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Loop subdivision surface boundary integral method simulations of vesicles at low reduced volume ratio in shear and extensional flow
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1.
1. Y. Malam, M. Loizidou, and A. M. Seifalian, “Liposomes and nanoparticles: nanosized vesicles for drug delivery in cancer,” Trends Pharmacol. Sci. 30, 592599 (2009).
http://dx.doi.org/10.1016/j.tips.2009.08.004
2.
2. I. F. Uchegbu and S. P. Vyas, “Non-ionic surfactant-based vesicles (niosomes) in drug delivery,” Int. J. Pharm. 172, 3370 (1998).
http://dx.doi.org/10.1016/S0378-5173(98)00169-0
3.
3. N.-J. Cho, S.-J. Cho, K. H. Cheong, J. S. Glenn, and C. W. Frank, “Employing an amphipathic viral peptide to create a lipid bilayer on Au and TiO2,” J. Am. Chem. Soc. 129, 1005010051 (2007).
http://dx.doi.org/10.1021/ja0701412
4.
4. M. Kraus, W. Wintz, U. Seifert, and R. Lipowsky, “Fluid vesicles in shear flow,” Phys. Rev. Lett. 77, 36853688 (1996).
http://dx.doi.org/10.1103/PhysRevLett.77.3685
5.
5. J. M. Rallison and A. Acrivos, “A numerical study of the deformation and burst of a viscous drop in extensional flow,” J. Fluid Mech. 89, 191200 (1978).
http://dx.doi.org/10.1017/S0022112078002530
6.
6. J. M. Rallison, “A numerical study of the deformation and burst of a viscous drop in general shear flows,” J. Fluid Mech. 109, 465482 (1981).
http://dx.doi.org/10.1017/S002211208100116X
7.
7. H. Zhao and E. S. G. Shaqfeh, “Shear-induced platelet margination in a microchannel,” Phys. Rev. E 83, 061924 (2011).
http://dx.doi.org/10.1103/PhysRevE.83.061924
8.
8. C. Pozrikidis, “Numerical simulation of the flow-induced deformation of red blood cells,” Ann. Biomed. Eng. 31, 11941205 (2003).
http://dx.doi.org/10.1114/1.1617985
9.
9. J. Li, M. Dao, C. T. Lim, and S. Suresh, “Spectrin-level modeling of the cytoskeleton and optical tweezers stretching of the erythrocyte,” Biophys. J. 88, 37073719 (2005).
http://dx.doi.org/10.1529/biophysj.104.047332
10.
10. I. V. Pivkin and P. E. Karniadakis, “Accurate coarse-grained modeling of red blood cells,” Phys. Rev. Lett. 101, 118105 (2008).
http://dx.doi.org/10.1103/PhysRevLett.101.118105
11.
11. J. Deschamps, V. Kantsler, and V. Steinberg, “Phase diagram of single vesicle dynamical states in shear flow,” Phys. Rev. Lett. 102, 118105 (2009).
http://dx.doi.org/10.1103/PhysRevLett.102.118105
12.
12. V. Kantsler, E. Segre, and V. Steinberg, “Dynamics of interacting vesicles and rheology of vesicle suspension in shear flow,” Europhys. Lett. 82, 58005 (2008).
http://dx.doi.org/10.1209/0295-5075/82/58005
13.
13. V. Kantsler and V. Steinberg, “Orientation and dynamics of a vesicle in tank-treading motion in shear flow,” Phys. Rev. Lett. 95, 258101 (2005).
http://dx.doi.org/10.1103/PhysRevLett.95.258101
14.
14. V. Kantsler and V. Steinberg, “Transition to tumbling and two regimes of tumbling motion of a vesicle in shear flow,” Phys. Rev. Lett. 96, 036001 (2006).
http://dx.doi.org/10.1103/PhysRevLett.96.036001
15.
15. M. Mader, V. Vitkova, M. Abkarian, A. Viallat, and T. Podgorski, “Dynamics of viscous vesicles in shear flow,” Eur. Phys. J. E 19, 389397 (2006).
http://dx.doi.org/10.1140/epje/i2005-10058-x
16.
