Physics of Fluids
Feedback | Help | Exit
   
 
 
 
Previous Article
Wave impact loads: The role of the flip-through
The impact of waves upon a vertical, rigid wall during sloshing is analyzed with specific focus on the modes that lead to the generation of a flip-through [M. J. Cooker and D. H. Peregrine, “A m...
Next Article
Small amplitude oscillations of a flexible thin blade in a viscous fluid: Exact analytical solution
The oscillation of a thin blade immersed in a viscous fluid has received considerable attention recently due to its importance in technological applications such as the atomic force microscope and mic...

Cross-stream-line migration in confined flowing polymer solutions: Theory and simulation

Phys. Fluids 18, 123101 (2006); doi:10.1063/1.2397571

Published 6 December 2006

You are not logged in to this journal. Log in

Juan P. Hernández-Ortiz, Hongbo Ma, Juan J. de Pablo, and Michael D. Graham
Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706-1691
Theory and Brownian dynamics (BD) simulations are used to study cross-stream migration in confined dilute flowing polymer solutions, using bead-spring chain and dumbbell models for the polymer molecules. Different degrees of confinement are explored, from a chain above a single wall to slits whose widths 2h are much bigger than the polymer contour length L and radius of gyration Rg (2h>>L>>Rg), much bigger than the radius of gyration but comparable with the contour length (2h~L>Rg), and comparable with the polymer radius of gyration (2h~Rg). The results show that except in the latter case, polymer chains migrate in shear flow away from the confining surfaces due to the hydrodynamic interactions between chains and walls. In contrast, when 2h~Rg, the chain migration in flow is toward the walls. This is a steric effect, caused by extension of the chain in the flow direction and corresponding shrinkage of the chains in the confined direction; here the hydrodynamic effects of each wall cancel one another out. Considering the polymer chain as a Stokeslet-doublet (point-force-dipole) as in a previously developed kinetic theory captures the correct far-field (relative to the walls) behavior. Once a finite-size dipole is used, the theory improves its near-wall predictions. In the regime 2h~L>Rg, the results are significantly affected by the level of discretization of the polymer chain, i.e., number of springs, because the spatial distribution of the forces exerted by the chain on the fluid acts on the scale of the channel geometry. ©2006 American Institute of Physics
History: Received 23 May 2006; accepted 20 October 2006; published 6 December 2006
Permalink: http://link.aip.org/link/?PHFLE6/18/123101/1
BUY THIS ARTICLE   (US$28)
Download PDF (309 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 47.57.Ng
    Polymers and polymer solutions
  • 47.60.+i
    Flows in ducts, channels, nozzles, and conduits
  • 47.11.-j
    Computational methods in fluid dynamics
  • 05.40.Jc
    Brownian motion
  • YEAR: 2006

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (84)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. T. W. Odom, V. R. Thalladi, J. C. Love, and G. M. Whitesides, “Generation of 30–50  nm structures using easily fabricated, composite PDMS masks,” J. Am. Chem. Soc. 124, 12112 (2002).
  2. C. K. Fredrickson and Z. H. Fan, “Macro-to-micro interfaces for microfluidic devices,” Lab Chip 4, 526 (2004).
  3. M. G. Roper, C. J. Easley, and J. P. Landers, “Advances in polymerase chain reaction on microfluidic chips,” Anal. Chem. 77, 3887 (2005).
  4. C. W. Kan, C. P. Fredlake, E. A. S. Doherty, and A. E. Barron, “DNA sequencing and genotyping in miniaturized electrophoresis systems,” Electrophoresis 25, 3564 (2004).
  5. J. Jing, J. Reed, J. Huang, X. Hu, V. Clarke, J. Edington, D. Housman, T. Anantharaman, E. Huff, B. Mishra, B. Porter, A. Shenker, E. Wolfson, C. Hiort, R. Kantor, C. Aston, and D. Schwartz, “Automated high resolution optical mapping using arrayed, fluid-fixed DNA molecules,” Proc. Natl. Acad. Sci. U.S.A. 95, 8046 (1998).
