A moving-frame boundary-integral method for particle transport in microchannels of complex shape

Physics of Fluids

Volumn 24, Issue 4, 2012, Pages

  Zinchenko, Alexander Z ^a   Ashley, John F ^a   Davis, Robert H ^a  

^a University of Colorado   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); FRACTIONATION; MICROCHANNELS; MICROFLUIDICS; PARTICLE SEPARATORS; REYNOLDS NUMBER;

BOUNDARY INTEGRAL METHODS; BUOYANT SPHERICAL PARTICLES; LOW REYNOLDS NUMBER; MICRO-FLUIDIC DEVICES; PARALLEL MICROCHANNELS; PINCHED-FLOW FRACTIONATIONS; STRAIGHT-LINE SEGMENTS; THREE DIMENSIONAL ALGORITHM;

ITERATIVE METHODS;

EID: 84860507108     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4704816     Document Type: Article

References (57)

1. Happel J. Brenner H. Low Reynolds Number Hydrodynamics 1986, and 4th ed. (Martinus Nijhoff, Dordecht
2. Couillette C. Pozrikids C. Flow due to a periodic array of point forces, and the motion of small particles within a cylindrical tube of arbitrary cross section. Phys. Fluids 1996, 8:2019-2031. 10.1063/1.869005.
3. Staben M.E. Zinchenko A.Z. Davis R.H. Motion of a particle between two parallel walls in low-Reynolds-number Poiseuille flow. Phys. Fluids 2003, 15:1711-1733. 10.1063/1.1568341.
4. Ganatos P. Pfeffer R. Weinbaum S. A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries. 2. Parallel motion. J. Fluid Mech. 1980, 99:755-783. 10.1017/S0022112080000882.
5. Staben M.E. Zinchenko A.Z. Davis R.H. Dynamic simulation of spheroid motion between two parallel plane walls in low-Reynolds-number Poiseuille flow. J. Fluid Mech. 2006, 553:187-226. 10.1017/S0022112006008731.
6. Bhattacharya S. Bławzdziewicz J. Wajnryb E. Many-particle hydrodynamic interactions in parallel-wall geometry: Cartesian-representation method. Physica A 2005, 356:294-340. 10.1016/j.physa.2005.03.031.
7. Bhattacharya S. Bławzdziewicz J. Wajnryb E. Hydrodynamic interactions of spherical particles in suspensions confined between two planar walls. J. Fluid Mech. 2005, 541:263-292. 10.1017/S0022112005005938.
8. Bhattacharya S. Bławzdziewicz J. Wajnryb E. Far-field approximation for hydrodynamic interactions in parallel-wall geometry. J. Comput. Phys. 2006, 212:718-738. 10.1016/j.jcp.2005.07.015.
9. Bhattacharya S. Bławzdziewicz J. Wajnryb E. Hydrodynamic interactions of spherical particles in Poiseuille flow between two parallel walls. Phys. Fluids 2006, 18:053301. 10.1063/1.2195992.
10. Nakashima M. Yamada M. Seki M. Pinched flow fractionation (PFF) for continuous particle separation in a microfluidic device. Proceedings of 17th IEEE International Conference on Micro Electro Mechanical Systems 2004, 33-36. and in (IEEE, Piscataway, NJ)
11. Yamada M. Nakashima M. Seki M. Pinched flow fractionation: Continuous size separation of particles utilizing a laminar flow profile in a pinched microchannel. Anal. Chem. 2004, 76:5465-5471. 10.1021/ac049863r.
12. Sai Y. Yamada M. Yasuda M. Seki M. Continuous separations of particles using a microfluidic device equipped with flow rate control valves. J. Chromatogr. A 2006, 1127:214-220. 10.1016/j.chroma.2006.05.020.
13. Jain A. Posner J.D. Particle dispersion and separation resolution of pinched flow fractionation. Anal. Chem. 2008, 80:1641-1648. 10.1021/ac0713813.
14. Ho B.P. Leal L.G. Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech. 1974, 65:365-400. 10.1017/S0022112074001431.
