Lateral Capillary Forces Between Two Spherical Particles: a Lattice Boltzmann Study

LIANG Gong-you; ZENG Zhong; ZHANG Yong-xiang; ZHANG Liang-qi; XIE Hai-qiong; CHEN Yu

doi:10.3879/j.issn.1000-0887.2013.05.002

Volume 34 Issue 5

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2013 > 34(5): 445-453

LIANG Gong-you, ZENG Zhong, ZHANG Yong-xiang, ZHANG Liang-qi, XIE Hai-qiong, CHEN Yu. Lateral Capillary Forces Between Two Spherical Particles: a Lattice Boltzmann Study[J]. Applied Mathematics and Mechanics, 2013, 34(5): 445-453. doi: 10.3879/j.issn.1000-0887.2013.05.002

Citation:

PDF( 1112 KB)

Lateral Capillary Forces Between Two Spherical Particles: a Lattice Boltzmann Study

doi: 10.3879/j.issn.1000-0887.2013.05.002

¹Department of Engineering Mechanics, College of Resource and Environment Science, Chongqing University, Chongqing 400044, P.R.China;²State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, P.R.China;³Department of Human and Engineered Environmental Studies, Graduate School of Frontier Sciences, The University of Tokyo, Tokyo 1138656, Japan

Received Date: 2013-03-25
Rev Recd Date: 2013-04-07
Publish Date: 2013-05-15

Abstract

Abstract

A three-dimensional simulation study on the lateral capillary forces (LCFs) between two floating and immersion spherical particles was carried out, using a modeling approach introduced in the framework of Shan-Chen lattice Boltzmann model for multi-component fluids. Solid-fluid interactions and wetting property of a colloidal particle could be taken into account at the mesoscopic level using a simple manner. Results show good agreement with theoretical results, and the so called “1/L” theory is demonstrated. At the same time, the linear relationship between immersion LCF and fluid interfacial tension for fixed interparticle distance is well achieved. These demonstrate that the model is a promising tool for the simulation of phenomenon such as self-assemblies of colloidal particles.
- lattice Boltzmann method,
- solid-liquid two-phase flow,
- lateral capillary forces,
- hydrodynamic interactions

FullText(HTML)

References(25)

References

[1]	Grzelczak M, Vermant J, Furst E M, LizMarzn L M. Directed selfassembly of nanoparticles[J].ACS Nano,2010,4(7): 3591-3605.
[2]	Kralchevsky P A, Denkov N D. Capillary forces and structuring in layers of colloid particles[J].Curr Opin Colloid Interface Sci,2001,6(4): 383-401.
[3]	Madivala B, Vandebril S, Fransaer J, Vermant J. Exploiting particle shape in solid stabilized emulsions[J]. Soft Matter,2009,5(8): 1717-1727.
[4]	Furst E M. Directing colloidal assembly at fluid interfaces[J].PNAS,2011,108(52): 20853-20854.
[5]	Kralchevsky P A, Nagayama K. Capillary forces between colloidal particles[J].Langmuir,1994,10(1): 23-36.
[6]	Li Q, Jonas U, Zhao X S, Kappl M. The forces at work in colloidal selfassembly: a review on fundamental interactions between colloidal particles[J].AsiaPac J Chem Eng,2008,3(3): 255-268.
[7]	Dushkin C D, Kralchevsky P A, Yoshimura H, Nagayama K. Lateral capillary forces measured by torsion microbalance[J].Phys Rev Lett,1995,75(19): 3454-3457.
[8]	Leonardo R Di, Saglimbeni F, Ruocco G. Very-long-range nature of capillary interactions in liquid films[J].Phys Rev Lett,2008,100(10): 106103(1-3).
[9]	Nishikawa H, Maenosono S, Yamaguchi Y, Okubo T. Selfassembling process of colloidal particles into twodimensional arrays induced by capillary immersion force: a simulation study with discrete element method[J].J Nanopart Res,2003,5(1): 103-110.
[10]	Rabideau B D, Pell L E, Bonnecaze R T, Korgel B A. Observation of longrange orientational order in monolayers of polydisperse colloids[J].Langmuir,2007,23(3): 1270-1274.
[11]	Benzi R, Succi S, Vergassola M. The lattice Boltzmann equation: theory and applications[J].Phys Rep,1992,222(3): 145-197.
[12]	Chen S, Doolen G. Lattice Boltzmann method for fluid flows[J].Annu Rev Fluid Mech,1998,30(1): 329-364.
[13]	郭照立, 郑楚光. 格子Boltzmann方法的原理及应用[M]. 北京: 科学出版社, 2009.（GUO Zhao-li, ZHENG Chu-guang.Theory and Applications of Lattice Boltzmann Method [M]. Beijing: Science Press, 2009.（in Chinese））
[14]	Ladd A J C. Numerical simulations of particulate suspensions via a discretized Boltzmann equation—part 1: theoretical foundation[J].J Fluid Mech,1994,271: 285-309.
[15]	Aidun C, Lu Y. Lattice Boltzmann simulation of solid particles suspended in fluid[J].J Stat Phys,1995,81(1): 49-61.
[16]	Stratford K, Adhikari R, Pagonabarraga I, Desplat J. Lattice Boltzmann for binary fluids with suspended colloids[J].J Stat Phys,2005,121(1): 163-178.
[17]	Jansen F, Harting J. From bijels to pickering emulsions: a lattice Boltzmann study[J].Phys Rev E,2011,83(4): 046707(1-11).
[18]	Shinto H, Komiyama D, Higashitani K. Lateral capillary forces between solid bodies on liquid surface: a lattice Boltzmann study[J].Langmuir,2006,22(5): 2058-2064.
[19]	Tanaka H, Araki T. Simulation method of colloidal suspensions with hydrodynamic interactions: fluid particle dynamics[J].Phys Rev Lett,2000,85(6): 1338-1341.
[20]	Onishi J, Kawasaki A, Chen Y, Ohashi H. Lattice Boltzmann simulation of capillary interactions among colloidal particles[J].Comput Math Appl,2008,55(7): 1541-1553.
[21]	Shan X, Chen H. Lattice Boltzmann model for simulating flows with multiple phases and components[J].Phys Rev E,1993,47(3): 1815-1819.
[22]	Liang G, Chen Y, Zeng Z, Ohashi H, Chen S. Simulation of selfassemblies of colloidal particles partially immersed in a liquid layer on a substrate with a lattice Boltzmann pseudo-solid mode[R]. Bangalore: DSFD, 2012.
[23]	Shan X. Multicomponent lattice Boltzmann model from continuum kinetic theory[J].Phys Rev E,2010,81(4): 045701(1-4).
[24]	Guo Z, Zheng C, Shi B. Discrete lattice effects on the forcing term in the lattice Boltzmann method[J].Phy Rev E,2002,65(4): 46308(1-6).
[25]	Yunker P J, Still T, Lohr M A, Yodh A G. Suppression of the coffee-ring effect by shape-dependent capillary interactions[J].Nature,2011,476(7360): 308-311.