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Håkansson A, Nilsson L. The effect of emulsifier concentration on turbulent drop breakup - An experimental study based on single drop visualizations. J Colloid Interface Sci 2025; 679:344-353. [PMID: 39454265 DOI: 10.1016/j.jcis.2024.10.078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2024] [Revised: 10/10/2024] [Accepted: 10/15/2024] [Indexed: 10/28/2024]
Abstract
HYPOTHESIS A modified Weber number can capture the effect of emulsifier concentration and the effect of external stress in turbulent drop breakup. Moreover, the effect of emulsifiers on turbulent drop breakup cannot be adequately understood from classic slow/laminar techniques and quasi steady state interfacial tension. EXPERIMENTS Single drop breakup visualizations are used to study the effect of polysorbate 20 on turbulent drop deformation and breakup. Comparisons are made to drop tensiometry and emulsification experiments. FINDINGS A high concentration of the emulsifier increases breakup probability and breakup rate and decreases breakup timescales. These effects scale with a Weber number, indicating a lowering of the effective interfacial tension to 71 % of its pure interface value. This is far less than the observed lowering of interfacial tension as measured by quiescent drop tensiometry. Mechanistically, this shows that adsorption during emulsification cannot be limited by diffusion. Studying the effect cross a range of emulsifier concentrations suggest an elastic resistance at intermediate concentrations, further helping to understand the origin of similar effects previously reported in emulsification experiments. Overall, the results show the need to study emulsifiers under turbulent conditions to understand their effects during emulsification, as opposed to the slow/laminar techniques previously used.
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Affiliation(s)
- Andreas Håkansson
- Department of Process and Life Science Engineering, Lund University, Lund, Sweden.
| | - Lars Nilsson
- Department of Process and Life Science Engineering, Lund University, Lund, Sweden
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2
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The effect of disperse phase viscosity in the emulsification of a semi-dairy beverage–combining emulsification experiments and numerical single drop breakup simulations. FOOD AND BIOPRODUCTS PROCESSING 2023. [DOI: 10.1016/j.fbp.2023.01.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
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3
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Olad P, Innings F, Crialesi-Esposito M, Brandt L, Håkansson A. Comparison of turbulent drop breakup in an emulsification device and homogeneous isotropic turbulence: insights from numerical experiments. Colloids Surf A Physicochem Eng Asp 2022. [DOI: 10.1016/j.colsurfa.2022.130569] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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4
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Numerical study of bubble induced mixing in stratified fluids. Chem Eng Sci 2022. [DOI: 10.1016/j.ces.2022.118135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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5
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Håkansson A, Crialesi-Esposito M, Nilsson L, Brandt L. A criterion for when an emulsion drop undergoing turbulent deformation has reached a critically deformed state. Colloids Surf A Physicochem Eng Asp 2022. [DOI: 10.1016/j.colsurfa.2022.129213] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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6
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Håkansson A, Brandt L. Deformation and initial breakup morphology of viscous emulsion drops in isotropic homogeneous turbulence with relevance for emulsification devices. Chem Eng Sci 2022. [DOI: 10.1016/j.ces.2022.117599] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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7
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The Role of Stochastic Time-Variations in Turbulent Stresses When Predicting Drop Breakup—A Review of Modelling Approaches. Processes (Basel) 2021. [DOI: 10.3390/pr9111904] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Many industrially relevant emulsification devices are of the high-energy type, where drop deformation and subsequent breakup, take place due to intense turbulent fluid–drop interactions. This includes high-pressure homogenizers as well as rotor-stator mixers (also known as high-shear mixers) of various designs. The stress acting on a drop in a turbulent flow field varies over time, occasionally reaching values far exceeding its time-averaged value, but only during limited stretches of time, after which it decreases down to low values again. This it is one factor separating turbulent from laminar emulsification. This contribution reviews attempts to take this intermittently time-varying stress into account in models predicting the characteristic drop diameter resulting from emulsification experiments, focusing on industrially applicable emulsification devices. Two main frameworks are discussed: the Kolmogorov–Hinze framework and the oscillatory resonance framework. Modelling suggestions are critically discussed and compared, with the intention to answer how critical it is to correctly capture this time-varying stress in emulsification modelling. The review is concluded by a list of suggestions for future investigations.