15. Chien S. Tvetenstrand C.D. Epstein M.A. Schmid-Schonbein G.W. Model studies on distributions of blood cells at microvascular bifurcations. Am. J. Physiol. Heart Circ. Physiol. 1985, 248:H568-H576
16. Ditchfield R. Olbricht W.L. Effects of particle concentration on the partitioning of suspensions at small divergent bifurcations. J. Biomech. Eng. 1996, 118:287-294. 10.1115/1.2796009.
17. Svanes K. Zweifach B. Variations in small blood vessel hematocrits produced in hypothermic rats by micro-occlusion. Microvasc. Res. 1968, 1:210-220. 10.1016/0026-2862(68)90019-8.
18. Fung Y.-C. Stochastic flow in capillary blood vessels. Microvasc. Res. 1973, 5:34-48. 10.1016/S0026-2862(73)80005-6.
19. Roberts B.W. Olbricht W.L. Flow-induced particulate separations. AIChE J. 2003, 49:2842-2849. 10.1002/aic.690491116.
20. Roberts B.W. Olbricht W.L. The distribution of freely suspended particles at microfluidic bifurcations. AIChE J. 2006, 52:199-206. 10.1002/aic.10613.
21. Audet D.M. Olbricht W.L. The motion of model cells at capillary bifurcations. Microvasc. Res. 1987, 33:377-396. 10.1016/0026-2862(87)90029-X.
22. Peskin C.S. Numerical analysis of blood flow in the heart. J. Comput. Phys. 1977, 25:220-252. 10.1016/0021-9991(77)90100-0.
23. Fadlun E.A. Verzicco R. Orlandi P. Mohd-Yusof J. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 2000, 161:35-60. 10.1006/jcph.2000.6484.
24. Pinelli A. Naqavi I.Z. Piomelli U. Favier J. Immersed-boundary methods for general finite-difference and finite-volume Navier-Stokes solvers. J. Comput. Phys. 2010, 229:9073-9091. 10.1016/j.jcp.2010.08.021.
25. Glowinski R. Pan T.-W. Hesla T.I. Joseph D.D. A distributed Lagrange multiplier/fictitious domain method for particulate flows. Int. J. Multiphase Flow 1999, 25:755-794. 10.1016/S0301-9322(98)00048-2.
26. Patankar N.A. Singh P. Joseph D.D. Glowinski R. Pan T.-W. A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows. Int. J. Multiphase Flow 2000, 26:1509-1524. 10.1016/S0301-9322(99)00100-7.
27. Sharma N. Chen Y. Patankar N.A. A distributed Lagrange multiplier based computational method for the simulation of particulate-Stokes flow. Comput. Methods Appl. Mech. Eng. 2005, 194:4716-4730. 10.1016/j.cma.2004.12.013.
28. Wagner G.J. Moës N. Liu W.K. Belytschko T. The extended finite element method for rigid particles in Stokes flow. Int. J. Numer. Methods Eng. 2001, 51:293-313. 10.1002/nme.169.
29. Wagner G.J. Ghosal S. Liu W.K. Particulate flow simulations using lubrication theory solution enrichment. Int. J. Numer. Methods Eng. 2003, 56:1261-1289. 10.1002/nme.608.
30. Zinchenko A.Z. Davis R.H. An efficient algorithm for hydrodynamical interaction of many deformable drops. J. Comput. Phys. 2000, 157:539-587. 10.1006/jcph.1999.6384.
31. Zinchenko A.Z. Davis R.H. Shear flow of highly concentrated emulsions of deformable drops by numerical simulations. J. Fluid Mech. 2002, 455:21-62. 10.1017/S0022112001007042.
32. Zinchenko A.Z. Davis R.H. Algorithm for direct numerical simulation of emulsion flow through a granular material. J. Comput. Phys. 2008, 227:7841-7888. 10.1016/j.jcp.2008.05.004.
33. Pozrikidis C. Boundary Integral and Singularity Methods for Linearized Viscous Flow 1992, (Cambridge University Press, Cambridge, MA
34. Kim S. Karilla S. Microhydrodynamics: Principles and Selected Applications 1991, and (Butterworth-Heinemann, Boston, MA
35. Power H. Wrobel L.C. Boundary Integral Methods in Fluid Mechanics 1995, and (Computational Mechanics, Southampton-Boston