16. N. J. Zabusky, E. Segre, J. Deschamps, V. Kantsler, and V. Steinberg, “Dynamics of vesicles in shear and rotational flows: Modal dynamics and phase diagram,” Phys. Fluids 23, 041905 (2011).
http://dx.doi.org/10.1063/1.3556439
17.
17. A. Farutin, T. Biben, and C. Misbah, “Analytical progress in the theory of vesicles under linear flow,” Phys. Rev. E 81, 061904 (2010).
http://dx.doi.org/10.1103/PhysRevE.81.061904
18.
18. V. V. Lebedev, K. S. Turitsyn, and S. S. Vergeles, “Dynamics of nearly spherical vesicles in an external flow,” Phys. Rev. Lett. 99, 218101 (2007).
http://dx.doi.org/10.1103/PhysRevLett.99.218101
19.
19. C. Misbah, “Vacillating breathing and tumbling of vesicles under shear flow,” Phys. Rev. Lett. 96, 028104 (2006).
http://dx.doi.org/10.1103/PhysRevLett.96.028104
20.
20. P. M. Vlahovska and R. S. Gracia, “Dynamics of a viscous vesicle in linear flows,” Phys. Rev. E 75, 016313 (2007).
http://dx.doi.org/10.1103/PhysRevE.75.016313
21.
21. T. Biben, A. Farutin, and C. Misbah, “Three-dimensional vesicles under shear flow: Numerical study of dynamics and phase diagram,” Phys. Rev. E 83, 031921 (2011).
http://dx.doi.org/10.1103/PhysRevE.83.031921
22.
22. G. Boedec, M. Leonetti, and M. Jaeger, “3D vesicle dynamics simulations with a linearly triangulated surface,” J. Comput. Phys. 230, 10201034 (2011).
http://dx.doi.org/10.1016/j.jcp.2010.10.021
23.
23. A. Farutin, O. Aouane, and C. Misbah, “Vesicle dynamics under weak flows: application to large excess area,” Phys. Rev. E 85, 061922 (2012).
http://dx.doi.org/10.1103/PhysRevE.85.061922
24.
24. D. V. Le, “Effect of bending stiffness on the deformation of liquid capsules enclosed by thin shells in shear flow,” Phys. Rev. E 82, 016318 (2010).
http://dx.doi.org/10.1103/PhysRevE.82.016318
25.
25. D. V. Le and Z. Tan, “Large deformation of liquid capsules enclosed by thin shells immersed in the fluid,” J. Comput. Phys. 229, 40974116 (2010).
http://dx.doi.org/10.1016/j.jcp.2010.01.042
26.
26. X. Li, P. M. Vlahovska, and G. E. Karniadakis, “Continuum- and particle-based modeling of shapes and dynamics of red blood cells in health and disease,” Soft Matter 9, 2837 (2013).
http://dx.doi.org/10.1039/c2sm26891d
27.
27. S. Meßlinger, B. Schmidt, H. Noguchi, and G. Gompper, “Dynamical regimes and hydrodynamic lift of viscous vesicles under shear,” Phys. Rev. E 80, 011901 (2009).
http://dx.doi.org/10.1103/PhysRevE.80.011901
28.
28. H. Noguchi and G. Gompper, “Swinging and tumbling of fluid vesicles in shear flow,” Phys. Rev. Lett. 98, 128103 (2007).
http://dx.doi.org/10.1103/PhysRevLett.98.128103
29.
29. S. K. Veerapaneni, D. Gueyffier, G. Biros, and D. Zorin, “A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows,” J. Comput. Phys. 228, 72337249 (2009).
http://dx.doi.org/10.1016/j.jcp.2009.06.020
30.
30. S. K. Veerapaneni, D. Gueyffier, D. Zorin, and G. Biros, “A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D,” J. Comput. Phys. 228, 23342353 (2009).
http://dx.doi.org/10.1016/j.jcp.2008.11.036
31.
31. S. K. Veerapaneni, A. Rahimian, G. Biros, and D. Zorin, “A fast algorithm for simulating vesicle flows in three dimensions,” J. Comput. Phys. 230, 56105634 (2011).
http://dx.doi.org/10.1016/j.jcp.2011.03.045
32.
32. A. Yazdani and P. Bagchi, “Three-dimensional numerical simulation of vesicle dynamics using a front-tracking method,” Phys. Rev. E 85, 056308 (2012).
http://dx.doi.org/10.1103/PhysRevE.85.056308
33.
