Comptes Rendus
Vesicles and red blood cells in flow: From individual dynamics to rheology
[Vésicules et globules rouges sous écoulement : De la dynamique individuelle à la rhéologie]
Comptes Rendus. Physique, Volume 10 (2009) no. 8, pp. 775-789.

La rhéologie des suspensions de particules molles, telles les globules rouges, constitue depuis longtemps un défi pour les sciences et l'ingénierie à cause du caractère complexe du couplage entre la microstructure et l'écoulement global. La source de la difficulté provient du caractère libre des surfaces des entités en suspension. Les bicouches lipidiques qui composent les membranes des cellules vivantes et des vésicules sont des surfaces particulièrement complexes à cause de leur mécanique inhabituelle : la membrane d'épaisseur moléculaire est très flexible mais en même temps il s'agit d'une surface incompressible. Il en résulte que les particules composées de ces membranes (comme les globules rouges et vésicules) révèlent plus de richesses que ne le font les gouttes ou les capsules. Nous passons en revue les principaux résultats expérimentaux et les progrès théoriques réalisés dans l'étude des vésicules et globules rouges sous écoulement.

The rheology of suspensions of soft particles, such as red blood cells, is a long-standing problem in science and engineering due to the complex interplay between deformable microstructure and the macroscale flow. The major challenge stems from the free-boundary nature of the particle interface. Lipid bilayer membranes that envelop cells and vesicles are particularly complex interfaces because of their unusual mechanics: the molecularly thin membrane is a highly-flexible incompressible fluid sheet. As a result, particles made of closed lipid bilayers (red cells and vesicles) can exhibit richer dynamics than would capsules and drops. We overview the key experimental observations and recent advances in the theoretical modeling of the vesicles and red blood cells in flow.

Publié le :
DOI : 10.1016/j.crhy.2009.10.001
Keywords: Lipid membrane, Stokes flow, Blood rheology
Mot clés : Membrane lipidique, Écoulement de Stokes, Rhéologie du sang
Petia M. Vlahovska 1 ; Thomas Podgorski 2 ; Chaouqi Misbah 2

1 Thayer School of Engineering, Dartmouth College, 8000 Cummings Hall, Hanover, NH 03755, USA
2 Laboratoire de Spectrométrie Physique, UMR 5588, 140, avenue de la Physique, Université Joseph-Fourier, and CNRS, 38402 Saint Martin d'Heres, France
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Petia M. Vlahovska; Thomas Podgorski; Chaouqi Misbah. Vesicles and red blood cells in flow: From individual dynamics to rheology. Comptes Rendus. Physique, Volume 10 (2009) no. 8, pp. 775-789. doi : 10.1016/j.crhy.2009.10.001. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2009.10.001/

[1] B. Alberts; A. Johnson; J. Lewis; M. Raff; K. Roberts; P. Walter Molecular Biology of the Cell, Garland Publishing Inc., New York, 2002

[2] R. Lipowsky; E. Sackmann Structure and Dynamics of Membranes, Elsevier, Amsterdam, 1995

[3] R. Lipowsky The conformation of membranes, Nature, Volume 349 (1991), pp. 475-481

[4] P.R. Leduc; M.S. Wong; P.M. Ferreira; R.E. Groff; K. Haslinger; M.P. Koonce; W.Y. Lee; J.C. Love; J.A. McCammon; N.A. Monteiro-Riviere; V.M. Rotello; G.W. Rubloff; R. Westervelt; M. Yoda Towards an in vivo biologically inspired nanofactory, Nat. Nanotechnol., Volume 2 (2007), pp. 3-7

[5] V. Noireaux; A. Libchaber A vesicle bioreactor as a step toward an artificial cell assembly, PNAS, Volume 101 (2004), pp. 17669-17674

[6] M. Karlsson; M. Davidson; R. Karlsson; A. Karlsson; J. Bergenholtz; Z. Konkoli; A. Jesorka; T. Lobovkina; J. Hurtig; M. Voinova; O. Orwar Biomimetic nanoscale reactors and networks, Ann. Rev. Phys. Chem., Volume 55 (2004), pp. 613-649

[7] T.M. Allen; P.R. Cullis Drug delivery systems: Entering the mainstream, Science, Volume 303 (2004), pp. 1818-1822

