Simulating 3D deformable particle suspensions using lattice Boltzmann method with discrete external boundary force

International Journal for Numerical Methods in Fluids

Volumn 62, Issue 7, 2010, Pages 765-783

  Wu, Jingshu ^a   Aidun, Cyrus K ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Bounce back; External boundary force; Fluid solid interaction; Lattice Boltzmann; Lattice spring; No slip condition; Red blood cell

Indexed keywords

DEFORMABLE PARTICLES; FLUID SOLID INTERACTION; FLUID-SOLID INTERFACES; HIGHER ORDER; INTERPOLATED BOUNCE-BACK; LAGRANGIAN FRAMES; LATTICE BOLTZMANN; LATTICE BOLTZMANN EQUATIONS; LATTICE-BOLTZMANN METHOD; MOVING BOUNDARIES; NEWTONIAN DYNAMICS; NO-SLIP BOUNDARY CONDITIONS; NO-SLIP CONDITION; RED BLOOD CELL; SOLID PARTICLES; SPRING MODEL; THEORETICAL RESULT; VOLUME OF FLUID METHOD;

BLOOD; BOLTZMANN EQUATION; CELLS; DEFORMATION; DROP FORMATION; EQUATIONS OF MOTION; FLUIDS; HEMOGLOBIN OXYGEN SATURATION; INCOMPRESSIBLE FLOW; NUMERICAL ANALYSIS; THREE DIMENSIONAL; TWO PHASE FLOW;

SUSPENSIONS (FLUIDS);

EID: 77950248808     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.2043     Document Type: Article

References (51)

