Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-02-05T07:23:07.540Z Has data issue: false hasContentIssue false
  • English
  • Français

Simulating deformable particle suspensions using a coupled lattice-Boltzmann and finite-element method

Published online by Cambridge University Press:  10 January 2009

ROBERT M. MacMECCAN ,
J. R. CLAUSEN ,
G. P. NEITZEL  and
C. K. AIDUN
ROBERT M. MacMECCAN
Affiliation:
G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 500 10th Street NW, Atlanta, GA 30318, USA
J. R. CLAUSEN
Affiliation:
G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 500 10th Street NW, Atlanta, GA 30318, USA
G. P. NEITZEL
Affiliation:
G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 500 10th Street NW, Atlanta, GA 30318, USA
C. K. AIDUN*
Affiliation:
G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 500 10th Street NW, Atlanta, GA 30318, USA
*
†Author to whom correspondence should be addressed.
Get access Rights & Permissions [Opens in a new window]

Abstract

A novel method is developed to simulate suspensions of deformable particles by coupling the lattice-Boltzmann method (LBM) for the fluid phase to a linear finite-element analysis (FEA) describing particle deformation. The methodology addresses the need for an efficient method to simulate large numbers of three-dimensional and deformable particles at high volume fraction in order to capture suspension rheology, microstructure, and self-diffusion in a variety of applications. The robustness and accuracy of the LBM–FEA method is demonstrated by simulating an inflating thin-walled sphere, a deformable spherical capsule in shear flow, a settling sphere in a confined channel, two approaching spheres, spheres in shear flow, and red blood cell deformation in flow chambers. Additionally, simulations of suspensions of hundreds of biconcave red blood cells at 40% volume fraction produce continuum-scale physics and accurately predict suspension viscosity and the shear-thinning behaviour of blood. Simulations of fluid-filled spherical capsules which have red-blood-cell membrane properties also display deformation-induced shear-thinning behaviour at 40% volume fraction, although the suspension viscosity is significantly lower than blood.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 618 , 10 January 2009 , pp. 13 - 39
Copyright
Copyright © Cambridge University Press 2008

