Fluid dynamics of dissolved polymer molecules in confined geometries

Annual Review of Fluid Mechanics

Volumn 43, Issue , 2011, Pages 273-298

  Graham, Michael D ^a  

^a University of Wisconsin Madison   (United States)

Author keywords

cross stream migration; diffusion; DNA; microfluidics; multiscale simulation; nanofluidics

Indexed keywords

CONFINED GEOMETRIES; CROSS-STREAM MIGRATION; DILUTE SOLUTION; DNA MOLECULES; FLEXIBLE POLYMERS; FLUID MOTIONS; GENOMIC APPLICATIONS; MULTI-SCALE SIMULATION; POLYMER MODELS; POLYMER MOLECULE; POLYMER PHYSICS; SEMI-QUANTITATIVE; SIMULATION METHODS;

CLARIFICATION; DIFFUSION; DNA; FLUID DYNAMICS; FLUIDS; GEOMETRY; HYDRAULICS; MICROFLUIDICS; NANOFLUIDICS; NUCLEIC ACIDS; PIPE FLOW; VISUALIZATION;

EXPERIMENTS;

DIFFUSION; FLUID MECHANICS; GENOMICS; GEOMETRY; KINETICS; LITERATURE REVIEW; POLYMER;

EID: 79951984188     PISSN: 00664189     EISSN: None     Source Type: Book Series    
DOI: 10.1146/annurev-fluid-121108-145523     Document Type: Article

References (112)

