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Annual Review of Fluid Mechanics

Volume 48, 2016

Motion and Deformation of Elastic Capsules and Vesicles in Flow

Abstract

This article reviews the mechanical behavior of a capsule under the influence of viscous deforming forces due to a flowing fluid. It focuses on artificial capsules and vesicles with an internal liquid core enclosed by a very thin membrane with different constitutive laws. The recent modeling strategies are outlined together with their respective advantages and limitations. I then consider the motion and deformation of a single, initially spherical capsule freely suspended in a simple shear or plane hyperbolic flow and discuss the effect of the membrane constitutive law, initial prestress, membrane buckling, and bulk or membrane viscosity. Finally, I consider the flow of spherical capsules in small pores and show how numerical models can be used to evaluate the mechanical properties of the membrane.

Keyword(s): capsule, hyperelastic membrane, lipid bilayers, red blood cells, vesicle
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2016-01-03
2024-04-29
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Literature Cited

  1. Abkarian M, Faivre M, Viallat A. 2007. Swinging of red blood cells under shear flow. Phys. Rev. Lett. 98:188302 [Google Scholar]
  2. Abkarian M, Viallat A. 2008. Vesicles and red blood cells in shear flow. Soft Matter 4:653–57 [Google Scholar]
  3. Angelova M, Soléau S, Méléard P, Faucon J, Bothorel P. 1992. Preparation of giant vesicles by external AC electric fields: kinetics and applications. Prog. Colloid Polym. Sci. 89:127–31 [Google Scholar]
  4. Bagchi P, Kalluri RM. 2009. Dynamics of nonspherical capsules in shear flow. Phys. Rev. E 80:016307 [Google Scholar]
  5. Bagchi P, Kalluri RM. 2010. Rheology of a dilute suspension of liquid-filled elastic capsules. Phys. Rev. E 81:056320 [Google Scholar]
  6. Barthès-Biesel D. 1991. Role of interfacial properties on the motion and deformation of capsules in shear flow. Physica A 172:103–24 [Google Scholar]
  7. Barthès-Biesel D, Diaz A, Dhenin E. 2002. Effect of constitutive laws for two-dimensional membranes on flow-induced capsule deformation. J. Fluid Mech. 460:211–22 [Google Scholar]
  8. Barthès-Biesel D, Rallison JM. 1981. The time-dependent deformation of a capsule freely suspended in a linear shear flow. J. Fluid Mech. 113:251–67 [Google Scholar]
  9. Barthès-Biesel D, Sgaier H. 1985. Role of membrane viscosity in the orientation and deformation of a capsule suspended in shear flow. J. Fluid Mech. 160:119–35 [Google Scholar]
  10. Barthès-Biesel D, Walter J, Salsac AV. 2010. Flow-induced deformation of artificial capsules. Computational Hydrodynamics of Capsules and Biological Cells C Pozrikidis 35–70 Boca Raton, FL: CRC [Google Scholar]
  11. Carin M, Barthès-Biesel D, Edwards-Lévy F, Postel C, Andrei D. 2002. Compression of biocompatible liquid-filled HSA-alginate capsules: determination of the membrane mechanical properties. Biotechnol. Bioeng. 82:207–12 [Google Scholar]
  12. Chang KS, Olbricht WL. 1993a. Experimental studies of the deformation and breakup of a synthetic capsule in extensional flow. J. Fluid Mech. 250:587–608 [Google Scholar]
  13. Chang KS, Olbricht WL. 1993b. Experimental studies of the deformation and breakup of a synthetic capsule in steady and unsteady simple shear flow. J. Fluid Mech. 250:609–33 [Google Scholar]
  14. Chapelle D, Bathe KJ. 2003. The Finite Element Analysis of Shells: Fundamentals New York: Springer
  15. Chu TX, Salsac AV, Leclerc E, Barthès-Biesel D, Wurtz H, Edwards-Lévy F. 2011. Comparison between measurements of elasticity and free amino group content of ovalbumin microcapsule membranes: discrimination of the cross-linking degree. J. Colloid Interface Sci. 355:81–88 [Google Scholar]