[8] G. Gregoriadis Engineering liposomes for drug delivery, Trends Biotechnol., Volume 13 (1995), pp. 527-537

[9] D.R. Arifin; A.F. Palmer Polymersome encapsulated hemoglobin: A novel type of oxygen carrier, Biomacromolecules, Volume 6 (2005), pp. 2172-2181

[10] R. Dimova; K.A. Riske; S. Aranda; N. Bezlyepkina; R.L. Knorr; R. Lipowsky Giant vesicles in electric fields, Soft Matter, Volume 3 (2007), pp. 817-827

[11] R. Dimova, personal communication

[12] M.-A. Mader; V. Vitkova; M. Abkarian; A. Viallat; T. Podgorski Dynamics of viscous vesicles in shear flow, Eur. Phys. J. E, Volume 19 (2006), pp. 389-397

[13] W. Helfrich Elastic properties of lipid bilayers – Theory and possible experiments, Z. Naturforsch., Volume 28c (1973), pp. 693-703

[14] U. Seifert Configurations of fluid membranes and vesicles, Adv. Phys., Volume 46 (1997), pp. 13-137

[15] D. Barthes-Biesel Role of interfacial properties on the motion and deformation of capsules in shear flow, Physica A, Volume 172 (1991), pp. 103-124

[16] C. Pozrikidis Modeling and Simulation of Capsules and Biological Cells, CRC Press, 2003

[17] M. Bloom; E. Evans; O.G. Mouritsen Physical properties of the fluid lipid bilayer component of cell membranes – A perspective, Q. Rev. Biophys., Volume 24 (1991), pp. 293-397

[18] R. Dimova; S. Aranda; N. Bezlyepkina; V. Nikolov; K.A. Riske; R. Lipowsky A practical guide to giant vesicles: Probing the membrane nanoregime via optical microscopy, J. Phys. Condens. Matter, Volume 18 (2006), p. S1151-S1176

[19] F.L. Brown Elastic modeling of biomembranes and lipid bilayers, Annu. Rev. Phys. Chem., Volume 59 (2008), pp. 685-712

[20] H. Dobereiner Properties of giant vesicles, Curr. Opin. Colloid Interface Sci., Volume 5 (2000), pp. 256-263

[21] D. Barthes-Biesel Capsule motion is flow: Deformation and membrane buckling, C. R. Physique, Volume 10 (2009) no. 8, pp. 764-774 (this issue)

[22] E. Evans; R. Skalak Mechanics and Thermodynamics of Biomembranes, CRC Press, Boca Raton, Florida, 1980

[23] J.T. Jenkins The equations of mechanical equilibrium of a model membrane, SIAM J. Appl. Math., Volume 32 (1977), p. 755

[24] M.M. Kozlov Membrane shape equations, J. Phys. Condens. Matter, Volume 18 (2006), p. S1177-S1190

[25] U. Seifert Fluid membranes in hydrodynamic flow fields: Formalism and an application to fluctuating quasispherical vesicles, Eur. Phys. J. B, Volume 8 (1999), pp. 405-415

[26] U. Seifert; K. Berndl; R. Lipowsky Shape transformations of vesicles: Phase diagram for spontaneous-curvature and bilayer-coupling models, Phys. Rev. A, Volume 44 (1991), pp. 1182-1202

[27] R. Blowers; E.M. Clarkson; M. Maizels Flicker phenomenon in human erythrocytes, J. Physiol., Volume 113 (1951), pp. 228-239

[28] F. Brochard; J.F. Lennon Frequency spectrum of the flicker phenomenon in erythrocytes, J. Phys. (France), Volume 36 (1975), pp. 1035-1047

[29] L. Miao; M.A. Lomholt; J. Kleis Dynamics of shape fluctuations of quasi-spherical vesicles revisited, Eur. Phys. J. E, Volume 9 (2002), pp. 143-160

[30] L.G. Leal Advanced Transport Phenomena, Cambridge University Press, 2007

[31] K.H. de Haas; C. Blom; D. van den Ende; M.H.G. Duits; J. Mellema Deformation of giant lipid bilayer vesicles in shear flow, Phys. Rev. E, Volume 56 (1997), pp. 7132-7137

[32] V. Kantsler; V. Steinberg Orientation and dynamics of a vesicle in tank-treading motion in shear flow, Phys. Rev. Lett., Volume 95 (2005), p. 258101