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

REFERENCES

Aidun, C. K. & Lu, Y. 1995 Lattice Boltzmann simulation of solid particles suspended in fluid. J. Stat. Phys. 81, 49–61.CrossRefGoogle Scholar
Aidun, C. K., Lu, Y. & Ding, E. J. 1998 Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. J. Fluid Mech. 373, 287–311.CrossRefGoogle Scholar
Bagchi, P., Johnson, P. C. & Popel, A. S. 2005 Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow. J. Biomech. Engng 127, 1070.CrossRefGoogle Scholar
Barthès-Biesel, D. & Sgaier, H. 1985 Role of membrane viscosity in the orientation and deformation of a spherical capsule suspended in shear flow. J. Fluid Mech. 160, 119–135.CrossRefGoogle Scholar
Barthès-Biesel, D., Diaz, A. & Dhenin, E. 2002 Effect of constitutive laws for two-dimensional membranes on flow-induced capsule deformation. J. Fluid Mech. 460, 211–222.CrossRefGoogle Scholar
Batchelor, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570.CrossRefGoogle Scholar
Bathe, K. J. 1996 Finite Element Procedures. Prentice-Hall.Google Scholar
Bessis, M., Mohandas, N. & Feo, C. 1980 Automated ektacytometry: a new method of measuring red cell deformability and red cell indices. Blood Cells 6, 315–327.Google ScholarPubMed
Bitbol, M. 1986 Red blood cell orientation in orbit C = 0. Biophys. J. 49, 1055–1068.CrossRefGoogle ScholarPubMed
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Annu. Rev. Fluid Mech. 20, 111–157.CrossRefGoogle Scholar
Breyiannis, G. & Pozrikidis, C. 2000 Simple shear flow of suspensions of elastic capsules. Theor. Comput. Fluid Dyn. 13, 327–347.CrossRefGoogle Scholar
Brooks, D. E., Goodwin, J. W. & Seaman, G. V. 1970 Interactions among erythrocytes under shear. J. Appl. Physiol. 28, 172–177.CrossRefGoogle ScholarPubMed
Buxton, G. A., Verberg, R., Jasnow, D. & Balazs, A. C. 2005 Newtonian fluid meets an elastic solid: coupling lattice Boltzmann and lattice-spring models. Phys. Rev. E 71, 56707.Google ScholarPubMed
Campanelli, M., Berzeri, M. & Shabana, A. A. 2000 Performance of the incremental and non-incremental finite element formulations in flexible multibody problems. J. Mech. Design 122, 498.CrossRefGoogle Scholar
Cha, W. & Beissinger, R. L. 1996 Augmented mass transport of macromolecules in sheared suspensions to surfaces b. bovine serum albumin. J. Colloid Interface Sci. 178, 1–9.CrossRefGoogle Scholar
Chen, S. & Doolen, G. D. 1998 Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364.CrossRefGoogle Scholar
Cohu, O. & Magnin, A. 1995 Rheometry of paints with regard to roll coating process. J. Rheol. 39, 767.CrossRefGoogle Scholar
Cox, R. G. 1974 The motion of suspended particles almost in contact. Intl J. Multiphase Flow 1, 343–371.CrossRefGoogle Scholar
Dao, M., Lim, C. T. & Suresh, S. 2003 Mechanics of the human red blood cell deformed by optical tweezers. J. Mech. Phys. Solids 51, 2259–2280.CrossRefGoogle Scholar
Ding, E. J. & Aidun, C. K. 2000 The dynamics and scaling law for particles suspended in shear flow with inertia. J. Fluid Mech. 423, 317–344.CrossRefGoogle Scholar
Ding, E. J. & Aidun, C. K. 2003 Extension of the lattice-Boltzmann method for direct simulation of suspended particles near contact. J. Stat. Phys. 112, 685–708.CrossRefGoogle Scholar
Ding, E. J. & Aidun, C. K. 2006 Cluster size distribution and scaling for spherical particles and red blood cells in pressure-driven flows at small Reynolds number. Phys. Rev. Lett. 96, 204502.CrossRefGoogle ScholarPubMed
Dupin, M. M., Halliday, I., Care, C. M., Alboul, L. & Munn, L. L. 2007 Modeling the flow of dense suspensions of deformable particles in three dimensions. Phys. Rev. E 75, 66707.Google ScholarPubMed
Eggleton, C. D. & Popel, A. S. 1998 Large deformation of red blood cell ghosts in a simple shear flow. Phys. Fluids 10 (8), 1834–1845.CrossRefGoogle Scholar
