Deformation of elastic particles in viscous shear flow

Journal of Computational Physics

Volumn 228, Issue 6, 2009, Pages 2132-2151

  Gao, Tong ^a   Hu, Howard H ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Elastic particle deformation; Eulerian Almansi strain tensor; Finite elements; Fluid structure interactions; Particle particle interactions

Indexed keywords

ELASTICITY; FINITE ELEMENT METHOD; FLUID STRUCTURE INTERACTION; REYNOLDS NUMBER; TENSORS; TURBULENT FLOW;

ELASTIC PARTICLE DEFORMATION; ELASTIC PARTICLES; EULERIAN; EULERIAN ALMANSI STRAIN TENSOR; FINITE ELEMENT; FLUID-STRUCTURE INTERACTION; PARTICLE DEFORMATION; PARTICLE-PARTICLE INTERACTIONS; STRAIN TENSOR; VISCOUS SHEAR;

SHEAR FLOW;

EID: 59149101763     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.11.029     Document Type: Article

References (40)

1. Hu H.H. Direct simulation of flows of solid-liquid mixtures. Int. J. Multiphase Flow 22 (1996) 335-352
2. Feng J.J., Huang P., and Joseph D.D. Dynamic simulation of sedimentation of solid particles in an Oldroyd-B fluid. J. Non-Newtonian Fluid Mech. 26 (1996) 63-88
3. Hu H.H., Zhu M.Y., and Patankar N. Direct numerical simulations of fluid solid systems using the arbitrary Lagrangian Eulerian technique. J. Comput. Phys. 169 (2001) 427-462
4. Seifert U. Configurations of fluid membranes and vesicles. Adv. Phys. 46 (1997) 13-137
5. Stone H.A. Drop deformation and breakup in viscous flows. Annu. Rev. Fluid Mech. 26 (1994) 65-1021
6. Subramaniam A.B., Abkarian M., Mahadevan L., and Stone H.A. Non-spherical gas bubbles. Nature 438 (2005) 930
7. Peskin C.S. Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10 (1972) 252-271
8. Peskin C.S. The immersed boundary method. Acta Numerica 10 (2002) 479-517
9. Ye T., Mittal R., Udaykumar H.S., and Shyy W. An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries. J. Comput. Phys. 156 (1999) 209-240
10. LeVeque R.J., and Li Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Num. Anal. 31 (1994) 1019-1044
11. Zhang L., Gerstenberger A., Wang X., and Liu W.K. Immersed finite element method. Comput. Methods Appl. Mech. Eng. 193 (2004) 2051-2067
12. Mittal R., and Iaccarino G. Immersed boundary methods. Annu. Rev. Fluid Mech. 37 (2005) 239-261
13. Hirt C.W., Amsden A.A., and Cook J.L. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. Comput. Phys. 14 (1974) 227-253
14. Tezduyar T.E., Behr M., and Liou J. A new strategy for finite element computation involving moving boundaries and interfaces - the deforming-spatial-domain/space-time procedure: I. The concept and the preliminary numerical tests. Comput. Meth. Appl. Mech. Eng. 94 (1992) 339-351
15. Masud A., and Hughes T.J.R. A space-time Galerkin/least-squares finite element formulation of the Navier-Stokes equations for moving domain problems. Comput. Meth. Appl. Mech. Eng. 146 (1997) 91-126
16. Farhat C., and Lesoinne M. Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems. Comput. Meth. Appl. Mech. Eng. 182 (2000) 499-515
17. Kalro V., and Tezduyar T.E. A parallel 3D computational method for fluid-structure interactions in parachute systems. Comput. Meth. Appl. Mech. Eng. 190 (2000) 321-332
18. Le Tallec P., and Mouro J. Fluid structure interaction with large structural displacements. Comput. Meth. Appl. Mech. Eng. 190 (2001) 3039-3067
19. Hübner B., Walhorn E., and Dinkler D. A monolithic approach to fluid-structure interaction using space-time finite elements. Comput. Meth. Appl. Mech. Eng. 193 (2004) 2087-2104
20. Blom F.J. A monolithical fluid-structure interaction algorithm applied to the piston problem. Comput. Meth. Appl. Mech. Eng. 167 (1998) 369-391
21. Fischer T.M., Stöhr-Liesen M., and Schmid-Schönbein H. The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow. Science 202 (1978) 894-896
22. Chien S. Red cell deformability and its relevance to blood flow. Annals Rev. Physiol. 49 (1987) 177-192
23. Barthěs-Biesel D. Motion of a spherical microcapsule freely suspended in a linear shear flow. J. Fluid Mech. 100 (1980) 831-853
24. Barthěs-Biesel D., and Rallison J.M. The time-dependent deformation of a capsule freely suspended in a linear shear flow. J. Fluid Mech. 113 (1981) 251-267
25. Keller S.R., and Skalak R. Motion of a tank-treading ellipsoidal particle in a shear flow. J. Fluid Mech. 120 (1982) 27-47
26. Eggleton C.D., and Popel A.S. Large deformation of red blood cell ghosts in a simple shear flow. Phys. Fluids 10 (1998) 1834-1845
27. Zhou H., and Pozrikidis C. Deformation of liquid capsules with incompressible interfaces in simple shear flow. J. Fluid Mech. 283 (1982) 175-200
28. Ramanujan S., and Pozrikidis C. Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of capsule viscosity. J. Fluid Mech. 361 (1998) 117-143
29. Pozrikidis C. Numerical simulation of the flow-induced deformation of red blood cells. Annals Biomed. Eng. 31 (2003) 1194-1205
30. Sui Y., Chew Y.T., Roy P., and Low H.T. A hybrid method to study flow-induced deformation of three-dimensional capsules. J. Comput. Phys. 227 (2008) 6351-6371
31. Bird R.B., Armstrong R.C., and Hassager O. Dynamics of polymeric liquids. Fluid Mech. vol. 1 (1987), John Wiley & Sons, New York
32. Joseph D.D. Fluid dynamics of viscoelastic liquids. Appl. Math. Sci. vol. 84 (1990), Springer Verlag, New York
33. Oldroyd J.G. Non-Newtonian effects in steady motion of some idealized elastico-viscous liquids. Proc. R. Soc. Lond. A 245 (1958) 278-297
34. Thomasset F. Implementation of Finite Element Methods for Navier-Stokes Equations (1981), Springer Verlag, New York
35. Saad Y., and Schultz Y. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7 (1986) 856-869
36. Chow E., and Saad Y. Experimental study of ILU preconditioners for indefinite matrices. J. Comput. Appl. Math. 86 (1997) 387-414
37. Timoshenko S.P., and Goodier J.N. Theory of Elasticity. third ed. (1970), McGraw Hill, New York
38. Taylor G.I. The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. A 138 (1932) 41-48
39. Milliken W.J., and Leal L.G. Deformation and breakup of viscoelastic drops in plannar extensional flows. J. Non-Newtonian Fluid Mech. 40 (1991) 355-379
40. Bretherton F.P. The motion of rigid particles in a shear flow at low Reynolds number. J. Fluid Mech. 14 (1962) 284-304