[33] V. Kantsler; V. Steinberg Transition to tumbling and two regimes of tumbling motion of a vesicle in shear flow, Phys. Rev. Lett., Volume 96 (2006), p. 036001

[34] M. Abkarian; A. Viallat Vesicles and red blood cells in shear flow, Soft Matter, Volume 4 (2008), pp. 653-657

[35] J. Deschamps; V. Kantsler; V. Steinberg Phase diagram of single vesicle dynamical states in shear flow, Phys. Rev. Lett., Volume 102 (2009) no. 11, p. 118105

[36] C. Misbah Vacillating breathing and tumbling of vesicles under shear flow, Phys. Rev. Lett., Volume 96 (2006), p. 028104

[37] S.R. Keller; R. Skalak Motion of a tank-reading ellipsoidal particle in shear flow, J. Fluid Mech., Volume 120 (1982), pp. 27-47

[38] H. Noguchi; G. Gompper Swinging and tumbling of fluid vesicles in shear flow, Phys. Rev. Lett., Volume 98 (2007), p. 128103

[39] P.M. Vlahovska; R. Gracia Dynamics of a viscous vesicle in linear flows, Phys. Rev. E, Volume 75 (2007), p. 016313

[40] M.-A. Mader; H. Ez-Zahraouy; C. Misbah; T. Podgorski On coupling between the orientation and the shape of a vesicle under a shear flow, Eur. Phys. J. E, Volume 22 (2007), pp. 275-280

[41] G. Danker; T. Biben; T. Podgorski; C. Verdier; C. Misbah Dynamics and rheology of a dilute suspension of vesicles: Higher order theory, Phys. Rev. E, Volume 76 (2007), p. 041905

[42] V.V. Lebedev; K.S. Turitsyn; S.S. Vergeles Nearly spherical vesicles in an external flow, New J. Phys., Volume 10 (2008), p. 043044

[43] B. Kaoui, A. Farutin, C. Misbah, Vesicles under simple shear flow: Elucidating the role of relevant control parameters, Phys. Rev. E, in press

[44] A. Farutin, T. Biben, C. Misbah, New progress in analytical theory for vesicles under flow, preprint, 2009

[45] T. Biben, C. Misbah, On quantitative and new qualitative features of vesicles under flow: A numerical study, preprint, 2009

[46] P. Olla The behavior of closed inextensible membranes in linear and quadratic shear flows, Physica A, Volume 278 (2000), pp. 87-106

[47] V.V. Lebedev; K.S. Turitsyn; S.S. Vergeles Dynamics of nearly spherical vesicles in an external flow, Phys. Rev. Lett., Volume 99 (2007), p. 218101

[48] R. Finken; A. Lamura; U. Seifert; G. Gompper Two-dimensional fluctuating vesicles in linear shear flow, Eur. Phys. J. E, Volume 25 (2008), pp. 309-321

[49] H. Noguchi; G. Gompper Dynamics of fluid vesicles in shear flow: Effect of membrane viscosity and thermal fluctuations, Phys. Rev. E, Volume 72 (2005), p. 011901

[50] N. Fa; C.M. Marques; E. Mendes; A.P. Schroder Rheology of giant vesicles: A micropipette study, Phys. Rev. Lett., Volume 92 (2004), p. 108103

[51] V. Kantsler; E. Segre; V. Steinberg Vesicle dynamics in time-dependent elongation flow: Wrinkling instability, Phys. Rev. Lett., Volume 99 (2007), p. 178102

[52] K.S. Turitsyn; S.S. Vergeles Wrinkling of vesicles during transient dynamics in elongational flow, Phys. Rev. Lett., Volume 100 (2008), p. 028103

[53] H. Noguchi Membrane simulation models from nanometer to micrometer scale, J. Phys. Soc. Japan, Volume 78 (2009), p. 041007

[54] J.C. Shillcock; R. Lipowsky The computational route from bilayer membranes to vesicle fusion, J. Phys. Condens. Matter, Volume 18 (2006), p. S1191-S1219

[55] M. Muller; K. Katsov; M. Schick Biological and synthetic membranes: What can be learned from a coarse-grained description?, Phys. Rep., Volume 434 (2006), pp. 113-176