  6. S. Zhou, E. Kvikstad, A. Kile, J. Severin, D. Forrest, R. Runnheim, C. Churas, J. Hickman, C. Mackenzie, M. Choudhary, T. Donohue, S. Kaplan, and D. Schwartz, “Whole-genome shotgun optical mapping of Rhodobacter sphaeroides strain 2.4.1. and its use for whole-genome shotgun sequence assembly,” Genome Res. 13, 2142 (2003).
  7. E. Dimalanta, A. Lim, R. Runnheim, C. Lamers, C. Churas, D. Forrest, J. de Pablo, M. Graham, S. Coppersmith, S. Goldstein, and D. Schwartz, “A microfluidic system for large DNA molecule arrays,” Anal. Chem. 76, 5293 (2004).
  8. E. Y. Chan, N. M. Goncalves, R. A. Haeusler, A. J. Hatch, J. W. Larson, A. M. Maletta, G. R. Yantz, E. D. Carstea, M. Fuchs, G. G. Wong, S. R. Gullans, and R. Gilmanshin, “DNA mapping using microfluidic stretching and single-molecule detection of fluorescent site-specific tags,” Genome Res. 14, 1137 (2004).
  9. J. Tegenfeldt, C. Prinz, H. Cao, S. Chou, W. Reisner, R. Riehn, Y. Wang, E. Cox, J. Sturm, P. Silberzan, and R. Austin, “The dynamics of genomic-length DNA molecules in 100-nm channels,” Proc. Natl. Acad. Sci. U.S.A. 101, 10979 (2004).
  10. W. Reisner, K. Morton, R. Riehn, Y. Wang, Z. Yu, M. Rosen, J. Sturn, S. Chou, E. Frey, and R. Austin, “Statics and dynamics of singe DNA molecules confined in nanochannels,” Phys. Rev. Lett. 94, 196101 (2005).
  11. U. S. Agarwal, A. Dutta, and R. A. Mashelkar, “Migration of macromolecules under flow: The physical origin and engineering implications,” Chem. Eng. Sci. 49, 1693 (1994).
  12. Y.-L. Chen, M. D. Graham, J. J. de Pablo, K. Jo, and D. C. Schwartz, “DNA molecules in microfluidic oscillatory flow,” Macromolecules 38, 6680 (2005).
  13. L. Fang, H. Hu, and R. G. Larson, “DNA configurations and concentrations in shearing flow near a glass surface in a microchannel,” J. Rheol. 49, 127 (2005).
  14. L. Li, H. Hu, and R. G. Larson, “DNA molecular configurations in flows near adsorbing and nonadsorbing surfaces,” Rheol. Acta 44, 38 (2004).
  15. Y. Cohen and A. B. Metzner, “Apparent slip flow of polymer solutions,” J. Rheol. 29, 67 (1985).
  16. R. G. Horn, O. I. Vinogradova, M. E. Mackay, and N. Phan-Thien, “Hydrodynamic slippage inferred from thin-film drainage measurements in a solution of nonadsorbing polymer,” J. Chem. Phys. 112, 6424 (2000).
  17. A. B. Metzner, “Flow of polymeric solutions and emulsions through porous media—Current status,” in Improved Oil Recovery by Surfactant and Polymer Flooding, edited by D. O. Shah and R. S. Schechter (Academic Press, New York, 1977), p. 439.
  18. M. Tirrell and M. F. Malone, “Stress induced diffusion of macromolecules,” J. Polym. Sci., Polym. Phys. Ed. 15, 1569 (1977).
  19. E. Helfand and G. H. Fredrickson, “Large fluctuations in polymer solutions under shear,” Phys. Rev. Lett. 62, 2468 (1989).
