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Boundary element approach for the slow viscous migration of spherical bubbles
Boundary integral and fast multipole method for two dimensional vesicle sets in Poiseuille flow
1. | Laboratoire d'Ingénierie Mathématique, Ecole Polytechnique de Tunisie, Université de Carthage, B.P. 743 - 2078 La Marsa, Tunisia |
2. | Laboratoire Interdisciplinaire de Physique, 140, rue de la Physique, 38402 Saint Martin d'Hères, France, France |
References:
[1] |
D. Barthès-Biesel and J. M. Rallison, The time-dependent deformation of a capsule freely suspended in a linear shear flow, J. Fluid Mech., 113 (1981), 251-267.
doi: doi:10.1017/S0022112081003480. |
[2] |
C. D. Eggleton and A. S. Popel, Large deformation of red blood cell ghosts in a simple shear flow, Phys. Fluids, 10 (1998), 1834-1845.
doi: doi:10.1063/1.869703. |
[3] |
G. Ghigliotti, T. Biben and C. Misbah, Rheology of a dilute two-dimensional suspension of vesicles, J. Fluid Mech., 653 (2010), 489-518.
doi: doi:10.1017/S0022112010000431. |
[4] |
L. Greengard and V. Rokhlin, A fast algorithm for particle simulations, J. Comp. Phys., 73 (1987), 325-348.
doi: doi:10.1016/0021-9991(87)90140-9. |
[5] |
L. Greengard and V. Rokhlin, "On the Effficient Implementation of the Fast Multipole Algorithm," Technical report, Yale University, Department of Computer Science, 1988. |
[6] |
N. A. Gumerov and R. Duraiswami, Fast multipole method for the biharmonic equation in three dimensions, J. Comp. Phys., 215 (2006), 363-383.
doi: doi:10.1016/j.jcp.2005.10.029. |
[7] |
W. Helfrich, Elastic properties of lipid bilayers:l theory and possible experiments, Z. Naturforschung, 28 (1973), 693-703. |
[8] |
B. Kaoui, G. Biros and C. Misbah, Why do red blood cells have asymmetric shapes even in a symmetric flow? Phys. Rev. Lett., 103 (2009), 188101.
doi: doi:10.1103/PhysRevLett.103.188101. |
[9] |
B. Kaoui, G. H. Ristow, I. Cantat, C. Misbah and W. Zimmermann, Lateral migration of a two-dimensional vesicle in unbounded Poiseuille flow, Phys. Rev. E, 77 (2008), 021903.
doi: doi:10.1103/PhysRevE.77.021903. |
[10] |
S. R. Keller and R. Skalak, Motion of a tank-treading ellipsoidal particle in a shear flow, J. Fluid Mech., 120 (1982), 27-47.
doi: doi:10.1017/S0022112082002651. |
[11] |
M. Kraus, W. Wintz, U. Seifert and R. Lipowsky, Fluid vesicles in shear flow, Phys. Rev. Lett., 77 (1996), 3685-3688.
doi: doi:10.1103/PhysRevLett.77.3685. |
[12] |
J. L. McWhirter, H. Noguchi and G. Gompper, Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries, PNAS, 106 (2009), 6039-6043.
doi: doi:10.1073/pnas.0811484106. |
[13] |
N. Nishimura, Fast multipole accelerated boundary integral equation methods, Appl. Mech. Rev., 55 (2002), 299-324.
doi: doi:10.1115/1.1482087. |
[14] |
C. Pozrikidis, "Boundary Integral and Singularity Methods for Linearized Viscous Flow," Cambridge University Press, Cambridge, UK, 1992.