1. Agarwal US, Dutta A, Mashelkar RA. 1994. Migration of macromolecules under flow: the physical origin and engineering implications. Chem. Eng. Sci. 49:1693-717 (Pubitemid 281955)
2. Alvarez A, Soto R. 2005. Dynamics of a suspension confined in a thin cell. Phys. Fluids 17:093103
3. Anekal SG, Bevan MA. 2005. Interpretation of conservative forces from Stokesian dynamic simulations of interfacial and confined colloids. J. Chem. Phys. 122:034903
4. Aubert JH, Tirrell M. 1980. Flows of dilute polymer solutions through packed porous chromatographic columns. Rheol. Acta 19:452-61
5. Bakajin OB, Duke TAJ, Chou CF, Chan SS, Austin RH, Cox EC. 1998. Electrohydrodynamic stretching of DNA in confined environments. Phys. Rev. Lett. 80:2737-40 (Pubitemid 128621655)
6. Balducci A, Mao P, Han J, Doyle PS. 2006. Double-stranded DNA diffusion in slitlike nanochannels. Macromolecules 39:6273-81 (Pubitemid 44418875)
7. Banchio AJ, Brady JF. 2003. Accelerated Stokesian dynamics: Brownian motion. J. Chem. Phys. 118:10323-32
8. Beck VA, Shaqfeh ESG. 2006. Ergodicity breaking and conformational hysteresis in the dynamics of a polymer tethered at a surface stagnation point. J. Chem. Phys. 124:094902
9. Bird RB, Curtis CF, Armstrong RC, Hassager O. 1987. Dynamics of Polymeric Liquids, Vol. 2. New York: Wiley. 2nd ed.
10. Blake JR. 1971. A note on the image system for a stokeslet in a no-slip boundary. Proc. Camb. Philos. Soc. 70:303-10
11. Bonthuis DJ, Meyer C, Stein D, Dekker C. 2008. Conformation and dynamics of DNA confined in slitlike nanofluidic channels. Phys. Rev. Lett. 101:108303
12. Brochard F, De Gennes PG. 1977. Dynamics of confined polymer chains. J. Chem. Phys. 67:52-56
13. Brunn PO. 1984. Polymer migration phenomena based on the general bead-spring model for flexible polymers. J. Chem. Phys. 80:5821-26
14. Brunn PO. 1985. Linear polymers in nonhomogeneous flow fields. II. The cross-stream migration velocity. J. Polym. Sci. Polym. Phys. 23:89-103 (Pubitemid 15465856)
15. Brunn PO, Grisafi S. 1985. Linear polymers in nonhomogeneous flow fields. I. Translational diffusion coefficient. J. Polym. Sci. Polym. Phys. 23:73-87 (Pubitemid 15465855)
16. Butler JE, Usta OB, Kekre R, Ladd AJC. 2007. Kinetic theory of a confined polymer driven by an external force and pressure-driven flow. Phys. Fluids 19:113101
17. Casassa EF. 1967. Equilibrium distribution of flexible polymer chains between a macroscopic solution phase and small voids. J. Polym. Sci. B Polym. Lett. 5:773-78
18. Chen YL, Graham MD, De Pablo JJ, Jo K, Schwartz DC. 2005. DNA molecules in microfluidic oscillatory flow. Macromolecules 38:6680-87 (Pubitemid 41118727)
19. Chen YL, Graham MD, De Pablo JJ, Randall GC, Gupta M, Doyle PS. 2004. Conformation and dynamics of single DNA molecules in parallel-plate slit microchannels. Phys. Rev. E 70:060901
20. Daoud M, De Gennes PG. 1977. Statistics of macromolecular solutions trapped in small pores. J. Phys. Paris 38:85-93
21. De Gennes PG. 1979. Scaling Concepts in Polymer Physics. Ithaca, NY: Cornell Univ. Press
22. De Pablo JJ, Ottinger HC, Rabin Y. 1992. Hydrodynamic changes in the depletion layer of dilute polymer solutions near a wall. AIChE J. 38:273-83
23. Del Bonis-O'Donnell JT, Reisner W, Stein D. 2009. Pressure-driven DNA transport across an artificial nanotopography. New J. Phys. 11:075032
24. Deserno M, Holm C. 1998a. How to mesh up Ewald sums. I. A theoretical and numerical comparison of various particle mesh routines. J. Chem. Phys. 109:7678-93 (Pubitemid 128678339)
25. Deserno M, Holm C. 1998b. How to mesh up Ewald sums. II. An accurate error estimate for the particle-particle-particle-mesh algorithm. J. Chem. Phys. 109:7694-701 (Pubitemid 128678340)
26. Diamant H. 2009. Hydrodynamic interaction in confined geometries. J. Phys. Soc. Jpn. 78:041002
27. Diamant H, Cui B, Lin B, Rice SA. 2005. Hydrodynamic interaction in quasi-two-dimensional suspensions. J. Phys. Condens. Matter 17:S2787-93 (Pubitemid 41067767)
28. Dimalanta ET, Lim A, Runnheim R, Lamers C, Churas C, et al. 2004. A microfluidic system for large DNA molecule arrays. Anal. Chem. 76:5293-301 (Pubitemid 39249409)
29. Doi M, Edwards SF. 1986. The Theory of Polymer Dynamics. New York: Oxford Univ. Press
30. Dufresne ER, Squires TM, Brenner MP, Grier DG. 2000. Hydrodynamic coupling of two Brownian spheres to a planar surface. Phys. Rev. Lett. 85:3317-20
31. Dünweg B, Ladd AJC. 2009. Lattice Boltzmann simulations of soft matter systems. Adv. Polym. Sci. 221:89-166
32. Español P, Warren P. 1995. Statistical mechanics of dissipative particle dynamics. Europhys. Lett. 30:191-96
33. Fan XJ, Phan-Thien N, Yong NT, Wu XH, Xu D. 2003. Microchannel flow of a macromolecular suspension. Phys. Fluids 15:11-21 (Pubitemid 36225351)
34. Fang L, Hsieh CC, Larson RG. 2007. Molecular imaging of shear-induced polymer migration in dilute solutions near a surface. Macromolecules 40:8490-99 (Pubitemid 350150567)