Fischer, T. M., Stohr-Lissen, M. & Schmid-Schonbein, H. 1978 The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow. Science 202, 894–896.CrossRefGoogle ScholarPubMed
Fung, Y. 1993 Biomechanics: Mechanical Properties of Living Tissues. Springer.CrossRefGoogle Scholar
Goddard, J. D. & Miller, C. 1967 Nonlinear effects in the rheology of dilute suspensions. J. Fluid Mech. 28, 657–673.CrossRefGoogle Scholar
Goldsmith, H. L., Bell, D. N., Braovac, S., Steinberg, A. & McIntosh, F. 1995 Physical and chemical effects of red cells in the shear-induced aggregation of human platelets. Biophys. J. 69, 1584–1595.CrossRefGoogle ScholarPubMed
Haga, J. H., Beaudoin, A. J., White, J. G. & Strony, J. 1998 Quantification of the passive mechanical properties of the resting platelet. Ann. Biomed. Engng 26, 268–277.CrossRefGoogle ScholarPubMed
Harkness, J. & Whittington, R. B. 1970 Blood-plasma viscosity: an approximate temperature-invariant arising from generalised concepts. Biorheology 6 (3), 169–187.CrossRefGoogle ScholarPubMed
Hofman, J. M. A., Clercx, H. J. H. & Schram, P. 2000 Effective viscosity of dense colloidal crystals. Phys. Rev. E 62, 8212–8233.Google ScholarPubMed
Hwang, W. C. & Waugh, R. E. 1997 Energy of dissociation of lipid bilayer from the membrane skeleton of red blood cells. Biophys. J. 72, 2669–2678.CrossRefGoogle ScholarPubMed
Kim, D. & Beissinger, R. L. 1993 Augmented mass transport of macromolecules in sheared suspensions to surfaces. J. Colloid Interface Sci. 159, 9–20.CrossRefGoogle Scholar
Konstantopoulos, K., Kukreti, S. & McIntire, L. V. 1998 Biomechanics of cell interactions in shear fields. Adv. Drug Delivery Rev. 33, 141–164.CrossRefGoogle ScholarPubMed
Kroll, M. H., Hellums, J. D., McIntire, L. V., Schafer, A. I. & Moake, J. L. 1996 Platelets and shear stress. Blood 88, 1525–1541.CrossRefGoogle ScholarPubMed
Ladd, A. J. C. 1994 Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285–309.CrossRefGoogle Scholar
Ladd, A. J. C. & Verberg, R. 2001 Lattice-Boltzmann simulations of particle–fluid suspensions. J. Stat. Phys. 104, 1191–1251.CrossRefGoogle Scholar
Lallemand, P. & Luo, L. S. 2000 Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E 61, 6546–6562.Google ScholarPubMed
Lin, C. J., Peery, J. H. & Schowalter, W. R. 1970 Simple shear flow round a rigid sphere: inertial effects and suspension rheology. J. Fluid Mech. 44, 1–17.CrossRefGoogle Scholar
Liu, X., Tang, Z., Zeng, Z., Chen, X., Yaob, W., Yana, Z., Shic, Y., Shand, H., Sun, D., Hee, D. & Wen, Z. 2007 The measurement of shear modulus and membrane surface viscosity of RBC membrane with ektacytometry: a new technique. Math. Biosci. 209, 190–204.CrossRefGoogle ScholarPubMed
Liu, Y. & Liu, W. K. 2006 Rheology of red blood cell aggregation by computer simulation. J. Comput. Phys. 220, 139–154.CrossRefGoogle Scholar
MacMeccan, R. 2007 Mechanistic effects of erythrocytes on platelet deposition in coronary thrombosis. PhD thesis, Georgia Institute of Technology.Google Scholar
McNamara, G. R. & Zanetti, G. 1988 Use of the Boltzmann equation to simulate lattice-gas automata. Phys. Rev. Lett. 61, 2332–2335.CrossRefGoogle ScholarPubMed
Merrill, E. W., Cokelet, G. C., Britten, A. & Wells, R. 1963 Non-Newtonian rheology of human blood-effect of fibrinogen deduced by ‘subtraction’. Circ. Res. 13, 48–55.CrossRefGoogle ScholarPubMed
Mikulencak, D. R. & Morris, J. F. 2004 Stationary shear flow around fixed and free bodies at finite Reynolds number. J. Fluid Mech. 520, 215–242.CrossRefGoogle Scholar
Miyamura, A., Iwasaki, S. & Ishii, T. 1981 Experimental wall correction factors of single solid spheres in triangular and square cylinders, and parallel plates. Intl J. Multiphase Flow 7, 41–46.CrossRefGoogle Scholar
Möller, T. & Trumbore, B. 1997 Fast, minimum storage ray-triangle intersection. J. Graphics Tools 2, 21–28.CrossRefGoogle Scholar