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Ding G, Chen J, Li Z, Cai X. Numerical Simulation on the Motion and Breakup Characteristics of a Single Bubble in a Venturi Channel. Ind Eng Chem Res 2021. [DOI: 10.1021/acs.iecr.1c02567] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Guodong Ding
- School of Mechanical and Transportation Engineering, China University of Petroleum-Beijing, 102249 Beijing, China
| | - Jiaqing Chen
- School of Mechanical Engineering, Beijing Institute of Petrochemical Technology, 102617 Beijing, China
- Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deep Water Oil & Gas Development, 102617 Beijing, China
| | - Zhenlin Li
- School of Mechanical and Transportation Engineering, China University of Petroleum-Beijing, 102249 Beijing, China
| | - Xiaolei Cai
- School of Mechanical Engineering, Beijing Institute of Petrochemical Technology, 102617 Beijing, China
- Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deep Water Oil & Gas Development, 102617 Beijing, China
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9
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Numerical studies on bubble dynamics in an unsteady turbulence of the venturi bubble generator applied to TMSR. ANN NUCL ENERGY 2021. [DOI: 10.1016/j.anucene.2021.108322] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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10
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Gharibi F, Ashrafizaadeh M. Simulation of high-viscosity-ratio multicomponent fluid flow using a pseudopotential model based on the nonorthogonal central-moments lattice Boltzmann method. Phys Rev E 2020; 101:043311. [PMID: 32422822 DOI: 10.1103/physreve.101.043311] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2019] [Accepted: 03/29/2020] [Indexed: 11/07/2022]
Abstract
In this research, the development of a pseudopotential multicomponent model with the capability of simulating high-viscosity-ratio flows is discussed and examined. The proposed method is developed based on the non-orthogonal central moments model in the lattice Boltzmann method, and the exact difference model (EDM) is used to apply the intercomponent interaction force. In contrast to the original Shan-Chen model, in which the applying force has the viscosity-dependent error term, the error term of this model does not depend on the viscosity. A GPU parallel cuda code has been developed and is employed to study the proposed method. Different cases are considered to evaluate the ability of the model, including the Laplace test, a static droplet, and a two-component concurrent channel flow. Also, wetting and nonwetting relative permeabilities for flows with dynamic viscosity ratios between 0.0002 and 5000 are predicted. Numerical results are compared with those of available analytical solutions. Very good agreement between these results are observed. The model has the capability of simulating multicomponent flows with very low kinematic viscosities of the order of 10^{-5} and dynamic viscosity ratios of up to an order of 10^{4}, which is a much wider range compared with that of existing pseudopotential models. Furthermore, the results showed that the parallel processing on GPU significantly accelerated computations. The present parallel performance evaluation shows that the cuda parallel can achieve about 41 times improvement than the CPU serial implementation. The aforementioned enhancement increases the flexibility of the multicomponent lattice Boltzmann method and its applicability to a broader spectrum of engineering applications.
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Affiliation(s)
- Farshad Gharibi
- Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156, Iran
| | - Mahmud Ashrafizaadeh
- Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156, Iran
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11
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Su B, Cao J, Huang X, Cai Z, Gao Z. Single bubble breakup in the flow field induced by a horizontal jet—The numerical simulation. ASIA-PAC J CHEM ENG 2019. [DOI: 10.1002/apj.2363] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Baiquan Su
- State Key Laboratory of Chemical Resource Engineering, School of Chemical EngineeringBeijing University of Chemical Technology Beijing China
| | - Jiaying Cao
- Appraisal Center for Environment & Engineering Ministry of Environmental Protection Beijing China
| | - Xiongbin Huang
- State Key Laboratory of Chemical Resource Engineering, School of Chemical EngineeringBeijing University of Chemical Technology Beijing China
| | - Ziqi Cai
- State Key Laboratory of Chemical Resource Engineering, School of Chemical EngineeringBeijing University of Chemical Technology Beijing China
| | - Zhengming Gao
- State Key Laboratory of Chemical Resource Engineering, School of Chemical EngineeringBeijing University of Chemical Technology Beijing China
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13