doi: doi:10.1017/CBO9780511624124. |
[15] |
C. Pozrikidis, Interfacial dynamics for stokes flow, J. Comp. Phys., 169 (2001), 250-301.
doi: doi:10.1006/jcph.2000.6582. |
[16] |
C. Pozrikidis, "Modeling and Simulation of Capsules and Biological Cells," CRC Press, 2003.
doi: doi:10.1201/9780203503959. |
[17] |
E. Sackmann, Physical basis of self-organization and functions of membranes: Physics of vesicles, chapter 5, pages 213-302. Elsevier Science B.V., 1995. |
show all references
References:
[1] |
D. Barthès-Biesel and J. M. Rallison, The time-dependent deformation of a capsule freely suspended in a linear shear flow, J. Fluid Mech., 113 (1981), 251-267.
doi: doi:10.1017/S0022112081003480. |
[2] |
C. D. Eggleton and A. S. Popel, Large deformation of red blood cell ghosts in a simple shear flow, Phys. Fluids, 10 (1998), 1834-1845.
doi: doi:10.1063/1.869703. |
[3] |
G. Ghigliotti, T. Biben and C. Misbah, Rheology of a dilute two-dimensional suspension of vesicles, J. Fluid Mech., 653 (2010), 489-518.
doi: doi:10.1017/S0022112010000431. |
[4] |
L. Greengard and V. Rokhlin, A fast algorithm for particle simulations, J. Comp. Phys., 73 (1987), 325-348.
doi: doi:10.1016/0021-9991(87)90140-9. |
[5] |
L. Greengard and V. Rokhlin, "On the Effficient Implementation of the Fast Multipole Algorithm," Technical report, Yale University, Department of Computer Science, 1988. |
[6] |
N. A. Gumerov and R. Duraiswami, Fast multipole method for the biharmonic equation in three dimensions, J. Comp. Phys., 215 (2006), 363-383.
doi: doi:10.1016/j.jcp.2005.10.029. |
[7] |
W. Helfrich, Elastic properties of lipid bilayers:l theory and possible experiments, Z. Naturforschung, 28 (1973), 693-703. |
[8] |
B. Kaoui, G. Biros and C. Misbah, Why do red blood cells have asymmetric shapes even in a symmetric flow? Phys. Rev. Lett., 103 (2009), 188101.
doi: doi:10.1103/PhysRevLett.103.188101. |
[9] |
B. Kaoui, G. H. Ristow, I. Cantat, C. Misbah and W. Zimmermann, Lateral migration of a two-dimensional vesicle in unbounded Poiseuille flow, Phys. Rev. E, 77 (2008), 021903.
doi: doi:10.1103/PhysRevE.77.021903. |
[10] |
S. R. Keller and R. Skalak, Motion of a tank-treading ellipsoidal particle in a shear flow, J. Fluid Mech., 120 (1982), 27-47.
doi: doi:10.1017/S0022112082002651. |
[11] |
M. Kraus, W. Wintz, U. Seifert and R. Lipowsky, Fluid vesicles in shear flow, Phys. Rev. Lett., 77 (1996), 3685-3688.
doi: doi:10.1103/PhysRevLett.77.3685. |
[12] |
J. L. McWhirter, H. Noguchi and G. Gompper, Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries, PNAS, 106 (2009), 6039-6043.
doi: doi:10.1073/pnas.0811484106. |
[13] |
N. Nishimura, Fast multipole accelerated boundary integral equation methods, Appl. Mech. Rev., 55 (2002), 299-324.
doi: doi:10.1115/1.1482087. |
[14] |
C. Pozrikidis, "Boundary Integral and Singularity Methods for Linearized Viscous Flow," Cambridge University Press, Cambridge, UK, 1992.
doi: doi:10.1017/CBO9780511624124. |
[15] |
C. Pozrikidis, Interfacial dynamics for stokes flow, J. Comp. Phys., 169 (2001), 250-301.
doi: doi:10.1006/jcph.2000.6582. |
[16] |
C. Pozrikidis, "Modeling and Simulation of Capsules and Biological Cells," CRC Press, 2003.
doi: doi:10.1201/9780203503959. |
[17] |
E. Sackmann, Physical basis of self-organization and functions of membranes: Physics of vesicles, chapter 5, pages 213-302. Elsevier Science B.V., 1995. |
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