33. H. Zhao and E. S. G. Shaqfeh, “The dynamics of a vesicle in simple shear flow,” J. Fluid Mech. 674, 578604 (2011).
http://dx.doi.org/10.1017/S0022112011000115
34.
34. H. Zhao, A. P. Spann, and E. S. G. Shaqfeh, “The dynamics of a vesicle in a wall-bound shear flow,” Phys. Fluids 23, 121901 (2011).
http://dx.doi.org/10.1063/1.3669440
35.
35. A. Farutin and C. Misbah, “Squaring, parity breaking, and S tumbling of vesicles under shear flow,” Phys. Rev. Lett. 109, 248106 (2012).
http://dx.doi.org/10.1103/PhysRevLett.109.248106
36.
36. H. Zhao and E. S. G. Shaqfeh, “The shape stability of a lipid vesicle in a uniaxial extensional flow,” J. Fluid Mech. 719, 345361 (2013).
http://dx.doi.org/10.1017/jfm.2013.10
37.
37. V. Kantsler, E. Segre, and V. Steinberg, “Critical dynamics of vesicle stretching transition in elongational flow,” Phys. Rev. Lett. 101, 048101 (2008).
http://dx.doi.org/10.1103/PhysRevLett.101.048101
38.
38. J. Spjut and S. Muller, “Phospholipid vesicle: stagnation point flow studies,” private communication (2008).
39.
39. C. T. Loop, “Smooth subdivision surfaces based on triangles,” Master's thesis (University of Utah, 1987).
40.
40. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge University Press, Cambridge, 1992).
41.
41. A. Ramachandran, T. H. Anderson, L. G. Leal, and J. N. Israelachvili, “Adhesive interactions between vesicles in the strong adhesion limit,” Langmuir 27, 5973 (2011).
http://dx.doi.org/10.1021/la1023168
42.
42. K. H. De Haas, C. Blom, D. Van den Ende, M. H. G. Duits, and J. Mellema, “Deformation of giant lipid bilayer vesicles in shear flow,” Phys. Rev. E 56, 71327137 (1997).
http://dx.doi.org/10.1103/PhysRevE.56.7132
43.
43. W. Helfrich, “Elastic properties of lipid bilayers: theory and possible experiments,” Z. Naturforsch., C 28, 693703 (1973).
44.
44.O. Y. Zhong-can and W. Helfrich, “Bending energy of vesicle membranes: General expressions for the first, second, and third variation of shape energy and applications to spheres and cylinders,” Phys. Rev. A 39, 52805288 (1989).
http://dx.doi.org/10.1103/PhysRevA.39.5280
45.
45. E. Catmull and J. Clark, “Recursively generated B-spline surfaces on arbitrary topological meshes,” Comput.-Aided Des. 10, 350355 (1978).
http://dx.doi.org/10.1016/0010-4485(78)90110-0
46.
46. J. Stam, “Evaluation of loop subdivision surfaces,” SIGGRAPH ’98 Conference Proceedings CDROM (ACM, New York, NY, 1998).
47.
47. P. O. Persson, M. J. Aftosmis, and R. H. Haimes, “On the use of Loop subdivision surfaces for surrogate geometry,” in Proceedings of the 15th International Meshing Roundtable (Springer, Berlin/Heidelberg/New York, 2006), pp. 375392.
48.
48. F. Cirak, M. Ortiz, and P. Schröder, “Subdivision surfaces: a new paradigm for thin-shell finite-element analysis,” Int. J. Numer. Methods Eng. 47, 20392072 (2000).
http://dx.doi.org/10.1002/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-1
49.
49. F. Cirak and M. Ortiz, “Fully C1-conforming subdivision elements for finite deformation thin-shell analysis,” Int. J. Numer. Methods Eng. 51, 813833 (2001).
http://dx.doi.org/10.1002/nme.182.abs
50.
50. F. Feng and W. S. Klug, “Finite element modeling of lipid bilayer membranes,” J. Comput. Phys. 220, 394408 (2006).
http://dx.doi.org/10.1016/j.jcp.2006.05.023
51.