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Siva SP, Kow KW, Chan CH, Tang SY, Ho YK. Prediction of droplet sizes for oil-in-water emulsion systems assisted by ultrasound cavitation: Transient scaling law based on dynamic breakup potential. ULTRASONICS SONOCHEMISTRY 2019; 55:348-358. [PMID: 30871878 DOI: 10.1016/j.ultsonch.2018.12.040] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2018] [Revised: 12/27/2018] [Accepted: 12/28/2018] [Indexed: 06/09/2023]
Abstract
The dynamics of droplet breakup during emulsification is a complicated process due to the interplay between multiple physico-chemical and hydrodynamic factors, especially in an energy-intensive ultrasound-assisted emulsification process. In this work, by mapping the physical processing parameters of ultrasound emulsification into a reduced domain that is governed by the power density and the initial average droplet diameter, a dimensionless parameter that resembles the dynamic breakup potential (η) was established via dimensional analysis. In addition to shedding important insights into the emulsification process, η further facilitates the establishment of a transient scaling relationship that is a function of the characteristic value (a) of the emulsion system. Experimental case study on a cellulose nanocrystals (CNC)-based olein-in-water emulsion system prepared via ultrasound cavitation confirmed the validity of the scaling relationship and sub-universal self-similarity was observed. Using the proposed model, good predictions of the transient of droplet size evolution were attained where the value of η, i.e. the proportionality constant, can be conveniently computed using data from a single time point. Application on other emulsion systems further suggested that the value of a possibly indicates the relative minimum size limit of a particular fluids-emulsifier system. Our approach is general, which encourages widespread adoption for emulsification related studies.
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Affiliation(s)
- Sangeetaprivya P Siva
- Chemical Engineering Discipline, School of Engineering, Monash University Malaysia, Jalan Lagoon Selatan, Bandar Sunway, 47500 Selangor, Malaysia
| | - Kien-Woh Kow
- Department of Chemical and Environmental Engineering, Faculty of Science and Engineering, The University of Nottingham Ningbo China, Ningbo 315100, PR China
| | - Chung-Hung Chan
- Advanced Oleochemical Technology Division, Malaysian Palm Oil Board, 43000 Kajang, Selangor, Malaysia
| | - Siah Ying Tang
- Chemical Engineering Discipline, School of Engineering, Monash University Malaysia, Jalan Lagoon Selatan, Bandar Sunway, 47500 Selangor, Malaysia; Monash-Industry Palm Oil Education and Research Platform, Monash University Malaysia, Jalan Lagoon Selatan, Bandar Sunway, 47500 Selangor, Malaysia
| | - Yong Kuen Ho
- Chemical Engineering Discipline, School of Engineering, Monash University Malaysia, Jalan Lagoon Selatan, Bandar Sunway, 47500 Selangor, Malaysia; Monash-Industry Palm Oil Education and Research Platform, Monash University Malaysia, Jalan Lagoon Selatan, Bandar Sunway, 47500 Selangor, Malaysia.
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14
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Energy Optimization of Gas–Liquid Dispersion in Micronozzles Assisted by Design of Experiment. Processes (Basel) 2017. [DOI: 10.3390/pr5040057] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
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15
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Paul MTY, Yee BB, Bruce DR, Gates BD. Hexagonal Arrays of Cylindrical Nickel Microstructures for Improved Oxygen Evolution Reaction. ACS APPLIED MATERIALS & INTERFACES 2017; 9:7036-7043. [PMID: 28164693 DOI: 10.1021/acsami.6b14129] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Fuel-cell systems are of interest for a wide range of applications, in part for their utility in power generation from nonfossil-fuel sources. However, the generation of these alternative fuels, through electrochemical means, is a relatively inefficient process due to gas passivation of the electrode surfaces. Uniform microstructured nickel surfaces were prepared by photolithographic techniques as a systematic approach to correlating surface morphologies to their performance in the electrochemically driven oxygen evolution reaction (OER) in alkaline media. Hexagonal arrays of microstructured Ni cylinders were prepared with features of proportional dimensions to the oxygen bubbles generated during the OER process. Recessed and pillared features were investigated relative to planar Ni electrodes for their influence on OER performance and, potentially, bubble release. The arrays of cylindrical recesses were found to exhibit an enhanced OER efficiency relative to planar nickel electrodes. These microstructured electrodes had twice the current density of the planar electrodes at an overpotential of 100 mV. The results of these studies have important implications to guide the preparation of more-efficient fuel generation by water electrolysis and related processes.