36. Higdon J.J. L. Stokes flow in arbitrary two-dimensional domains: Shear flow over ridges and cavities. J. Fluid Mech. 1985, 159:195-226. 10.1017/S0022112085003172.
37. Kelmanson M.A. Modified integral equation solution of viscous flows near sharp corners. Comput. Fluids 1983, 11:307-324. 10.1016/0045-7930(83)90017-8.
38. Kelmanson M.A. An integral equation method for the solution of singular slow flow problems. J. Comput. Phys. 1983, 51:139-158. 10.1016/0021-9991(83)90084-0.
39. Ladyzhenskaya O.A. The Mathematical Theory of Viscous Incompressible Flow 1969, 2nd ed. (Gordon and Breach, New York
40. Odqvist F.K. G. Über die randwertaufgaben der hydrodynamik zäher Flüssigkeiten. Math. Z. 1930, 32:329-375. 10.1007/BF01194638.
41. Power H. Miranda G. Second kind integral equation formulation of Stokes flow past a particle of arbitrary shape. SIAM J. Appl. Math. 1987, 47:689-698. 10.1137/0147047.
42. Zinchenko A.Z. Rother M.A. Davis R.H. A novel boundary-integral algorithm for viscous interaction of deformable drops. Phys. Fluids 1997, 9:1493-1511. 10.1063/1.869275.
43. Loewenberg M. Hinch E.J. Numerical simulation of a concentrated emulsion in shear flow. J. Fluid Mech. 1996, 321:395-419. 10.1017/S002211209600777X.
44. Cristini V. Bławzdziewicz J. Loewenberg M. An adaptive mesh algorithm for evolving surfaces: Simulations of drop breakup and coalescence. J. Comput. Phys. 2001, 168:445-463. 10.1006/jcph.2001.6713.
45. Rallison J.M. A numerical study of the deformation and burst of a viscous drop in general shear flows. J. Fluid Mech. 1981, 109:465-482. 10.1017/S002211208100116X.
46. Zinchenko A.Z. Davis R.H. A boundary-integral study of a drop squeezing through interparticle constrictions. J. Fluid Mech. 2006, 564:227-266. 10.1017/S0022112006001479.
47. Bazhlekov J.B. Anderson P.D. Meijer H.E. H. Nonsingular boundary integral method for deformable drops in viscous flows. Phys. Fluids 2004, 16:1064-1081. 10.1063/1.1648639.
48. Pan F. Acrivos A. Steady flows in rectangular cavities. J. Fluid Mech. 1967, 28:643-655. 10.1017/S002211206700237X.
49. Burggraf O. Analytical and numerical studies on the structure of steady separated flows. J. Fluid Mech. 1966, 24:113-151. 10.1017/S0022112066000545.
50. Gupta R.P. Manohar M.M. Boundary approximations and accuracy in viscous flow computations. J. Comput. Phys. 1979, 31:265-288. 10.1016/0021-9991(79)90072-X.
51. Gupta R.P. Manohar M.M. Noble B. Nature of viscous flows near sharp corners. Comput. Fluids 1981, 9:379-388. 10.1016/0045-7930(81)90009-8.
52. Dean W.R. Montagnon P.E. On the steady motion of viscous liquid in a corner. Proc. Cambridge Philos. Soc. 1949, 45:389-394. 10.1017/S0305004100025019.
53. Moffatt H.K. Viscous and resistive eddies near a sharp corner. J. fluid Mech. 1964, 18:1-18. 10.1017/S0022112064000015.
54. Liron N. Mochon N. Stokes flow for a Stokes-let between two parallel flat plates. J. Eng. Math. 1976, 10:287-303. 10.1007/BF01535565.
55. Blake J.R. A note on the image system for a Stokeslet in a no-slip boundary. Proc. Cambridge Philos. Soc. 1971, 70:303-310. 10.1017/S0305004100049902.
56. Staben M. Zinchenko A.Z. Davis R.H. Erratum: Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow. Phys. Fluids 2004, 16:4204-4206. 10.1063/1.1804107.
57. Goldman A.J. Cox R.G. Brenner H. Slow viscous motion of a sphere parallel to a plane wall. I. Motion through a quiescent fluid. Chem. Eng. Sci. 1967, 22:637-651. 10.1016/0009-2509(67)80047-2.