1. Chen H, Chen S, Matthaeus WH. Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. Physical Review A 1992; 45:5339.
2. Hou S, Zou Q, Chen S, Doolen G, Cogley AC. Simulation of cavity flow by lattice Boltzmann method. Journal of Computational Physics 1995; 118:329.
3. Mcnamara GR, Zanetti G. Use of the Boltzmann equation to simulate lattice-gas automata. Physical Review Letters 1988; 61:2332.
4. Aidun CK, Lu Y. Lattice-Boltzmann simulation of solid particles suspended in fluid. Journal of Statistical Physics 1995; 81:49-61.
5. Aidun CK, Lu Y, Ding E. Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. Journal of Fluid Mechanics 1998; 373:287.
6. Ladd AJC. Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. Journal of Fluid Mechanics 1994; 271:285.
7. Buxton GA, Verberg R, Jasnow D, Balazs AC. Newtonian fluid meets an elastic solid: coupling lattice Boltzmann and lattice-spring models. Physical Review E 2005; 71:056707.
8. Dupin M, Halliday I, Care C, Alboul L, Munn L. Modeling the flow of dense suspensions of deformable particles in three dimensions. Physical Review E 2007; 75:066707.
9. MacMeccan RM, Clausen JR, Neitzel GP, Aidun CK. Simulating deformable particle suspensions using a coupled lattice-Boltzmann and finite-element method. Journal of Fluid Mechanics 2009; 618:13.
10. Bouzidi M, Firdaouss M, Lallemand P. Momentum transfer of a Boltzmann-lattice fluid with boundaries. Physics of Fluids 2001; 13:3452.
11. Ginzburg I, d'Humieres D. Multireflection boundary conditions for lattice Boltzmann models. Physical Review E 2003; 68:066614.
12. Yu D, Mei R, Luo L, Shyy W. Viscous flow computations with the method of lattice Boltzmann equation. Progress in Aerospace Sciences 2003; 39:329.
13. Chun B, Ladd AJC. Interpolated boundary condition for lattice Boltzmann simulations of flows in narrow gaps. Physical Review E 2007; 75:066705.
14. Ding E, Aidun CK. Extension of the lattice-Boltzmann method for direct simulation of suspended particles near contact. Journal of Statistical Physics 2003; 112:685.
15. Holdych DJ. Lattice Boltzmann method for diffuse and mobile interfaces. Ph.D. Thesis, University of Illinois at Urbana Champaign, 2003.
16. Noble DR, Torczynski JR. A lattice Boltzmann method for partially saturated computational cells. International Journal of Modern Physics C 1998; 9:1189-1201.
17. Strack O, Cook B. Three-dimensional immersed boundary conditions for moving solids in the lattice-Boltzmann method. International Journal for Numerical Methods in Fluids 2007; 55:103.
18. Peskin CS. Numerical analysis of blood flow in the heart. Journal of Computational Physics 1977; 25:220-252.
19. Feng Z, Michaelides E. The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems. Journal of Computational Physics 2004; 195:602.
20. Zhang J, Johnson P, Popel A. An immersed boundary lattice Boltzmann approach to simulate deformable liquid capsules and its application to microscopic blood flows. Physical Biology 2007; 4:285.
21. Goldstein D, Handler R, Sirovich L. Modeling a no-slip flow boundary with an external force field. Journal of Computational Physics 1993; 105:354-366.
22. Buxton GA, Care CM, Cleaver DJ. A lattice spring model of heterogeneous materials with plasticity. Modelling and Simulation in Materials Science and Engineering 2001; 9:485-497.
23. Liboff R. Kinetic Theory: Classical, Quantum, and Relativistic Descriptions (3rd edn). Springer: Berlin, 2003.
24. Buick JM, Greated CA. Gravity in a lattice Boltzmann model. Physical Review E 2000; 61:5307.
25. Guo Z, Zheng C, Shi B. Discrete lattice effects on the forcing term in the lattice Boltzmann method. Physical Review E 2002; 65:046308.
26. He X, Zou Q, Luo LS, Dembo M. Analytic solutions and analysis on non-slip boundary condition for the lattice Boltzmann BGK model. Journal of Statistical Physics 1997; 87:115.
27. Ladd AJC, Verberg R. Lattice-Boltzmann simulation of particle-fluid suspensions. Journal of Statistical Physics 2001; 104:1191.
28. Martys NS, Shan X, Chen H. Evaluation of the external force term in the discrete Boltzmann equation. Physical Review E 1998; 58:6855.
29. Peskin CS. The immersed boundary method. Acta Numerica 2002; 11:479.
30. Chapman S. On the law of distribution of molecular velocities, and on the theory of viscosity and thermal conduction, in a non-uniform simple monatomic gas. Philosophical Transactions of the Royal Society 1916; 216:279-348.
31. Enskog D. Kinetische theorie der vorgaenge in maessig verduennten G. Ph.D. Thesis, Uppsala, 1917.
32. Ginzburg I, d'Humieres D. Principles of the kinetic theory of gases. Handbuch der Physik 1958; 12:205.
33. Arbabi S, Sahimi M. Test of universality for three-dimensional models of mechanical breakdown in disordered solids. Physical Review B 1990; 41:772.
34. Schwartz LM, Feng S, Thorpe MF, Sen PN. Behavior of depleted elastic networks: comparison of effective-medium and numerical calculations. Physical Review B 1985; 32:4607.
35. Alexeev A, Verberg R, Balazs AC. Modeling the motion of microcapsules on compliant polymeric surfaces. Macromolecules 2005; 38:10244.
36. Poe GG, Acrivos A. Closed-streamline flows past rotating single cylinders and spheres: inertia effects. Journal of Fluid Mechanics 1975; 72:605.
37. Zettner CM, Yoda M. The circular cylinder in simple shear at moderate Reynolds numbers: an experimental study. Experiments in Fluids 2001; 30:346.
38. Ding E, Aidun CK. The dynamics and scaling law for particles suspended in shear flow with inertia. Journal of Fluid Mechanics 2000; 423:317.
39. Jeffery GB. The motion of ellipsoidal particles immersed in a viscous fluid. Proceedings of the Royal Society of London, Series A 1922; 102:161.
40. Mikulencak DR, Morris JF. Stationary shear flow around fixed and free bodies at finite Reynolds number. Journal of Fluid Mechanics 2004; 520:215.
41. Miyamura A, Iwasaki S, Ishii T. Experimental wall correction factors of single solid spheres in triangular and square cylinders, and parallel plates. International Journal of Multiphase Flow 1981; 7:41.
42. Kim D, Beissinger RL. Augmented mass transport of macromolecules in sheared suspensions to surfaces. Journal of Colloid and Interface Science 1993; 159:9-20.
43. Shin S, Ku Y, Park MS, Suh JS. Measurement of red cell deformability and whole blood viscosity using laser-diffraction slit rheometer. Korea-Australia Rheology Journal 2004; 16:85-90.
44. Cha W, Beissinger RL. Augmented mass transport of macromolecules in sheared suspensions to surfaces b. Bovine serum albumin. Journal of Colloid and Interface Science 1996; 178:1.
45. Waugh R, Evans EA. Thermoelasticity of red blood cell membrane. Biophysical Journal 1979; 26:115.
46. Tsukada K, Sekizuka E, Oshio C. Direct measurement of erythrocyte deformability in diabetes mellitus with transparent microchannel capillary model and high-speed video camera system. Microvascular Research 2001; 61:231-239.
47. Brooks DE, Goodwin JW, Seaman GV. Interactions among erythrocytes under shear. Journal of Applied Physiology 1970; 28:172-177.
48. Merrill EW, Cokelet GC, Britten A, Wells RE. Non-Newtonian rheology of human blood-effect of fibrinogen deduced by 'subtraction'. Circulation Research 1963; 13:48-55.
49. Sierou A, Brady JF. Rheology and microstructure in concentrated noncolloidal suspensions. Journal of Rheology 2002; 46:1031-1056.
50. Harkness J, Whittington RB. Blood-plasma viscosity: an approximate temperature invariant arising from generalised concepts. Biorheology 1970; 6:169-187.
51. Fung Y. Biomechanics: Mechanical Properties of Living Tissues. Springer: Berlin, 1993.