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Affiliation(s)
- Michael T Y Paul
- Department of Chemistry, Simon Fraser University , 8888 University Drive, Burnaby, British Columbia V5A 1S6, Canada
| | - Brenden B Yee
- Department of Chemistry, Simon Fraser University , 8888 University Drive, Burnaby, British Columbia V5A 1S6, Canada
| | - David R Bruce
- ZincNyx Energy Solutions , 8765 Ash Street no. 1, Vancouver, British Columbia V6P 6T3, Canada
| | - Byron D Gates
- Department of Chemistry, Simon Fraser University , 8888 University Drive, Burnaby, British Columbia V5A 1S6, Canada
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16
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Venkateswaran S, Henrique Dos Santos OD, Scholefield E, Lilienkampf A, Gwynne PJ, Swann DG, Dhaliwal K, Gallagher MP, Bradley M. Fortified interpenetrating polymers - bacteria resistant coatings for medical devices. J Mater Chem B 2016; 4:5405-5411. [PMID: 27746915 PMCID: PMC5038341 DOI: 10.1039/c6tb01110a] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2016] [Accepted: 07/15/2016] [Indexed: 12/04/2022]
Abstract
Infections arising from contaminated medical devices are a serious global issue, contributing to antibiotic resistance and imposing significant strain on healthcare systems. Since the majority of medical device-associated infections are biofilm related, efforts are being made to generate either bacteria-repellent or antibacterial coatings aimed at preventing bacterial colonisation. Here, we utilise a nanocapsule mediated slow release of a natural antimicrobial to improve the performance of a bacteria repellent polymer coating. Poly(lauryl acrylate) nanocapsules containing eugenol (4-allyl-2-methoxyphenol) were prepared and entrapped within a interpenetrating network designed to repel bacteria. When coated on a catheter and an endotracheal tube, this hemocompatible system allowed slow-release of eugenol, resulting in notable reduction in surface-bound Klebsiella pneumoniae and methicillin resistant Staphylococcus aureus.
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Affiliation(s)
- Seshasailam Venkateswaran
- EaStCHEM School of Chemistry , University of Edinburgh , King's Buildings , West Mains Road , Edinburgh , EH9 3FJ , UK .
| | - Orlando David Henrique Dos Santos
- Laboratório de Fitotecnologia , Departamento de Farmácia , Escola de Farmácia , Universidade Federal de Ouro Preto , Ouro Preto , Minas Gerais 35400-000 , Brazil
| | - Emma Scholefield
- MRC Centre for Inflammation Research , The Queens Medical Research Institute , University of Edinburgh , 47 Little France Crescent , Edinburgh EH16 4TJ , UK
| | - Annamaria Lilienkampf
- EaStCHEM School of Chemistry , University of Edinburgh , King's Buildings , West Mains Road , Edinburgh , EH9 3FJ , UK .
| | - Peter J Gwynne
- School of Biological Sciences , University of Edinburgh, King's Buildings , West Mains Road , Edinburgh , EH9 3JF , UK
| | - David G Swann
- Critical Care , NHS Lothian , Royal Infirmary of Edinburgh , 51 Little France Crescent , Edinburgh , EH16 4SA , UK
| | - Kevin Dhaliwal
- MRC Centre for Inflammation Research , The Queens Medical Research Institute , University of Edinburgh , 47 Little France Crescent , Edinburgh EH16 4TJ , UK
| | - Maurice P Gallagher
- School of Biological Sciences , University of Edinburgh, King's Buildings , West Mains Road , Edinburgh , EH9 3JF , UK
| | - Mark Bradley
- EaStCHEM School of Chemistry , University of Edinburgh , King's Buildings , West Mains Road , Edinburgh , EH9 3FJ , UK .