  16. Cordasco D, Bagchi P. 2013. Orbital drift of capsules and red blood cells in shear flow. Phys. Fluids 25:091902 [Google Scholar]
  17. Coupier G, Farutin A, Minetti C, Podgorski T, Misbah C. 2012. Shape diagram of vesicles in Poiseuille flow. Phys. Rev. Lett. 108:178106 [Google Scholar]
  18. de Loubens C, Deschamps J, Georgelin M, Charrier A, Edward-Lévy F, Leonetti M. 2014. Mechanical characterization of cross-linked serum albumin microcapsules. Soft Matter 10:4561–68 [Google Scholar]
  19. Deschamps J, Kantsler V, Steinberg V. 2009. Phase diagram of single vesicle dynamical states in shear flow. Phys. Rev. Lett. 102:118105 [Google Scholar]
  20. Diaz A, Barthès-Biesel D. 2002. Entrance of a bioartificial capsule in a pore. Comput. Model. Eng. Sci. 3:321–37 [Google Scholar]
  21. Diaz A, Barthès-Biesel D, Pelekasis NA. 2001. Effect of membrane viscosity on the dynamic response of an axisymmetric capsule. Phys. Fluids 13:3835–38 [Google Scholar]
  22. Diaz A, Pelekasis NA, Barthès-Biesel D. 2000. Transient response of a capsule subjected to varying flow conditions: effect of internal fluid viscosity and membrane elasticity. Phys. Fluids 12:948–57 [Google Scholar]
  23. Dimitrakopoulos P. 2014. Effects of membrane hardness and scaling analysis for capsules in planar extensional flows. J. Fluid Mech. 745:487–508 [Google Scholar]
  24. Doddi SK, Bagchi P. 2008a. Effect of inertia on the hydrodynamic interaction between two liquid capsules in simple shear flow. Int. J. Multiphase Flow 34:375–92 [Google Scholar]
  25. Doddi SK, Bagchi P. 2008b. Lateral migration of a capsule in a plane Poiseuille flow in a channel. Int. J. Multiphase Flow 34:966–86 [Google Scholar]
  26. Dodson WR, Dimitrakopoulos P. 2008. Spindles, cusps, and bifurcation for capsules in Stokes flow. Phys. Rev. Lett. 101:208102 [Google Scholar]
  27. Dodson WR, Dimitrakopoulos P. 2009. Dynamics of strain-hardening and strain-softening capsules in strong planar extensional flows via an interfacial spectral boundary element algorithm for elastic membranes. J. Fluid Mech. 641:011913 [Google Scholar]
  28. Dupire J, Socol M, Viallat A. 2012. Full dynamics of a red blood cell in shear flow. PNAS 109:20808–13 [Google Scholar]
  29. Dupont C, Salsac AV, Barthès-Biesel D. 2013. Off-plane motion of a prolate capsule in shear flow. J. Fluid Mech. 721:180–98 [Google Scholar]
  30. Dupont C, Salsac AV, Barthès-Biesel D, Vidrascu M, Le Tallec P. 2015. Influence of bending resistance on the dynamics of a spherical capsule in shear flow. Phys. Fluids 27:051920 [Google Scholar]
  31. Edwards-Lévy F, Lévy MC. 1999. Serum albumin-alginate coated beads: mechanical properties and stability. Biomaterials 20:2069–84 [Google Scholar]
  32. Eggleton CD, Popel AS. 1998. Large deformation of red blood cell ghosts in a simple shear flow. Phys. Fluids 10:1834–45 [Google Scholar]
  33. Erni P, Fisher P, Windhab E. 2005. Deformation of single emulsion drops covered with a viscoelastic adsorbed protein layer in simple shear flow. Appl. Phys. Lett. 87:244104 [Google Scholar]
  34. Evans EA, Skalak R. 1980. Mechanics and Thermodynamics of Biomembranes Boca Raton, FL: CRC
  35. Fery A, Weinkamer R. 2007. Mechanical properties of micro- and nanocapsules: single capsule measurements. Polymer 48:7221–35 [Google Scholar]
  36. Fischer T, Korzeniewski R. 2013. Threshold shear stress for the transition between tumbling and tank-treading of red blood cells in shear flow: dependence on the viscosity of the suspending medium. J. Fluid Mech. 736:351–65 [Google Scholar]
  37. Fischer T, Schmid-Schönbein H. 1977. Tank-treading motion of red cell membranes in viscometric flow: behavior of intracellular and extracellular markers (with film). Blood Cells 3:351–65 [Google Scholar]
  38. Foessel E, Walter J, Salsac AV, Barthès-Biesel D. 2011. Influence of internal viscosity on the large deformation and buckling of a spherical capsule in a simple shear flow. J. Fluid Mech. 672:477–86 [Google Scholar]
  39. Green AE, Adkins JE. 1960. Large Elastic Deformations New York: Oxford Univ. Press
  40. Guido S, Tomaiuolo G. 2009. Microconfined flow behavior of red blood cells in vitro. C.R. Phys. 10:751–63 [Google Scholar]
  41. Hang WX, Chang CB, Sung HJ. 2012. Three-dimensional simulation of elastic capsules in shear flow by the penalty immersed boundary method. J. Comput. Phys. 231:3340–64 [Google Scholar]
  42. Helfrich W. 1973. Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. C 28:693–703 [Google Scholar]
  43. Hu XQ, Salsac AV, Barthès-Biesel D. 2012. Flow of a spherical capsule in a pore with circular or square cross-section. J. Fluid Mech. 705:176–94 [Google Scholar]
  44. Hu XQ, Sévénié B, Salsac AV, Leclerc E, Barthès-Biesel D. 2013. Characterizing the membrane properties of capsules flowing in a square-section microfluidic channel: effects of the membrane constitutive law. Phys. Rev. E 87:063008 [Google Scholar]
  45. Kantsler V, Segre E, Steinberg V. 2007. Vesicle dynamics in elongational flow: wrinkling instability and bud formation. Phys. Rev. Lett. 99:178102 [Google Scholar]
  46. Kantsler V, Steinberg V. 2006. Transition to tumbling and two regimes of tumbling motion of a vesicle in shear flow. Phys. Rev. Lett. 96:036001 [Google Scholar]
  47. Kessler S, Finken R, Seifert U. 2008. Swinging and tumbling of elastic capsules in shear flow. J. Fluid Mech. 605:207–26 [Google Scholar]
  48. Koleva I, Rehage H. 2012. Deformation and orientation dynamics of polysiloxane microcapsules in linear shear flow. Soft Matter 8:3681–93 [Google Scholar]
  49. Kraus M, Wintz W, Seifert U, Lipowsky R. 1996. Fluid vesicle in shear flow. Phys. Rev. Lett. 77:3685–88 [Google Scholar]
  50. Kühtreiber WM, Lanza RP, Chick WL. 1998. Cell Encapsulation Technology and Therapeutics Boston: Birkhäuser
  51. Kumar A, Rivera RH, Graham M. 2014. Flow-induced segregation in confined multicomponent suspensions: effects of particle size and rigidity. J. Fluid Mech. 738:432–62 [Google Scholar]
  52. Kuriakose S, Dimitrakopoulos P. 2011. Motion of an elastic capsule in a square microfluidic channel. Phys. Rev. E 84:011906 [Google Scholar]
  53. Kwak S, Pozrikidis C. 2001. Effect of membrane bending stiffness on the deformation of capsules in uniaxial extensional flow. Phys. Fluids 13:1234–42 [Google Scholar]
  54. Lac E, Barthès-Biesel D. 2005. Deformation of a capsule in simple shear flow: effect of membrane prestress. Phys. Fluids 17:072105 [Google Scholar]
  55. Lac E, Barthès-Biesel D. 2008. Pair-wise interaction of capsules in simple shear flow: three-dimensional effects. Phys. Fluids 20:040801 [Google Scholar]
  56. Lac E, Barthès-Biesel D, Pelekasis NA, Tsamopoulos J. 2004. Spherical capsules in three-dimensional unbounded Stokes flow: effect of the membrane constitutive law and onset of buckling. J. Fluid Mech. 516:303–34 [Google Scholar]
  57. Lac E, Morel A, Barthès-Biesel D. 2007. Hydrodynamic interaction between two identical capsules in a simple shear flow. J. Fluid Mech. 573:149–69 [Google Scholar]
  58. Le DV. 2010. Subdivision elements for large deformation of liquid capsules enclosed by thin shells. Comput. Methods Appl. Mech. Eng. 199:2622–32 [Google Scholar]
  59. Le DV, Tan Z. 2010. Large deformation of liquid capsules enclosed by thin shells immersed in the fluid. J. Comput. Phys. 229:4097–116 [Google Scholar]
  60. Le DV, White J, Peraire J, Lim KM, Khoo BC. 2009. An implicit immersed boundary method for three-dimensional capsules. J. Comput. Phys. 228:8427–45 [Google Scholar]
