Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-26T03:13:45.988Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-Dimensional Lattice Boltzmann Simulation of Two-Phase Flow Containing a Deformable Body with a Viscoelastic Membrane

Published online by Cambridge University Press:  20 August 2015

Toshiro Murayama ,
Masato Yoshino  and
Tetsuo Hirata
Toshiro Murayama*
Affiliation:
Department of Mathematics and System Development Engineering, Interdisciplinary Graduate School of Science and Technology, Shinshu University, 4-17-1 Wakasato, Nagano-shi, Nagano 380-8553, Japan Satellite Venture Business Laboratory (SVBL), Shinshu University, 3-15-1 Tokida, Ueda-shi, Nagano 386-8567, Japan
Masato Yoshino*
Affiliation:
Department of Mechanical Systems Engineering, Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano-shi, Nagano 380-8553, Japan CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi-shi, Saitama 332-0012, Japan
Tetsuo Hirata*
Affiliation:
Department of Mechanical Systems Engineering, Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano-shi, Nagano 380-8553, Japan
*
Email:[email protected]
Corresponding author.Email:[email protected]
Email:[email protected]
Get access

Abstract

The lattice Boltzmann method (LBM) with an elastic model is applied to the simulation of two-phase flows containing a deformable body with a viscoelastic membrane. The numerical method is based on the LBM for incompressible two-phase fluid flows with the same density. The body has an internal fluid covered by a viscoelastic membrane of a finite thickness. An elastic model is introduced to the LBM in order to determine the elastic forces acting on the viscoelastic membrane of the body. In the present method, we take account of changes in surface area of the membrane and in total volume of the body as well as shear deformation of the membrane. By using this method, we calculate two problems, the behavior of an initially spherical body under shear flow and the motion of a body with initially spherical or biconcave discoidal shape in square pipe flow. Calculated deformations of the body (the Taylor shape parameter) for various shear rates are in good agreement with other numerical results. Moreover, tank-treading motion, which is a characteristic motion of viscoelastic bodies in shear flows, is simulated by the present method.