[56] M. Kraus; W. Wintz; U. Seifert; R. Lipowsky Fluid vesicle in shear flow, Phys. Rev. Lett., Volume 77 (1996), pp. 3685-3688

[57] I. Cantat; C. Misbah Lift force and dynamical unbinding of adhering vesicles under shear flow, Phys. Rev. Lett., Volume 83 (1999), pp. 880-883

[58] B. Kaoui; G.H. Ristow; I. Cantat; C. Misbah; W. Zimmermann Lateral migration of a two-dimensional vesicle in unbounded Poiseuille flow, Phys. Rev. E, Volume 77 (2008), p. 021903

[59] S.K. Veerapaneni; D. Gueyffier; D. Zorin; G. Biros A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, J. Comp. Phys., Volume 228 (2009) no. 7, pp. 2334-2353

[60] K.A. Smith; W.E. Uspal Shear-driven release of a bud from a multicomponent vesicle, J. Chem. Phys., Volume 126 (2007), p. 075102

[61] P.D. Richardson; I.V. Pivkin; G.E. Karniadakis Red cells in shear flow: Dissipative particle dynamics modeling, Biorheology, Volume 45 (2008), pp. 107-108

[62] H. Noguchi; G. Gompper Fluid vesicles with viscous membranes in shear flow, Phys. Rev. Lett., Volume 93 (2004), p. 258102

[63] H. Noguchi; G. Gompper Shape transitions of fluid vesicles and red-blood cells in capillary flows, PNAS, Volume 102 (2005), pp. 14159-14164

[64] J.L. McWhirter; H. Noguchi; G. Gompper Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries, PNAS, Volume 106 (2009) no. 15, pp. 6039-6043

[65] S. Messlinger; B. Schmidt; H. Noguchi; G. Gompper Dynamical regimes and hydrodynamic lift of viscous vesicles under shear, Phys. Rev. E, Volume 80 (2009), p. 011901

[66] T. Biben; C. Misbah Tumbling of vesicles under shear flow within an advected-field approach, Phys. Rev. E, Volume 67 (2003), p. 031908

[67] J. Beaucourt; F. Rioual; T. Seon; T. Biben; C. Misbah Steady to unsteady dynamics of a vesicle in a flow, Phys. Rev. E, Volume 69 (2004), p. 011906

[68] T. Biben; K. Kassner; C. Misbah Phase-field approach to three-dimensional vesicle dynamics, Phys. Rev. E, Volume 72 (2005), p. 041921

[69] Q. Du; C. Liu; X. Wang Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions, J. Comp. Phys., Volume 212 (2006), pp. 757-777

[70] F. Feng; W.S. Klug Finite element modeling of lipid bilayer membranes, J. Comp. Phys., Volume 220 (2006), pp. 394-408

[71] L. Ma; W. Klug Viscous regularization and r-adaptive remeshing for finite element analysis of lipid membrane mechanics, J. Comp. Phys., Volume 227 (2008), pp. 5816-5835

[72] S. Chien Red cell deformability and its relevance to blood flow, Annu. Rev. Physiol., Volume 49 (1987), pp. 177-192

[73] C.D. Eggleton; A.S. Popel Large deformation of red blood cell ghosts in a simple shear flow, Phys. Fluids, Volume 10 (1998), pp. 1834-1845

[74] P. Bagchi Mesoscale simulation of blood flow in small vessels, Biophys. J., Volume 92 (2007), pp. 1858-1877

[75] T.W. Secomb; R. Skalak; N. Ozkaya; J.F. Gross Flow of axisymmetrical red blood cells in narrow capillaries, J. Fluid Mech., Volume 163 (1986), pp. 405-423

[76] J.B. Freund Leukocyte margination in a model microvessel, Phys. Fluids, Volume 19 (2007), p. 023301

[77] C. Pozrikidis Effect of membrane bending stiffness on the deformation of capsules in simple shear flow, J. Fluid Mech., Volume 440 (2001), pp. 269-291

[78] M. Abkarian; M. Faivre; A. Viallat Swinging of red blood cells under shear flow, Phys. Rev. Lett., Volume 98 (2007), p. 188302

[79] M. Bibtol Red blood cell orientation in orbit C=0, Biophys. J., Volume 49 (1986), pp. 1055-1068

[80] A. Walter; H. Rehage; H. Leonhard Shear induced deformation of microcapsules: Shape oscillations and membrane folding, Colloids Surf. A, Volume 183–185 (2001), pp. 123-132

[81] P. Erni; P. Fischer; E. Windhab Deformation of single emulsion drops covered with a viscoelastic adsorbed protein layer in simple shear flow, Appl. Phys. Lett., Volume 87 (2005), p. 244104

[82] J.M. Skotheim; T.W. Secomb Red blood cells and other nonspherical capsules in shear flow: Oscillatory dynamics and the tank-treading-to-tumbling transition, Phys. Rev. Lett., Volume 98 (2007), p. 078301

[83] S. Kessler; R. Finken; U. Seifert Swinging and tumbling of elastic capsules in shear flow, J. Fluid Mech., Volume 605 (2008), pp. 207-226

[84] Y. Sui; Y.T. Chew; P. Roy; Y.P. Cheng; H.T. Low Dynamic motion of red blood cells in simple shear flow, Phys. Fluids, Volume 20 (2008), p. 112106

[85] P. Bagchi; R.M. Kalluri Dynamics of nonspherical capsules in shear flow, Phys. Rev. E, Volume 80 (2009), p. 016307

[86] P.M. Vlahovska, G. Danker, C. Misbah, Swinging of drops enclosed by elastic membranes, in preparation

[87] S. Guido; G. Tomaiuolo Microconfined flow behavior of red blood cells in vitro, C. R. Physique, Volume 10 (2009) no. 8, pp. 751-763 (this issue)

[88] S.P. Sutera; R. Skalak The history of Poiseuille's law, Annu. Rev. Fluid Mech., Volume 25 (1993), pp. 1-19

[89] A.S. Popel; P.C. Johnson Microcirculation and hemorheology, Annu. Rev. Fluid Mech., Volume 37 (2005) no. 1, pp. 43-69

[90] F.P. Bretherton The motion of rigid particles in a shear flow at low Reynolds number, J. Fluid Mech., Volume 14 (1962), pp. 284-304

[91] L.G. Leal Particle motions in a viscous fluid, Annu. Rev. Fluid Mech., Volume 12 (1980), pp. 435-476

[92] B. Lorz; R. Simson; J. Nardi; E. Sakmann Weakly adhering vesicles in shear flows: Tanktreading and anomalous lift force, Europhys. Lett., Volume 51 (2000), pp. 468-474

[93] M. Abkarian; C. Lartigue; A. Viallat Tank treading and unbinding of deformable vesicles in shear flow: Determination of the lift force, Phys. Rev. Lett., Volume 88 (2002), p. 068103

[94] M. Abkarian; A. Viallat Dynamics of vesicles in a wall-bounded shear flow, Biophys. J., Volume 89 (2005), pp. 1055-1066

[95] N. Callens; C. Minetti; G. Coupier; M.-A. Mader; F. Dubois; C. Misbah; T. Podgorski Hydrodynamic lift of vesicles under shear flow in microgravity, Europhys. Lett., Volume 83 (2008), p. 24002

[96] I. Cantat; C. Misbah Dynamics and similarity laws for adhering vesicles in haptotaxis, Phys. Rev. Lett., Volume 83 (1999), pp. 235-238

[97] S. Sukumaran; U. Seifert Influence of shear flow on vesicle near a wall: A numerical study, Phys. Rev. E, Volume 64 (2001), p. 011916

[98] U. Seifert Hydrodynamic lift on bound vesicles, Phys. Rev. Lett., Volume 83 (1999), pp. 876-879

[99] P. Olla The lift on a tank treading ellipsoidal cell in a shear flow, J. Phys. II France, Volume 7 (1997), pp. 1533-1540

[100] P. Olla The role of tank-treading motions in the transverse migration of a spheroidal vesicle in a shear flow, J. Phys. A: Math. Gen., Volume 30 (1997), pp. 317-329

[101] P. Olla Simplified model for red cell dynamics in small blood vessels, Phys. Rev. Lett., Volume 82 (1999), pp. 453-456

[102] S. Kim; S.J. Karrila Microhydrodynamics: Principles and Selected Applications, Butterworth-Heinemann, 1991

[103] R. Skalak Science, 164 (1969), p. 717

[104] Y. Suzuki; N. Tateishi; M. Soutani; N. Maeda Microcirculation, 3 (1996), p. 49

