Dynamics of strain-hardening and strain-softening capsules in strong planar extensional flows via an interfacial spectral boundary element algorithm for elastic membranes

Journal of Fluid Mechanics

Volumn 641, Issue , 2009, Pages 263-296

  Dodson, W R ^a   Dimitrakopoulos, P ^a  

^a UNIVERSITY OF MARYLAND   (United States)

Author keywords

Capsule cell dynamics; Interfacial flows (free surface); Low Reynolds number flows

Indexed keywords

DEFORMATION; FLOW RATE; NUMERICAL METHODS; REYNOLDS NUMBER; STRAIN HARDENING;

HYDRODYNAMIC FORCES; INTERFACIAL DEFORMATIONS; INTERFACIAL FLOW (FREE SURFACE); INTERFACIAL GEOMETRY; LOW REYNOLDS NUMBER FLOW; NUMERICAL COMPUTATIONS; PLANAR EXTENSIONAL FLOW; TRANSIENT EVOLUTION;

MEMBRANES;

ALGORITHM; BOUNDARY ELEMENT METHOD; CRITICAL FLOW; DEFORMATION; FLUID FLOW; GEOMETRY; HYDRODYNAMIC FORCE; INTERPOLATION; REYNOLDS NUMBER; STEADY-STATE EQUILIBRIUM; STOKES FORMULA; THREE-DIMENSIONAL FLOW; TRANSIENT FLOW;

EID: 76349124056     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112009991662     Document Type: Article

References (47)