  20. M. Doi, “Effects of viscoelasticity on polymer diffusion,” in Dynamics and Patterns in Complex Fluids: New Aspects of Physics and Chemistry of Interfaces, edited by A. Onuki and K. Kawasaki (Springer-Verlag, Berlin, 1990), p. 100.
  21. A. Onuki, “Dynamic equations of polymers with deformations in semidilute regions,” J. Phys. Soc. Jpn. 59, 3423 (1990).
  22. S. T. Milner, “Hydrodynamics of semidilute polymer solutions,” Phys. Rev. Lett. 66, 1477 (1991).
  23. V. G. Mavrantzas and A. N. Beris, “Modeling of the rheology and flow-induced concentration changes in polymer solutions,” Phys. Rev. Lett. 69, 273 (1992).
  24. S. T. Milner, “Dynamical theory of concentration fluctuations in polymer solutions under shear,” Phys. Rev. E 48, 3674 (1993).
  25. W. B. Black and M. D. Graham, “Slip, concentration fluctuations, and flow instability in sheared polymer solutions,” Macromolecules 24, 5731 (2001).
  26. J. H. Aubert and M. Tirrell, “Macromolecules in nonhomogeneous velocity gradient fields,” J. Chem. Phys. 72, 2694 (1980).
  27. A. V. Bhave, R. C. Armstrong, and R. A. Brown, “Kinetic theory and rheology of dilute, nonhomogeneous polymer solutions,” J. Chem. Phys. 95, 2988 (1991).
  28. H.-C. Öttinger, “Incorporation of polymer diffusivity and migration into constitutive equations,” Rheol. Acta 31, 14 (1992).
  29. A. N. Beris and V. G. Mavrantzas, “On the compatibility between various macroscopic formalisms for the concentration and flow of dilute polymer solutions,” J. Rheol. 38, 1235 (1994).
  30. C. F. Curtiss and R. B. Bird, “Statistical mechanics of transport phenomena: Polymeric liquid mixtures,” Adv. Polym. Sci. 125, 1 (1996).
  31. C. F. Curtiss and R. B. Bird, “Diffusion-stress relations in polymer mixtures,” J. Chem. Phys. 111, 10362 (1999).
  32. G. Sekhon, R. C. Armstrong, and M. S. Jhon, “The origin of polymer migration in a non-homogeneous flow field,” J. Polym. Sci., Polym. Phys. Ed. 20, 947 (1982).
  33. P. O. Brunn, “Hydrodynamically induced cross-stream migration of dissolved macromolecules (modelled as non-linearly elastic dumbbells),” Int. J. Multiphase Flow 9, 187 (1983).
  34. P. O. Brunn, “Polymer migration phenomena based on the general bead-spring model for flexible polymers,” J. Chem. Phys. 80, 5821 (1984).
  35. P. O. Brunn and S. Chi, “Macromolecules in non-homogeneous flow fields: A general study for dumbbell model macromolecules,” Rheol. Acta 23, 163 (1984).
  36. M. S. Jhon and K. F. Freed, “Polymer migration in Newtonian fluids,” J. Polym. Sci., Polym. Phys. Ed. 23, 955 (1985).
  37. X. Fan, N. Phan-Thien, N. T. Yong, X. Wu, and D. Xu, “Microchannel flow of a macromolecular suspension,” Phys. Fluids 15, 11 (2003).
  38. J. H. Aubert and M. Tirrell, “Effective viscosity of dilute polymer solutions near confining boundaries, interfaces,” J. Chem. Phys. 77, 553 (1982).
  39. V. G. Mavrantzas and A. N. Beris, “Theoretical study of wall effects on the rheology of dilute polymer solutions,” J. Rheol. 36, 175 (1992).
  40. J. J. de Pablo, H.-C. Öttinger, and Y. Rabin, “Hydrodynamic changes of the depletion layer of dilute polymer solutions near a wall,” AIChE J. 38, 273 (1992).
