbows Part II: Modeling , 2018, International Journal of Heat and Mass Transfer.

[24]  Jinfu Wang,et al.  A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow , 2003 .

[25]  T. Hibiki,et al.  Bubble breakup and coalescence models for bubbly flow simulation using interfacial area transport equation , 2018, International Journal of Heat and Mass Transfer.

[26]  M. Ishii,et al.  Two-phase flow structure in large diameter pipes , 2012 .

[27]  Ak Allen Chesters.  The modelling of coalescence processes in fluid-liquid dispersions : a review of current understanding , 1991 .

[28]  Mamoru Ishii,et al.  One-group interfacial area transport of bubbly flows in vertical round tubes , 2000 .

[29]  Costas Tsouris,et al.  Breakage and coalescence models for drops in turbulent dispersions , 1994 .

[30]  Eckhard Krepper,et al.  On the modelling of bubbly flow in vertical pipes , 2005 .

[31]  A. E. Dukler,et al.  Modelling flow pattern transitions for steady upward gas‐liquid flow in vertical tubes , 1980 .

[32]  M. Ishii,et al.  Progress in two-phase flow modeling: Interfacial area transport , 2021 .

[33]  M. Ishii,et al.  Interfacial area transport of vertical upward steam–water two-phase flow in an annular channel at elevated pressures , 2013 .

[34]  Xinyu Fu.  Interfacial area measurement and transport modeling in air -water two -phase flow , 2001 .

[35]  Kataoka Isao,et al.  Drift flux model for large diameter pipe and new correlation for pool void fraction , 1987 .

[36]  J. Bird,et al.  Quantifying the potential for bursting bubbles to damage suspended cells , 2017, Scientific Reports.

[37]  Bo Zhi Chen,et al.  Microneedles with Controlled Bubble Sizes and Drug Distributions for Efficient Transdermal Drug Delivery , 2016, Scientific Reports.

[38]  Chul H. Song,et al.  Modeling of bubble coalescence and break-up considering turbulent suppression phenomena in bubbly two-phase flow , 2013 .

[39]  Mamoru Ishii,et al.  One-group interfacial area transport in vertical bubbly flow , 1998 .

[40]  Mamoru Ishii,et al.  Modeling of bubble coalescence and disintegration in confined upward two-phase flow , 2004 .

[41]  Mamoru Ishii,et al.  Model evaluation of two-group interfacial area transport equation for confined upward flow , 2004 .

[42]  Vittorio Cristini,et al.  Effect of inertia on drop breakup under shear , 2001 .

[43]  Larry E. Erickson,et al.  BUBBLE BREAKUP AND COALESCENCE IN TURBULENT GAS-LIQUID DISPERSIONS , 1987 .

[44]  Mohammad Abul Kalam Azad.  Numerical model for bubble breakup and coalescence in turbulent gas liquid dispersion , 2006 .

[45]  M. Ishii,et al.  Micro four-sensor probe measurement of interfacial area transport for bubbly flow in round pipes , 2001 .

[46]  J. P. Gupta,et al.  A model for transitional breakage probability of droplets in agitated lean liquid-liquid dispersions , 1979 .

[47]  Y. Liao,et al.  A literature review of theoretical models for drop and bubble breakup in turbulent dispersions , 2009 .

[48]  M. Ishii,et al.  Prediction of interfacial area concentration in a small diameter round pipe , 2019, International Journal of Heat and Mass Transfer.

[49]  Xiaofeng Yang,et al.  Prediction of interfacial area transport in a scaled 8×8 BWR rod bundle , 2016 .

[50]  Seungjin Kim,et al.  Interfacial area transport equation and measurement of local interfacial characteristics , 1999 .

[51]  ARTHUR SCHUSTER,et al.  The Kinetic Theory of Gases , 1895, Nature.

[52]  M. Ishii,et al.  Thermo-Fluid Dynamics of Two-Phase Flow , 2007 .

[53]  Wei Ge,et al.  A theoretical bubble breakup model for slurry beds or three-phase fluidized beds under high pressure , 2007 .

[54]  Takashi Hibiki,et al.  Vertical upward two-phase flow CFD using interfacial area transport equation , 2015 .

[55]  Justin D. Talley.  Interfacial Area Transport Equation for Vertical and Horizontal Bubbly Flows and its Application to the TRACE Code , 2012 .

[56]  S. Qiao,et al.  Interfacial area transport across a 90° vertical-upward elbow in air–water bubbly two-phase flow , 2016 .

[57]  S. G. Bankoff,et al.  Structure of air-water bubbly flow in a vertical pipe—II. Void fraction, bubble velocity and bubble size distribution , 1993 .

[58]  Hailiang Wang,et al.  Direct electrosynthesis of methylamine from carbon dioxide and nitrate , 2021, Nature Sustainability.

[59]  W. M. Mann.  Oxygen in Steelmaking , 1948 .

[60]  Mamoru Ishii,et al.  Two-group interfacial area transport in vertical air–water flow: I. Mechanistic model , 2003 .

[61]  Yong Jin,et al.  Theoretical prediction of flow regime transition in bubble columns by the population balance model , 2005 .

[62]  Chul-Hwa Song,et al.  The Effect of Bubble-Induced Turbulence on the Interfacial Area Transport in Gas-Liquid Two-Phase Flow: , 2012 .

[63]  H. Blanch,et al.  Bubble coalescence and break‐up in air‐sparged bubble columns , 1990 .

[64]  Juan C. Lasheras,et al.  On the breakup of an air bubble injected into a fully developed turbulent flow. I - Breakup frequency , 1999 .

[65]  Joshua P. Schlegel,et al.  Mechanistic modeling of interfacial area transport in large diameter pipes , 2012 .

[66]  S. Bajorek,et al.  Interfacial area transport models for horizontal air-water bubbly flow in different pipe sizes , 2018, International Journal of Multiphase Flow.

[67]  Mamoru Ishii,et al.  Development of one-group interfacial area transport equation in bubbly flow systems , 2002 .

[68]  Seungjin Kim,et al.  Characterization of the dissipation of elbow effects in bubbly two-phase flows , 2014 .

[69]  Joakim Majander,et al.  Simulation of the population balances for liquid–liquid systems in a nonideal stirred tank. Part 2—parameter fitting and the use of the multiblock model for dense dispersions , 2002 .

[70]  Wei Yao,et al.  Volumetric interfacial area prediction in upward bubbly two-phase flow , 2004 .

[71]  Seungjin Kim,et al.  Experiments on geometric effects of 90-degree vertical-upward elbow in air water two-phase flow , 2014 .

[72]  D. Wallace,et al.  Rapid transfer of oxygen to the deep ocean mediated by bubbles , 2020, Nature Geoscience.

[73]  Seungjin Kim,et al.  Air-water two-phase bubbly flow across 90° vertical elbows. Part I: Experiment , 2018, International Journal of Heat and Mass Transfer.

[74]  Joshua P. Schlegel,et al.  Two-group modeling of interfacial area transport in large diameter channels , 2015 .