1. Acrivos, A. & Lo, T. S. 1978 Deformation and breakup of a single slender drop in an extensional flow. J. Fluid Mech. 86, 641-672.
2. Barthès-Biesel, D. 1980 Motion of a spherical microcapsule freely suspended in a linear shear flow. J. Fluid Mech. 100, 831-853.
3. Barthès-Biesel, D. 1991 Role of interfacial properties on the motion and deformation of capsules in shear flow. Physica A 172, 103-124.
4. 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, 211-222.
5. Barthès-Biesel, D. & Rallison, J. M. 1981 The time-dependent deformation of a capsule freely suspended in a linear shear flow. J. Fluid Mech. 113, 251-267.
6. Barthès-Biesel, D. & Sgaier, H. 1985 Role of membrane viscosity in the orientation and deformation of a spherical capsule suspended in shear flow. J. Fluid Mech. 160, 119-136.
7. Baskurt, O. K. & Meiselman, H. J. 2003 Blood rheology and hemodynamics. Sem. Thromb. Hem. 29, 435-450.
8. Bentley, B. J. & Leal, L. G. 1986 An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows. J. Fluid Mech. 167, 241-283.
9. Buckmaster, J. D. 1972 Pointed bubbles in slow viscous flow. J. Fluid Mech. 55, 385-400.
10. Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1998 Spectral Methods in Fluid Dynamics. Springer.
11. Carin, M., Barthès-Biesel, D., Edwards-Lévy, F., Postel, C. & Andrei, D. C. 2003 Compression of biocompatible liquid-filled HSA-alginate capsules: determination of the membrane mechanical properties. Biotech. Bioengng 82, 207-212.
12. Chang, K. S. & Olbricht, W. L. 1993a Experimental studies of the deformation of a synthetic capsule in extensional flow. J. Fluid Mech. 250, 587-608.
13. Chang, K. S. & Olbricht, W. L. 1993b Experimental studies of the deformation and breakup of a synthetic capsule in steady and unsteady simple shear flow. J. Fluid Mech. 250, 609-633.
14. Diaz, A., Pelekasis, N. & Barthès-Biesel, D. 2000 Transient response of a capsule subjected to varying fluid conditions: effect of internal fluid viscosity and membrane elasticity. Phys. Fluids 12, 948-957.
15. Dimitrakopoulos, P. 2007 Interfacial dynamics in Stokes flow via a three-dimensional fully-implicit interfacial spectral boundary element algorithm. J. Comput. Phys. 225, 408-426.
16. Dimitrakopoulos, P. & Higdon, J. J. L. 1998 On the displacement of three-dimensional fluid droplets from solid surfaces in low-Reynolds-number shear flows. J. Fluid Mech. 377, 189-222.
17. Dimitrakopoulos, P. & Wang, J. 2007 A spectral boundary element algorithm for interfacial dynamics in two-dimensional Stokes flow based on Hermitian interfacial smoothing. Engng Anal. Bound. Elem. 31, 646-656.
18. Doddi, S. K. & Bagchi, P. 2008 Effect of inertia on the hydrodynamic interaction between two liquid capsules in simple shear flow. Intl J. Multiphase Flow 34, 375-392.
19. Dodson, W. R., III & Dimitrakopoulos, P. 2008 Spindles, cusps and bifurcation for capsules in Stokes flow. Phys. Rev. Lett. 101, 208102.
20. Eggleton, C. D. & Popel, A. S. 1998 Large deformation of red blood cell ghosts in simple shear flow. Phys. Fluids 10, 1834-1845.
21. Gould, P. L. 1999 Analysis of Shells and Plates. Prentice Hall.
22. Ha, J. W. & Leal, L. G. 2001 An experimental study of drop deformation and breakup in extensional flow at high capillary number. Phys. Fluids 13, 1568-1576.
23. Hudson, S. D., Phelan, F. R., Jr., Handler, M. D., Cabral, J. T., Migler, K. B. & Amis, E. J., 2004 Microfluidic analog of the four-roll mill. Appl. Phys. Lett. 85 (2), 335-337.
24. Husmann, M., Rehage, H., Dhenin, E. & Barthès-Biesel, D. 2005 Deformation and bursting of nonspherical polysiloxane microcapsules in a spinning-drop apparatus. J. Colloid Interface Sci. 282, 109-119.
25. Kwak, S. & Pozrikidis, C. 2001 Effect of membrane bending stiffness on the axisymmetric deformation of capsules in uniaxial extensional flow. Phys. Fluids 13, 1234-1242. (Pubitemid 32449579)
26. Lac, E. & Barthès-Biesel, D., 2005 Deformation of a capsule in simple shear flow: effect of membrane prestress. Phys. Fluids 17, 072105.
27. Lac, E., Barthès-Biesel, D., Pelekasis, N. A., & Tsamopoulos, J. 2004 Spherical capsules in three-dimensional unbounded Stokes flows: effect of the membrane constitutive law and onset of buckling. J. Fluid Mech. 516, 303-334.
28. Lubarda, V. A. 2002 Elastoplasticity Theory. CRC Press.
29. Mohandas, N. & Chasis, J. A. 1993 Red blood cell deformability, membrane material properties and shape: regulation by transmembrane, skeletal and cytosolic proteins and lipids. Sem. Hematol. 30, 171-192.
30. Muldowney, G. P. & Higdon, J. J. L. 1995 A spectral boundary element approach to three-dimensional Stokes flow. J. Fluid Mech. 298, 167-192.
31. Navot, Y. 1998 Elastic membranes in viscous shear flow. Phys. Fluids 10, 1819-1833.
32. Papastavridis, J. G. 1999 Tensor Calculus and Analytical Dynamics. CRC Press.
33. Pieper, G., Rehage, H. & Barthès-Biesel, D. 1998 Deformation of a capsule in a spinning drop apparatus. J. Colloid Interface Sci. 202, 293-300.
34. Popel, A. S. & Johnson, P. C. 2005 Microcirculation and hemorheology. Annu. Rev. Fluid Mech. 37, 43-69.
35. Pozrikidis, C. 1995 Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow. J. Fluid Mech. 297, 123-152.
36. Pozrikidis, C. 2001 Effect of membrane bending stiffness on the deformation of capsules in simple shear flow. J. Fluid Mech. 440, 269-291. (Pubitemid 32739695)
37. Pozrikidis, C. 2001 Interfacial dynamics for Stokes flow. J. Comput. Phys. 169, 250-301
38. Pozrikidis, C. (Ed.) 2003 Modelling and Simulation of Capsules and Biological Cells. Chapman and Hall.
39. Ramanujan, S. & Pozrikidis, C. 1998 Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities. J. Fluid Mech. 361, 117-143.
40. Secomb, T. W., Hsu, R. & Pries, A. R. 1998 A model for red blood cell motion in glycocalyx-lined capillaries. Am. J. Physiol. Heart Circ. Physiol. 274, H1016-H1022.
41. Secomb, T. W., Hsu, R. & Pries, A. R. 2001 Motion of red blood cells in a capillary with an endothelial surface layer: effect of flow velocity. Am. J. Physiol. Heart Circ. Physiol. 281, H629-H636.
42. Secomb, T. W., Hsu, R. & Pries, A. R. 2002 Blood flow and red blood cell deformation in non-uniform capillaries: effects of the endothelial surface layer. Microcirculation 9, 189-196.
43. Skalak, R., Tozeren, A., Zarda, R. P. & Chien, S. 1973 Strain energy function of red blood cell membranes. Biophys. J. 13, 245-264.
44. Steigmann, D. J. & Ogden, R. W. 1999 Elastic surface-substrate interactions. Proc. R. Soc. Lond. A 455, 437-474.
45. Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. R. Soc. A 146, 501-523.
46. Wang, Y. & Dimitrakopoulos, P. 2006 A three-dimensional spectral boundary element algorithm for interfacial dynamics in Stokes flow. Phys. Fluids 18, 082106.
47. Waxman, A. M. 1984 Dynamics of a couple-stress fluid membrane. Stud. Appl. Math. 70, 63-86.