  41. V. G. Mavrantzas and A. N. Beris, “A hierarchical model for surface effects on chain conformation and rheology of poymer solutions. I. General formulation,” J. Chem. Phys. 110, 616 (1999).
  42. V. G. Mavrantzas and A. N. Beris, “A hierarchical model for surface effects on chain conformation and rheology of polymer solutions. II. Application to a neutral surface,” J. Chem. Phys. 110, 628 (1999).
  43. N. J. Woo, E. S. G. Shaqfeh, and B. Khomami, “Effect of confinement on dynamics and rheology of dilute DNA solutions. I. Entropic spring force under confinement and a numerical algorithm,” J. Rheol. 48, 281 (2004).
  44. N. J. Woo, E. S. G. Shaqfeh, and B. Khomami, “The effect of confinement on dynamics and rheology of dilute deoxyribose nucleic acid solutions. II. Effective rheology and single chain dynamics,” J. Rheol. 48, 299 (2004).
  45. R. M. Jendrejack, E. T. Dimalanta, D. C. Schwartz, M. D. Graham, and J. de Pablo, “DNA dynamics in a microchannel,” Phys. Rev. Lett. 91, 038102 (2003).
  46. R. M. Jendrejack, D. C. Schwartz, M. D. Graham, and J. J. de Pablo, “Effect of confinement on DNA dynamics in microfluidic devices,” J. Chem. Phys. 119, 1165 (2003).
  47. R. M. Jendrejack, D. C. Schwartz, J. J. de Pablo, and M. D. Graham, “Shear-induced migration in flowing polymer solutions: Simulation of long-chain DNA in microchannels,” J. Chem. Phys. 120, 2513 (2004).
  48. S. D. Hudson, “Wall migration and shear-induced diffusion of fluid droplets in emulsions,” Phys. Fluids 15, 1106 (2003).
  49. P. C. H. Chan and L. G. Leal, “The motion of a deformable drop in a second-order fluid,” J. Fluid Mech. 92, 131 (1979).
  50. J. R. Smart and D. T. Leighton, “Measurement of the drift of a droplet due to the presence of a plane,” Phys. Fluids A 3, 21 (1991).
  51. D. Santillan, E. Shaqfeh, and E. Darve, “Effect of flexibility on the shear-induced migration of short-chain polymers in parabolic channel flow,” J. Fluid Mech. 557, 297 (2006).
  52. H. B. Ma and M. D. Graham, “Theory of shear-induced migration in dilute polymer solutions near solid boundaries,” Phys. Fluids 17, 083103 (2005).
  53. O. Usta, J. Butler, and A. C. Ladd, “Flow-induced migration of polymers in dilute solution,” Phys. Fluids 18, 031703 (2006).
  54. J. Aubert and M. Tirrell, “Macromolecules in nonhomogeneous velocity gradient fields,” J. Chem. Phys. 72, 5731 (1980).
  55. L. Landau and E. Lifshitz, Fluid Mechanics, 2nd ed. (Butterworth-Heinemann, Oxford, 1987).
  56. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge University Press, Cambridge, 1992).
  57. R. B. Bird, C. Curtiss, F. R. C. Armstrong, and O. Hassager, Dynamics of Polymer Liquids: Kinetic Theory, 2nd ed. (John Wiley & Sons, New York, 1987), Vol. 2.
  58. R. M. Jendrejack, J. J. de Pablo, and M. D. Graham, “Stochastic simulations of DNA in flow: Dynamics and the effects of hydrodynamic interactions,” J. Chem. Phys. 116, 7752 (2002).
  59. H.-C. Öttinger, Stochastic Processes in Polymeric Fluids (Springer, Berlin, 1996).
  60. H.-C. Öttinger, Beyond Equilibrium Thermodynamics (Wiler-Interscience, New York, 2005).
  61. L. Reichl, A Modern Course in Statistical Physics, 2nd ed. (Wiley-Interscience, New York, 1998).
  62. R. Zwanzig, Nonequilibrium Statistical Mechanics (Oxford University Press, Oxford, 2001).
  63. S. Kim and S. Karrila, Microhydrodynamics: Principles and Selected Applications (Butterworth-Heinemann, Boston, 1991).