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17
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Wutz J, Lapin A, Siebler F, Schäfer JE, Wucherpfennig T, Berger M, Takors R. Predictability ofkLain stirred tank reactors under multiple operating conditions using an Euler-Lagrange approach. Eng Life Sci 2016. [DOI: 10.1002/elsc.201500135] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022] Open
Affiliation(s)
- Johannes Wutz
- Institute of Biochemical Engineering; University of Stuttgart; Stuttgart Germany
| | - Alexey Lapin
- Institute of Biochemical Engineering; University of Stuttgart; Stuttgart Germany
| | - Flora Siebler
- Institute of Biochemical Engineering; University of Stuttgart; Stuttgart Germany
| | - Jan Erik Schäfer
- BP Process Development Germany; Boehringer Ingelheim Pharma GmbH & Co. KG; Biberach/Riß Germany
| | - Thomas Wucherpfennig
- BP Process Development Germany; Boehringer Ingelheim Pharma GmbH & Co. KG; Biberach/Riß Germany
| | - Martina Berger
- BP Process Development Germany; Boehringer Ingelheim Pharma GmbH & Co. KG; Biberach/Riß Germany
| | - Ralf Takors
- Institute of Biochemical Engineering; University of Stuttgart; Stuttgart Germany
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18
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Numerical simulation of vapor bubble condensation in turbulent subcooled flow boiling. NUCLEAR ENGINEERING AND DESIGN 2015. [DOI: 10.1016/j.nucengdes.2015.04.036] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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19
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Biferale L, Perlekar P, Sbragaglia M, Srivastava S, Toschi F. A Lattice Boltzmann method for turbulent emulsions. ACTA ACUST UNITED AC 2011. [DOI: 10.1088/1742-6596/318/5/052017] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Fakhari A, Rahimian MH. Phase-field modeling by the method of lattice Boltzmann equations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:036707. [PMID: 20365904 DOI: 10.1103/physreve.81.036707] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2009] [Revised: 12/30/2009] [Indexed: 05/29/2023]
Abstract
In this paper, at first, a lattice Boltzmann method for binary fluids, which is applicable at low viscosity values, is developed. The presented scheme is extension of the free-energy-based approach to a multi-relaxation-time collision model. Various benchmark problems such as the well-known Laplace law for stationary bubbles and capillary-wave test are conducted for validation. As an appealing application, instability of a rising bubble in an enclosed duct is studied and irregular behavior of the bubble is observed at very high Reynolds numbers. In order to highlight its capability to simulate high Reynolds number flows, which is a challenge for many other models, a typical wobbling bubble in the turbulent regime is simulated successfully. Then, in the context of phase-field modeling, a lattice Boltzmann method is proposed for multiphase flows with a density contrast. Unlike most of the previous models based on the phase-field theory, the proposed scheme not only tolerates very low viscosity values but also emerges as a promising method for investigation of two-phase flow problems with moderate density ratios. In addition to comparison to the kinetic-based model, the proposed approach is further verified by judging against the theoretical solutions and experimental data. Various case studies including the rising bubble, droplet splashing on a wet surface, and falling droplet are conducted to show the versatility of the presented lattice Boltzmann model.
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Affiliation(s)
- Abbas Fakhari
- Hydraulic Machinery Research Institute, Faculty of Engineering, University of Tehran, Tehran, Iran
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Joshi AS, Sun Y. Multiphase lattice Boltzmann method for particle suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:066703. [PMID: 19658621 DOI: 10.1103/physreve.79.066703] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2008] [Indexed: 05/28/2023]
Abstract
A two-dimensional mass conserving lattice Boltzmann method (LBM) has been developed for multiphase (liquid and vapor) flows with solid particles suspended within the liquid and/or vapor phases. The main modification to previous single-phase particle suspension models is the addition of surface (adhesive) forces between the suspended particle and the surrounding fluid. The multiphase dynamics between fluid phases is simulated via the single-component multiphase model of Shan and Chen [Phys. Rev. E 47, 1815 (1993)]. The combined multiphase particle suspension model is first validated and then used to simulate the dynamics of a single-suspended particle on a planar liquid-vapor interface and the interaction between a single particle and a free-standing liquid drop. It is observed that the dynamics of suspended particles near free-standing liquid droplets is affected by spurious velocity currents although the liquid-vapor interface itself is a local energy minimum for particles. Finally, results are presented for capillary interactions between two suspended particles on a liquid-vapor interface subjected to different external forces and for spinodal decomposition of a liquid-vapor mixture in the presence of suspended particles. Qualitative agreements are reached when compared with results of suspended particles in a binary mixture based on multicomponent LBM models.
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