Keywords

76D9976T9974F1076M2874L15Lattice Boltzmann method (LBM)two-phase flowviscoelastic membraneshear flowtank-treading motion
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 5 , May 2011 , pp. 1397 - 1413
Copyright
Copyright © Global Science Press Limited 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Shiga, T., Maeda, N. and Kon, K., Erythrocyte rheology, Crit. Rev. Oncol. Hematol., 10 (1990), 9–48.Google Scholar
[2]Maeda, N. and Shiga, T., Red cell aggregation, due to interactions with plasma proteins, J. Blood. Rheol., 7 (1993), 3–12.Google Scholar
[3]Ramanujan, S. and Pozrikidis, C., Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities, J. Fluid. Mech., 361 (1998), 117–143.Google Scholar
[4]Boryczko, K., Dzwinel, W. and Yuen, D. A., Dynamical clustering of red blood cells in capillary vessels, J. Mol. Model., 9 (2003), 16–33.Google Scholar
[5]Dzwinel, W., Boryczko, K. and Yuen, D. A., A discrete-particle model of blood dynamics in capillary vessels, J. Colloid. Interface. Sci., 258 (2003), 163–173.CrossRefGoogle ScholarPubMed
[6]Tsubota, K., Wada, S. and Yamaguchi, T., Particle method for computer simulation of red blood cell motion in blood flow, Comput. Methods. Prog. Biomed., 83 (2006), 139–146.Google Scholar
[7]Koshizuka, S., Tamako, H. and Oka, Y., A particle method for incompressible viscous flow with fluid fragmentation, Comput. Fluid. Dyn. J., 4 (1995), 29–46.Google Scholar
[8]Fischer, T. M. and Schönbein, H. S., Tank treading motion of red cell membranes in viscometric flow: behavior of intracellular and extracellular markers (with film), Blood. Cells., 3 (1977), 351–365.Google Scholar
[9]Fischer, T. M., On the energy dissipation in a tank-treading human red blood cell, Biophys. J., 32 (1980), 863–868.Google Scholar
[10]Benzi, R., Succi, S. and Vergassola, M., The lattice Boltzmann equation: theory and applications, Phys. Rep., 222 (1992), 145–197.CrossRefGoogle Scholar
[11]Chen, S. and Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid. Mech., 30 (1998), 329–364.Google Scholar
[12]Succi, S., The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, Oxford, 2001.Google Scholar
[13]Ladd, A. J. C., Numerical simulations of particulate suspensions via a discretized Boltzmann equation, part 1, theoretical foundation, J. Fluid. Mech., 271 (1994), 285–309.Google Scholar
[14]Ladd, A. J. C., Hydrodynamic screening in sedimenting suspensions of non-Brownian spheres, Phys. Rev. Lett., 76 (1996), 1392–1395.Google Scholar
[15]Ladd, A. J. C., Sedimentation of homogeneous suspensions of non-Brownian spheres, Phys. Fluids., 9 (1997), 491–499.CrossRefGoogle Scholar
[16]Sui, Y., Chew, Y. T., Roy, P. and Low, H. T., A hybrid method to study flow-induced deformation of three-dimensional capsules, J. Comput. Phys., 227 (2008), 6351–6371.Google Scholar
[17]Sui, Y., Low, H. T., Chew, Y. T. and Roy, P., Tank-treading, swinging, and tumbling of liquid-filled elastic capsules in shear flow, Phys. Rev. E., 77 (2008), 06310.Google Scholar
[18]Dupin, M. M., Halliday, I., Care, C. M., Alboul, L. and Munn, L. L., Modeling the flow of dense suspensions of deformable particles in three dimensions, Phys. Rev. E., 75 (2007), 066707.Google Scholar
[19]Dupin, M. M., Halliday, I., Care, C. M. and Munn, L. L., Lattice Boltzmann modelling of blood cell dynamics, Int. J. Comput. Fluid. Dyn., 22 (2008), 481–492.Google Scholar
[20]Yoshino, M. and Murayama, T., A lattice Boltzmann method for a two-phase flow containing solid bodies with viscoelastic membranes, Eur. Phys. J. Special. Topics., 171 (2009), 151–157.Google Scholar
[21]Inamuro, T., Lattice Boltzmann methods for viscous fluid flows and for two-phase fluid flows, Fluid. Dyn. Res., 38 (2006), 641–659.Google Scholar
[22]Inamuro, T., Tomita, R. and Ogino, F., Lattice Boltzmann simulations of drop deformation and breakup in shear flows, Int. J. Mod. Phys. B., 17 (2003), 21–26.Google Scholar
[23]Inamuro, T. and Ii, T., Lattice Boltzmann simulation of the dispersion of aggregated particles under shear flows, Math. Comput. Simul., 72 (2006), 141–146.Google Scholar
[24]Evans, E. and Fung, Y. C., Improved measurements of the erythrocyte geometry, Microvasc. Res., 4 (1972), 335–347.Google Scholar
[25]Evans, E. A., Minimum energy analysis of membrane deformation applied to pipet aspiration and surface adhesion of red blood cells, Biophys. J., 30 (1980), 265–284.Google Scholar
[26]Sone, Y., Asymptotic theory of flow of rarefied gas over a smooth boundary II, in Rarefied Gas Dynamics, ed. Dini, D., Editrice Tecnico Scientifica, Pisa, 2 (1971), 737–749.Google Scholar
[27]Inamuro, T., Yoshino, M. and Ogino, F., Accuracy of the lattice Boltzmann method for small Knudsen number with finite Reynolds number, Phys. Fluids., 9 (1997), 3535–3542.Google Scholar
[28]Zahalak, G. I., Rao, P. R. and Sutera, S. P., Large deformations of a cylindrical liquid-filled membrane by a viscous shear flow, J. Fluid. Mech., 179 (1987), 283–305.Google Scholar
[29]Sheth, K. S. and Pozrikidis, C., Effects of inertia on the deformation of liquid drops in simple shear flow, Comput. Fluids., 24 (1995), 101–119.Google Scholar
[30]Li, J., Renardy, Y. Y. and Renardy, M., Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method, Phys. Fluids., 12 (2000), 269–282.Google Scholar
[31]Beaucourt, J., Rioual, F., Séon, T., Biben, T. and Misbah, C., Steady to unsteady dynamics of a vesicle in a flow, Phys. Rev. E., 69 (2004), 011906.Google Scholar
[32]Vitkova, V., Mader, M., Biben, T. and Podgorski, T., Tumbling of lipid vesicles, enclosing a viscous fluid, under a shear flow, J. Optoelectron. Adv. Mater., 7 (2005), 261–264.Google Scholar
[33]Gaehtgens, P. and Schmid-Schönbein, H., Mechanisms of dynamic flow adaptation of mammalian erythrocytes, Naturwissenschaften., 69 (1982), 294–296.Google Scholar
[34]Waugh, R. and Evans, E. A., Thermoelasticity of red blood cell membrane, Biophys. J., 26 (1979), 115–131.Google Scholar
[35]Waugh, R. E. and Hochmuth, R. M., Mechanics and deformability of hematocytes, in: ed. Bronzino, J. D., Biomedical Engineering Fundamentals, 3rd ed. CRC Press, Boca Raton, 2006.Google Scholar
[36]Skalak, R. and Chien, S., Handbook of Bioengineering, McGraw-Hill, New York, 1987.Google Scholar