51. L. Ma and W. S. Klug, “Viscous regularization and r-adaptive remeshing for finite element analysis of lipid membrane mechanics,” J. Comput. Phys. 227, 58165835 (2008).
http://dx.doi.org/10.1016/j.jcp.2008.02.019
52.
52. S. Balay, J. Brown, K. Buschelman, D. G. Gropp, D. Kaushik, M. G. Knepley, L. C. McInnes, B. F. Smith, and H. Zhang, “PETSC: Portable, Extensible Toolkit for Scientific Computation,” see http://www.mcs.anl.gov/petsc (2013).
53.
53. H. Zhao and E. S. Shaqfeh, “The dynamics of a non-dilute vesicle suspension in a simple shear flow,” J. Fluid Mech. 725, 709731 (2013).
http://dx.doi.org/10.1017/jfm.2013.207
54.
54. M. Loewenberg and E. J. Hinch, “Numerical simulation of a concentrated emulsion in shear flow,” J. Fluid Mech. 321, 395419 (1996).
http://dx.doi.org/10.1017/S002211209600777X
55.
55. U. Seifert, K. Berndl, and R. Lipowsky, “Shape transformations of vesicles: Phase diagram for spontaneous curvature and bilayer-coupling models,” Phys. Rev. A 44, 11821202 (1991).
http://dx.doi.org/10.1103/PhysRevA.44.1182
56.
56. D. Abreu and U. Seifert, “Noisy nonlinear dynamics of vesicles in flow,” Phys. Rev. Lett. 110, 238103 (2013).
http://dx.doi.org/10.1103/PhysRevLett.110.238103
57.
57. M. Levant and V. Steinberg, “Amplification of thermal noise by vesicle dynamics,” Phys. Rev. Lett. 109, 268103 (2012).
http://dx.doi.org/10.1103/PhysRevLett.109.268103
58.
58. H. Noguchi, “Swinging and synchronized rotations of red blood cells in simple shear flow,” Phys. Rev. E 80, 021902 (2009).
http://dx.doi.org/10.1103/PhysRevE.80.021902
59.
59. H. Noguchi and G. Gompper, “Shape transitions of fluid vesicles and red blood cells in capillary flows,” Proc. Natl. Acad. Sci. U.S.A. 102, 1415914164 (2005).
http://dx.doi.org/10.1073/pnas.0504243102
60.
60. V. Vitkova, M. A. Mader, B. Polack, C. Misbah, and T. Podgorski, “Micro-macro link in rheology of erythrocyte and vesicle suspensions,” Biophys. J. 95, L33L35 (2008).
http://dx.doi.org/10.1529/biophysj.108.138826
61.
61. G. Danker and C. Misbah, “Rheology of a dilute suspension of vesicles,” Phys. Rev. Lett. 98, 088104 (2007).
http://dx.doi.org/10.1103/PhysRevLett.98.088104
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/content/aip/journal/pof2/26/3/10.1063/1.4869307
2014-03-31
2014-08-21

Abstract

Using an unstructured boundary integral method with curvature determination via Loop subdivision surfaces, we explore a region of moderate reduced volume vesicles in flow that includes prolate, biconcave, and stomatocyte shapes. We validate our Loop subdivision code against previously published spectral method simulations. In shear flow, we report dynamic phase diagrams at reduced volumes ranging from 0.65 to 0.95 and determine the critical viscosity ratio at which the vesicle moves away from tank treading. We examine biconcave shapes and find the elimination of the trembling regime and a tumbling that includes significant stretch in the vorticity direction, as well as a general reduction in shear and normal stresses versus a prolate shape. Finally, we re-examine over a wider range of reduced volume the shape instability originally reported by Zhao and Shaqfeh [“The shape stability of a lipid vesicle in a uniaxial extensional flow,” J. Fluid Mech. , 345–361 (2013)] of a vesicle placed in an extensional flow. At sufficiently low reduced volume and high capillary number, we find the steady elongated dumbbell shape is unstable to odd perturbations and the vesicle's dumbbell ends become unequal in size. We also find that the critical capillary number as a function of reduced volume is similar between uniaxial and planar extensional flow.

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Scitation: Loop subdivision surface boundary integral method simulations of vesicles at low reduced volume ratio in shear and extensional flow
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