Munn, L. L., Melder, R. J. & Jain, R. K. 1996 Role of erythrocytes in leukocyte–endothelial interactions: mathematical model and experimental validation. Biophys. J. 71, 466–478.CrossRefGoogle ScholarPubMed
Nunan, K. C. & Keller, J. B. 1984 Effective viscosity of a periodic suspension. J. Fluid Mech. 142, 269–287.CrossRefGoogle Scholar
Pal, R. 2003 Rheology of concentrated suspensions of deformable elastic particles such as human erythrocytes. J. Biomech. 36, 981–9.CrossRefGoogle ScholarPubMed
Paulus, J. M. 1975 Platelet size in man. Blood 46, 321–336.CrossRefGoogle ScholarPubMed
Pozrikidis, C. 2003 Numerical simulation of the flow-induced deformation of red blood cells. Ann. Biomed. Engng 31, 1194–1205.CrossRefGoogle ScholarPubMed
Pozrikidis, C. 2005 Numerical simulation of cell motion in tube flow. Ann. Biomed. Engng 33, 165–178.CrossRefGoogle ScholarPubMed
Qi, D. 1999 Lattice-Boltzmann simulations of particles in non-zero-Reynolds-number flows. J. Fluid Mech. 385, 41–62.CrossRefGoogle Scholar
Rankin, C. C. & Brogan, F. A. 1986 An element independent corotational procedure for the treatment of large rotations. Trans. ASME J. Press. Vessel Technol. ASME 108, 165–174.CrossRefGoogle Scholar
Schmid-Schonbein, H., Grebe, R. & Heidtmann, H. 1983 A new membrane concept for viscous rbc deformation in shear: spectrin oligomer complexes as a Bingham-fluid in shear and a dense periodic colloidal system in bending. Ann. NY Acad. Sci. 416, 225–254.CrossRefGoogle Scholar
Shin, S., Ku, Y., Park, M. S. & Suh, J. S. 2004 Measurement of red cell deformability and whole blood viscosity using laser-diffraction slit rheometer. Korea-Aust. Rheol. J. 16, 85–90.Google Scholar
Sierou, A. & Brady, J. F. 2002 Rheology and microstructure in concentrated noncolloidal suspensions. J. Rheol. 46, 1031–1056.CrossRefGoogle Scholar
Sierou, A. & Brady, J. F. 2004 Shear-induced self-diffusion in non-colloidal suspensions. J. Fluid Mech. 506, 285–314.CrossRefGoogle Scholar
Skalak, R., Tozeren, A., Zarda, R. P. & Chien, S. 1973 Strain energy function of red blood cell membranes. Biophys J. 13, 245.CrossRefGoogle ScholarPubMed
Sun, C., Migliorini, C. & Munn, L. L. 2003 Red blood cells initiate leukocyte rolling in postcapillary expansions: a lattice Boltzmann analysis. Biophys. J. 85, 208–222.CrossRefGoogle ScholarPubMed
Thorp, B. A. & Kocurek, M. J. 1998 Pulp and Paper Manufacture. Volume 7, Paper Machine Operations. Technical Section, Canadian Pulp and Paper Association, Montreal, Quebec.Google Scholar
Wagner, A. J. & Pagonabarraga, I. 2002 Lees–Edwards boundary conditions for lattice Boltzmann. J. Stat. Phys. 107, 521–537.CrossRefGoogle Scholar
Watanabe, N., Kataoka, H., Yasuda, T. & Takatani, S. 2006 Dynamic deformation and recovery response of red blood cells to a cyclically reversing shear flow: effects of frequency of cyclically reversing shear flow and shear stress level. Biophys. J. 91, 1984.CrossRefGoogle ScholarPubMed
Waugh, R. & Evans, E. A. 1979 Thermoelasticity of red blood cell membrane. Biophys. J. 26, 115–131.CrossRefGoogle ScholarPubMed
Yao, W., Wen, Z., Yan, Z., Sun, D., Ka, W., Xie, L. & Chien, S. 2001 Low viscosity ektacytometry and its validation tested by flow chamber. J. Biomech. 34, 1501–1509.CrossRefGoogle ScholarPubMed
Young, W. C. & Budynas, R. G. 2002 Roark's Formulas for Stress and Strain. McGraw-Hill.Google Scholar
Zinchenko, A. Z. & Davis, R. H. 2002 Shear flow of highly concentrated emulsions of deformable drops by numerical simulations. J. Fluid Mech. 455, 21–62.CrossRefGoogle Scholar
Zuzovsky, M., Adler, P. M. & Brenner, H. 1983 Spatially periodic suspensions of convex particles in linear shear flows. III. Dilute arrays of spheres suspended in Newtonian fluids. Phys. Fluids 26, 1714.CrossRefGoogle Scholar