  61. Lebedev VV, Turitsyn KS, Vergeles SS. 2008. Nearly spherical vesicles in an external flow. New J. Phys. 10:043044 [Google Scholar]
  62. Leclerc E, Kinoshita H, Fujii T, Barthès-Biesel D. 2009. Transient flow of microcapsules through convergent-divergent microchannels. Microfluidics Nanofluids 12:761–70 [Google Scholar]
  63. Lefebvre Y, Barthès-Biesel D. 2007. Motion of a capsule in a cylindrical tube: effect of membrane pre-stress. J. Fluid Mech. 589:157–81 [Google Scholar]
  64. Lefebvre Y, Leclerc E, Barthès-Biesel D, Walter J, Edwards-Lévy F. 2008. Flow of artificial microcapsules in microfluidic channels: a method for determining the elastic properties of the membrane. Phys. Fluids 20:123102 [Google Scholar]
  65. Leyrat-Maurin A, Barthès-Biesel D. 1994. Motion of a deformable capsule through a hyperbolic constriction. J. Fluid Mech. 279:135–63 [Google Scholar]
  66. Li S, Nickels J, Palmer A. 2005. Liposome-encapsulated actin-hemoglobin (LEAcHb) artificial blood substitutes. Biomaterials 26:3759–69 [Google Scholar]
  67. Li X, Sarkar K. 2008. Front tracking simulation of deformation and buckling instability of a liquid capsule enclosed by an elastic membrane. J. Comput. Phys. 227:4998–5018 [Google Scholar]
  68. Li XZ, Barthès-Biesel D, Helmy A. 1988. Large deformations and burst of a capsule freely suspended in an elongational flow. J. Fluid Mech. 187:179–96 [Google Scholar]
  69. Lim F. 1984. Biomedical Applications of Microencapsulation Boca Raton, FL: CRC
  70. Ma G, Su ZG. 2013. Microspheres and Microcapsules in Biotechnology: Design, Preparation and Applications Singapore: Pan Stanford
  71. Mader MA, Vitkova V, Abkarian M, Viallat A, Podgorski T. 2006. Dynamics of viscous vesicles in shear flow. Eur. Phys. J. E 19:389–97 [Google Scholar]
  72. Matsunaga D, Imai Y, Yamaguchi T, Ishikawa T. 2015. Deformation of a spherical capsule under oscillating shear flow. J. Fluid Mech. 762:288–301 [Google Scholar]
  73. McMeccan R, Clausen JR, Neitzel G, Aidun C. 2009. Simulating deformable particle suspensions using a coupled Lattice-Boltzmann and finite-element method. J. Fluid Mech. 618:13–39 [Google Scholar]
  74. Misbah C. 2006. Vacillating breathing and tumbling of vesicles under shear flow. Phys. Rev. Lett. 96:028104 [Google Scholar]
  75. Omori T, Imai Y, Yamaguchi T, Ishikawa T. 2012. Reorientation of a nonspherical capsule in creeping shear flow. Phys. Rev. Lett. 108:138102 [Google Scholar]
  76. Park S, Dimitrakopoulos P. 2013. Transient dynamics of an elastic capsule in a microfluidic constriction. Soft Matter 9:8844–55 [Google Scholar]
  77. Peskin CS. 2002. The immersed boundary method. Acta Numer. 11:479–517 [Google Scholar]
  78. Pozrikidis C. 1992. Boundary Integral and Singularity Methods for Linearized Viscous Flow Cambridge, UK: Cambridge Univ. Press
  79. Pozrikidis C. 1995. Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow. J. Fluid Mech. 297:123–52 [Google Scholar]
  80. Pozrikidis C. 2001. Effect of membrane bending stiffness on the deformation of capsules in simple shear flow. J. Fluid Mech. 440:269–91 [Google Scholar]
  81. Pozrikidis C. 2003. Shell theory for capsules and cells. Modeling and Simulation of Capsules and Biological Cells C Pozrikidis 35–102 Boca Raton, FL: CRC [Google Scholar]
  82. Pozrikidis C. 2005. Numerical simulation of cell motion in tube flow. Ann. Biomed. Eng. 33:165–78 [Google Scholar]
  83. Rachik M, Barthès-Biesel D, Carin M, Edwards-Lévy F. 2006. Identification of a bioartificial microcapsule wall material parameter with an inverse method and the compression test. J. Colloid Interface Sci. 301:217–26 [Google Scholar]
  84. Ramanujan S, Pozrikidis C. 1998. Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of capsule viscosity. J. Fluid Mech. 361:117–43 [Google Scholar]