  64. H. Power and L. C. Wrobel, Boundary Integral Methods in Fluid Mechanics (Computational Mechanics Publications, Southampton, 1995).
  65. J. Blake, “A note on the image system for a Stokeslet in a no-slip boundary,” Proc. Cambridge Philos. Soc. 70, 30 (1971).
  66. N. Liron and S. Mochon, “Stokes flow for a Stokeslet between two parallel flat plates,” J. Eng. Math. 10, 287 (1976).
  67. M. Staben, A. Zinchenko, and R. Davis, “Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow,” J. Fluid Mech. 15, 1711 (2003).
  68. N. Liron and E. Barta, “Motion of a rigid particle in Stokes-flow-A new 2nd-kind boundary-integral equation formulation,” J. Fluid Mech. 238, 579 (1992).
  69. P. Ganatos, R. Pfeffer, and S. Weinbaum, “A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries. 2. Parallel motion,” J. Fluid Mech. 99, 755 (1980).
  70. P. Ganatos, S. Weinbaum, and R. Pfeffer, “A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries. 1. Perpendicular motion,” J. Fluid Mech. 99, 739 (1980).
  71. R. Jendrejack, M. Graham, and J. J. de Pablo, “Hydrodynamic interactions in long chain polymers: Application of the Chebyshev polynomial approximation in stochastic simulations,” J. Chem. Phys. 113, 2894 (2000).
  72. Y.-L. Chen, M. D. Graham, J. J. de Pablo, G. C. Randall, M. Gupta, and P. S. Doyle, “Conformation and dynamics of single DNA in parallel-plate slit microchannels,” Phys. Rev. E 70, 060901 (2004).
  73. P. J. Mucha, S.-Y. Tee, D. A. Weitz, B. I. Shraiman, and M. P. Brenner, “A model for velocity fluctuations in sedimentation,” J. Fluid Mech. 501, 71 (2004).
  74. J. Hernández-Ortiz, J. de Pablo, and M. Graham, “N  log  N method for hydrodynamic interactions of confined flowing polymer systems: Brownian dynamics,” J. Chem. Phys. 125, 164906 (2006).
  75. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77, 2nd ed. (Cambridge University Press, Cambridge, 1992).
  76. I. Bronstein, K. Semendjajew, G. Musiol, and H. Muehlig, Taschenbuch der Mathematik (Verlag Harri-Deutsch, Frankfurt am Main, 2001).
  77. M. Fixman, “Implicit algorithm for Brownian dynamics of polymers,” Macromolecules 19, 1195 (1986).
  78. M. Fixman, “Construction of Langevin forces in the simulation of hydrodynamic interaction,” Macromolecules 19, 1204 (1986).
  79. C. Stoltz, J. de Pablo, and M. Graham, “Concentration dependence of shear and extensional rheology of polymer solutions: Brownian dynamics simulations,” J. Rheol. 50, 137 (2006).
  80. R. Khare, M. Graham, and J. de Pablo, “Cross-stream migration of flexible molecules in a nanochannel,” Phys. Rev. Lett. 96, 224501 (2006).
  81. G. Segré and A. Silberberg, “Behaviour of macroscopic rigid spheres in Poiseuille flow. II. Experimental results and interpretation,” J. Fluid Mech. 14, 136 (1962).
  82. P. Vasseur and D. Cox, “The lateral migration of a spherical particle in two-dimensional shear flow,” J. Fluid Mech. 78, 385 (1976).
  83. L. Leal, “Particle motions in a viscous fluid,” Annu. Rev. Fluid Mech. 12, 435 (1980).
  84. J. Feng, H. Hu, and D. Joseph, “Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. II. Couette and Poiseuille flows,” J. Fluid Mech. 277, 271 (1994).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics