Large deformation of liquid capsules enclosed by thin shells immersed in the fluid

Journal of Computational Physics

Volumn 229, Issue 11, 2010, Pages 4097-4116

  Le, Duc Vinh ^a   Tan, Zhijun ^b  

^a INSTITUTE OF HIGH PERFORMANCE COMPUTING   (Singapore)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Immersed boundary method; Membrane capsules; Navier Stokes equations; Red blood cells; Thin shell

Indexed keywords

COMPUTATION THEORY; FLUID STRUCTURE INTERACTION; HYDROSTATIC PRESSURE; SHEAR FLOW; SHELLS (STRUCTURES); STRAIN; TURBULENT FLOW; YIELD STRESS;

FINITE DEFORMATIONS; IMMERSED BOUNDARY METHODS; KIRCHHOFF-LOVE THEORY; LARGER DEFORMATIONS; MEMBRANE CAPSULES; NAVIER-STOKES EQUATION; RED BLOOD CELL; SIMPLE SHEAR FLOW; THIN SHELLS; THIN-SHELL MODEL;

NAVIER STOKES EQUATIONS;

EID: 77950024230     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.01.042     Document Type: Article

References (48)

1. Abkarian M., Faivre M., Viallat A. Swinging of red blood cells under shear flow. Phys. Rev. Lett. 2007, 98:188302.
2. Başar Y., Ding Y. Finite-element analysis of hyperelastic thin shells with large strains. Comput. Mech. 1996, 18:200-214.
3. Barthès-Biesel D. Motion of spherical microcapsule freely suspended in a linear shear flow. J. Fluid Mech. 1980, 100:831-853.
4. Barthès-Biesel D., Rallison J.M. The time-dependent deformation of a capsule freely suspended in a linear shear flow. J. Fluid Mech. 1981, 113:251-267.
5. Brown D.L., Cortez R., Minion M.L. Accurate projection methods for the incompressible Navier-Stokes equations. J. Comput. Phys. 2001, 168:464-499.
6. Chang K.S., Olbricht W.L. Experimental studies of the deformation and break-up of a synthetic capsule in steady and unsteady simple shear flow. J. Fluid Mech. 1993, 250:609-633.
7. Charrier J.M., Shrivastava S., Wu R. Free and constrained inflation of elastic membranes in relation to thermoforming nonaxisymmetric problems. J. Strain Anal. 1989, 24:55-74.
8. 1-conforming subdivision elements for finite deformation thin-shell analysis. Int. J. Numer. Methods Eng. 2001, 51:813-833.
9. Cirak F., Ortiz M., Schroder P. Subdivision surfaces: a new paradigm for thin-shell finite-element analysis. Int. J. Numer. Methods Eng. 2000, 47:2039-2072.
10. Doddi S.K., Bagchi P. Three-dimensional computational modeling of multiple deformable cells flowing in microvessels. Phys. Rev. E 2009, 79:046318.
11. Douglas J. Alternating direction methods for three space variables. Numer. Math. 1962, 4:41-63.
12. Eberlein R., Wriggers P., Taylor R.L. A fully non-linear axisymmetrical quasi-Kirchhoff-type shell element for rubber-like materials. Int. J. Numer. Methods Eng. 1993, 36:4027-4043.
13. Eggleton C.D., Popel A.S. Large deformation of red blood cell ghosts in a simple shear flow. Phys. Fluids 1998, 10:1834-1845.
14. Evans E., Fung Y.C. Improved measurements of the erythrocyte geometry. Microvasc. Res. 1972, 4:335-347.
15. Fischer T.M. Shape memory of human red blood cells. Biophys. J. 2004, 86:3304-3313.
16. Gruttmann F., Taylor R.L. Theory and finite element formulation of rubberlike membrane shells using principal stretches. Int. J. Numer. Methods Eng. 1992, 35:1111-1126.
17. Hadjidimos A. On some high accuracy difference schemes for solving elliptic equations. Numer. Math. 1969, 13:396-403.
18. Kessler S., Finken R., Seifert U. Swinging and tumbling of elastic capsules in shear flow. J. Fluid. Mech. 2008, 605:207-226.
19. Kim J., Moin P. Application of a fractional step method to incompressible Navier-Stokes equations. J. Comput. Phys. 1985, 59:308-323.
20. Knoll D.A., Keyes D.E. Jacobian-free Newton-Krylov methods: a survey of approaches and applications. J. Comput. Phys 2004, 193:357-397.
21. Lac E., Barthès-Biesel D., Pelekasis N.A., Tsamopoulos J. Spherical capsules in three-dimensional unbounded Stokes flows: effect of the membrane constitutive law and onset of buckling. J. Fluid Mech. 2004, 516:303-334.
22. Le D.V., Khoo B.C., Lim K.M. An implicit-forcing immersed boundary method for simulating viscous flows in irregular domains. Comput. Methods Appl. Mech. Eng. 2008, 197:2119-2130.
23. Le D.V., White J., Peraire J., Lim K.M., Khoo B.C. An implicit immersed boundary method for three-dimensional fluid-membrane interactions. J. Comput. Phys. 2009, 228:8427-8445.
24. Li X., Sarkar K. Front tracking simulation of deformation and buckling instability of a liquid capsule enclosed by an elastic membrane. J. Comput. Phys. 2008, 227:4998-5018.
25. Marsden J.E., R Hughes T.J. Mathematical Foundations of Elasticity 1983, Prentice-Hall, Englewood Cliffs, NJ.
26. Misbah C. Vacillating breathing and tumbling of vesicles under shear flow. Phys. Rev. Lett. 2006, 96:028104.
27. Needleman A. Inflation of spherical rubber balloons. Int. J. Solids Struct. 1977, 13:409-421.
28. Noguchi H., Gompper G. Swinging and tumbling of fluid vesicles in shear flow. Phys. Rev. Lett. 2007, 98:128103.
29. Ogden R.W. Non-Linear Elastic Deformations 1984, Ellis Horwood, Chichester, UK.
30. Peskin C.S. The immersed boundary method. Acta Numer. 2002, 11(2):479-517.
31. Pozrikidis C. Numerical Computation in Science and Engineering 1998, Oxford University Press.
32. Pozrikidis C. Effect of membrane bending stiffness on the deformation of capsules in simple shear flow. J. Fluid Mech. 2001, 440:269-291.
33. Ramanujan S., Pozrikidis C. Deformation of liquid capsules enclosed by elastic membrane in simple shear flow: large deformations and the effect of fluid viscosities. J. Fluid Mech. 1998, 361:117-143.
34. Roma A.M., Peskin C.S., Berger M.J. An adaptive version of the immersed boundary method. J. Comput. Phys. 1999, 153:509-534.
35. Schmid-Schönbein H., Wells R.E. Fluid drop like transition of erythrocytes under shear. Science 1969, 165:288-291.
36. Schumann U., Sweet R.A. A direct method for the solution of Poisson's equation with Neumann boundary conditions on a staggered grid of arbitrary size. J. Comput. Phys. 1976, 20:171-182.
37. Shrivastava S., Tang J. Large deformation finite element analysis of non-linear viscoelastic membranes with reference to thermoforming. J. Strain Anal. 1993, 28:31-51.
38. Simo J.C., Fox D.D. On a stress resultant geometrically exact shell model. Part I: Formulation and optimal parametrization. Comput. Methods Appl. Mech. Eng. 1989, 72:267-304.
39. Simo J.C., Fox D.D. On a stress resultant geometrically exact shell model. Part IV: Variable thickness shells with through-the-thickness stretching. Comput. Methods Appl. Mech. Eng. 1990, 81:91-126.
40. Skalak R., Tozeren A., Zarda R.P., Chien S. Strain energy function of red blood cell membranes. Biophys. J. 1973, 13:245-264.
41. Skotheim J.M., Secomb T.W. Red blood cells and other nonspherical capsules in shear flow: oscillatory dynamics and the tank-treading-to-tumbling transition. Phys. Rev. Lett. 2007, 98:078301.
42. J. Stam, Fast evaluation of loop triangular subdivision surfaces at arbitrary parameter values, in: Computer Graphics (SIGGRAPH'98 Proceedings, CD-ROM supplement), 1998.
43. Sui Y., Chew Y.T., Roy P., Low H.T. A hybrid method to study flow-induced deformation of three-dimensional capsules. J. Comput. Phys. 2008, 227:6351-6371.
44. Sui Y., Low H.T., Chew Y.T., Roy P. Tank-treading, swinging, and tumbling of liquid-filled elastic capsules in shear flow. Phys. Rev. E 2008, 77:016310.
45. Tryggvason G., Bunner B., Esmaeeli A., Juric D., Al-Rawahi N., Tauber W., Han J., Nas S., Janz Y.-J. A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 2001, 169:708-759.
46. Unverdi S.O., Tryggvason G. A front-tracking method for viscous, incompressible flows, multi-fluid flows. J. Comput. Phys. 1992, 100:25-37.
47. Walter A., Rehage H., Leonhard H. Shear-induced deformation of polyamid microcapsules. Colloid Polymer Sci. 2000, 278:169-175.
48. Walter A., Rehage H., Leonhard H. Shear induced deformation of microcapsules: shape oscillations and membrane folding. Colloids Surf. A: Physicochem. Eng. Aspects 2001, 183-185:123-132.