  85. Rehage H, Husmann M, Walter A. 2002. From two-dimensional model networks to microcapsules. Rheol. Acta 41:292–306 [Google Scholar]
  86. Risso F, Carin M. 2004. Compression of a capsule: mechanical laws of membranes with negligible bending stiffness. Phys. Rev. E 69:061601 [Google Scholar]
  87. Risso F, Collé-Paillot FF, Zagzoule M. 2006. Experimental investigation of a bioartificial capsule flowing in a narrow tube. J. Fluid Mech. 547:149–73 [Google Scholar]
  88. Secomb T, Styp-Rekowska B, Pries A. 2007. Two-dimensional simulation of red blood cell deformation and lateral migration in microvessels. Ann. Biomed. Eng. 35:755–65 [Google Scholar]
  89. Seifert U. 1997. Configurations of fluid membranes and vesicles. Adv. Phys. 46:13–137 [Google Scholar]
  90. Seifert U. 1999. Fluid membranes in hydrodynamic flow fields: formalism and an application to fluctuating quasi-spherical vesicles in shear flow. Eur. Phys. J. B 8:405–15 [Google Scholar]
  91. Sherwood JD, Risso F, Collé-Paillot F, Edwards-Lévy F, Lévy MC. 2003. Transport rates through a capsule membrane to attain Donnan equilibrium. J. Colloid Interface Sci. 263:202–12 [Google Scholar]
  92. Skalak R, Tozeren A, Zarda RP, Chien S. 1973. Strain energy function of red blood cell membranes. Biophys. J. 13:245–64 [Google Scholar]
  93. Sui Y, Chen XB, Chew YT, Roy P, Low HT. 2010a. Numerical simulation of capsule deformation in simple shear flow. Comput. Fluids 39:242–50 [Google Scholar]
  94. Sui Y, Low HT, Chew YT, Roy P. 2008. Tank-treading, swinging, and tumbling of liquid-filled elastic capsules in shear flow. Phys. Rev. E 77:016310 [Google Scholar]
  95. Sui Y, Low HT, Chew YT, Roy P. 2010b. A front tracking lattice Bolzmann method to study flow-induced deformation of three-dimensional capsules. Comput. Fluids 39:499–511 [Google Scholar]
  96. Vitkova V, Mader M, Podgorski T. 2004. Deformation of vesicles flowing through capillaries. Europhys. Lett. 68:398–404 [Google Scholar]
  97. Vlahovska PM, Young YN, Danker G, Misbah C. 2011. Dynamics of a non-spherical microcapsule with incompressible interface in shear flow. J. Fluid. Mech. 678:221–47 [Google Scholar]
  98. Walter A, Rehage H, Leonhard H. 2000. Shear-induced deformation of polyamide microcapsules. Colloid Polym. Sci. 278:169–75 [Google Scholar]
  99. Walter J, Salsac AV, Barthès-Biesel D. 2011. Ellipsoidal capsules in simple shear flow: prolate versus oblate initial shapes. J. Fluid Mech. 676:318–47 [Google Scholar]
  100. Walter J, Salsac AV, Barthès-Biesel D, Le Tallec P. 2010. Coupling of finite element and boundary integral methods for a capsule in a Stokes flow. Int. J. Numer. Methods Eng. 83:829–50 [Google Scholar]
  101. Woolfenden HC, Blyth MG. 2011. Motion of a two-dimensional elastic capsule in a branching channel flow. J. Fluid Mech. 669:3–31 [Google Scholar]
  102. Yazdani A, Bagchi P. 2013. Influence of membrane viscosity on capsule dynamics in shear flow. J. Fluid Mech. 718:569–95 [Google Scholar]
  103. Zhou H, Pozrikidis C. 1995. Deformation of capsules with incompressible interfaces in simple shear flow. J. Fluid Mech. 283:175–200 [Google Scholar]
  104. Zuidam NJ, Nedovic V. 2010. Encapsulation Technologies for Active Food Ingredients and Food Processing New York: Springer
/content/journals/10.1146/annurev-fluid-122414-034345
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Motion and Deformation of Elastic Capsules and Vesicles in Flow
Annual Review of Fluid Mechanics 48, 25 (2016); https://doi.org/10.1146/annurev-fluid-122414-034345
/content/journals/10.1146/annurev-fluid-122414-034345
/content/journals/10.1146/annurev-fluid-122414-034345
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