[105] T.W. Secomb; R. Skalak Microvascular Research, 24 (1982), p. 194

[106] B. Kaoui; G. Biros; C. Misbah Why do red blood cells move asymmetric even in a symmetric flow?, Phys. Rev. Lett., Volume 103 (2009), p. 188101

[107] V. Vitkova; M. Mader; T. Podgorski Deformation of vesicles flowing through capillaries, Europhys. Lett., Volume 68 (2004), pp. 398-404

[108] R. Bruinsma Rheology and shape transitions of vesicles under capillary flow, Physica A, Volume 234 (1996), pp. 249-270

[109] G. Danker; P.M. Vlahovska; C. Misbah Vesicles in Poiseuille flow, Phys. Rev. Lett., Volume 102 (2009), p. 148102

[110] G. Coupier; B. Kaoui; T. Podgorski; C. Misbah Noninertial lateral migration of vesicles in bounded Poiseuille flow, Phys. Fluids, Volume 20 (2009), p. 111702

[111] P.C.-H. Chan; L.G. Leal Motion of a deformable drop in a second-order fluid, J. Fluid Mech., Volume 92 (1979), pp. 131-170

[112] M. Faivre; M. Abkarian; K. Bickraj; H.A. Stone Geometrical focusing of cells in a microfluidic device: An approach to separate blood plasma, Biorheology, Volume 43 (2006), pp. 147-159

[113] C. Pozrikidis Boundary Integral and Singularity Methods for Linearized Viscous Flow, Cambridge University Press, 1992

[114] G. Danker; C. Misbah Rheology of a dilute suspension of vesicles, Phys. Rev. Lett., Volume 98 (2007), p. 088104

[115] V. Vitkova; M. Mader; B. Polack; C. Misbah; T. Podgorski Micro–macro link in rheology of erythrocyte and vesicle suspensions, Biophys. J., Volume 95 (2008) no. 6, p. L33-L35

[116] S.S. Vergeles Rheological properties of a vesicle suspension, JETP, Volume 87 (2008), pp. 511-515

[117] V. Kantsler; E. Segre; V. Steinberg Dynamics of interacting vesicles and rheology of vesicle suspension in shear flow, Europhys. Lett., Volume 82 (2008), p. 58005

[118] T. Podgorski; N. Callens; C. Minetti; G. Coupier; F. Dubois; C. Misbah Biomics experiment: Structure and dynamics of a vesicle suspension in a shear flow, Proceedings of the 19th ESA-PAC Symposium on Rocket and Balloon Programmes and Related Research, 2009, pp. 1-6

[119] S. Kessler; R. Finken; U. Seifert Elastic capsules in shear flow: Analytical solutions for constant and time-dependent shear rates, Eur. Phys. J. E, Volume 29 (2009), pp. 399-413

[120] Y.-N. Young; J. Bławzdziewicz; V. Cristini; R.H. Goodman Hysteretic and chaotic dynamics of viscous drops in creeping flows with rotation, J. Fluid Mech., Volume 607 (2008), pp. 209-234

[121] R. Dimova, N. Bezlyepkina, M.D. Jordo, R.L. Knorr, K.A. Riske, M. Staykova, P.M. Vlahovska, T. Yamamoto, P. Yang, R. Lipowsky, Vesicles in electric fields: Some novel aspects of membrane behavior, Soft Matter (2009), in press, | DOI

[122] M. Staykova; R. Lipowsky; R. Dimova Membrane flow patterns in multicomponent giant vesicles induced by alternating electric fields, Soft Matter, Volume 4 (2008), pp. 2168-2171

[123] S. Lecuyer; W.D. Ristenpart; O. Vincent; H.A. Stone Electrohydrodynamic size stratification and flow separation of giant vesicles, Appl. Phys. Lett., Volume 92 (2008), p. 104105

[124] D. Lacoste; G.I. Menon; M.Z. Bazant; J.F. Joanny Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane, EPJE, Volume 28 (2009), pp. 243-264

[125] P.M. Vlahovska; R.S. Gracia; S. Aranda-Espinoza; R. Dimova Electrohydrodynamic model of vesicle deformation in alternating electric fields, Biophys. J., Volume 96 (2009), pp. 4789-4803

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