35. Fang L, Hu H, Larson RG. 2005. DNA configurations and concentration in shearing flow near a glass surface in a microchannel. J. Rheol. 49:127-38 (Pubitemid 43066243)
36. Fang L, Larson RG. 2007. Concentration dependence of shear-induced polymer migration in DNA solutions near a surface. Macromolecules 40:8784-87 (Pubitemid 350241383)
37. Fedosov DA, Karniadakis GE, Caswell B. 2008. Dissipative particle dynamics simulation of depletion layer and polymer migration in micro-and nanochannels for dilute polymer solutions. J. Chem. Phys. 128:144903
38. Fixman M. 1986. Construction of Langevin forces in the simulation of hydrodynamic interaction. Macromolecules 19:1204-207
39. Freund JB. 2007. Leukocyte margination in a model microvessel. Phys. Fluids 19:023301
40. Groot RD, Warren PB. 1997. Dissipative particle dynamics: bridging the gap between atomic and mesoscopic simulation. J. Chem. Phys. 107:4423-35 (Pubitemid 127611597)
41. Happel J, Brenner H. 1965. Low Reynolds Number Hydrodynamics. Englewood Cliffs, NJ: Prentice Hall
42. Harden JL, Doi M. 1992. Diffusion of macromolecules in narrow capillaries. J. Phys. Chem. 96:4046-52
43. Hasimoto H. 1959. On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5:317-28
44. Hernandez-Ortiz JP, De Pablo JJ, Graham MD. 2006a. N log N method for hydrodynamic interactions of confined polymer systems: Brownian dynamics. J. Chem. Phys. 125:164906
45. Hernandez-Ortiz JP, De Pablo JJ, Graham MD. 2007. Fast computation of many-particle hydrody-namic and electrostatic interactions in a confined geometry. Phys. Rev. Lett. 98:140602
46. Hernandez-Ortiz JP, Ma H, dePablo JJ, Graham MD. 2006b. Cross-stream-line migration in confinedflowing polymer solutions: theory and simulation. Phys. Fluids 18:123101
47. Hernandez-Ortiz JP, Ma H, De Pablo JJ, Graham MD. 2008. Concentration distributions during flow of confined flowing polymer solutions at finite concentration: slit and grooved channel. Korea-Aust. Rheol. J. 20:143-52
48. Hockney RW, Eastwood JW. 1988. Computer Simulation Using Particles. New York: Taylor & Francis
49. Hoda N, Kumar S. 2007. Kinetic theory of polyelectrolyte adsorption in shear flow. J. Rheol. 51:799-820 (Pubitemid 47330578)
50. Hsieh CC, Balducci A, Doyle PS. 2007. An experimental study of DNA rotational relaxation time in nanoslits. Macromolecules 40:5196-205 (Pubitemid 47179582)
51. Hsieh CC, Doyle PS. 2008. Studying confined polymers using single-molecule DNA experiments. Korea-Aust. Rheol. J. 20:127-42
52. Hudson SD. 2003. Wall migration and shear-induced diffusion of fluid droplets in emulsions. Phys. Fluids 15:1106-13 (Pubitemid 36751491)
53. Jendrejack RM, De Pablo JJ, Graham MD. 2002. Stochastic simulations of DNA in flow: dynamics and the effects of hydrodynamic interactions. J. Chem. Phys. 116:7752-59 (Pubitemid 34599089)
54. Jendrejack RM, Dimalanta ET, Schwartz DC, Graham MD, De Pablo JJ. 2003a. DNA dynamics in a microchannel. Phys. Rev. Lett. 91:038102
55. Jendrejack RM, Graham MD, De Pablo JJ. 2000. Hydrodynamic interactions in long chain polymers: application of the Chebyshev polynomial approximation in stochastic simulations. J. Chem. Phys. 113:2894-900
56. Jendrejack RM, Schwartz DC, De Pablo JJ, Graham MD. 2004. Shear-induced migration in flowing polymer solutions: simulation of long-chain deoxyribose nucleic acid in microchannels. J. Chem. Phys. 120:2513-29
57. Jendrejack RM, Schwartz DC, Graham MD, De Pablo JJ. 2003b. Effect of confinement on DNA dynamics in microfluidic devices. J. Chem. Phys. 119:1165-73
58. Jhon MS, Freed KF. 1985. Polymer migration in Newtonian fluids. J. Polym. Sci. Polym. Phys. 23:955-71
59. Jo K, Chen YL, De Pablo JJ, Schwartz DC. 2009. Elongation and migration of single DNA molecules in microchannels using oscillatory shear flows. Lab Chip 9:2348-55
60. Jo K, Dhingra DM, Odijk T, De Pablo JJ, Graham MD, et al. 2007. A single-molecule barcoding system using nanoslits for DNA analysis. Proc. Natl. Acad. Sci. USA 104:2673-78 (Pubitemid 46327938)
61. Khare R, Graham MD, De Pablo JJ. 2006. Cross-stream migration of flexible molecules in a nanochannel. Phys. Rev. Lett. 96:224505
62. Kohale SC, Khare R. 2009. Cross stream chain migration in nanofluidic channels: effects of chain length, channel height, and chain concentration. J. Chem. Phys. 130:104904
63. Larson JW, Yantz GR, Zhong Q, Charnas R, D'Antoni CM, et al. 2006. Single DNA molecule stretching in sudden mixed shear and elongational microflows. Lab Chip 6:1187-99 (Pubitemid 44290150)
64. Larson RG. 2005. The rheology of dilute solutions of flexible polymers: progress and problems. J. Rheol. 49:1-70 (Pubitemid 43066238)
65. Leal LG. 1980. Particle motions in a viscous fluid. Annu. Rev. Fluid Mech. 12:435-76
66. Liron N, Mochon S. 1976. Stokes flow for a stokeslet between 2 parallel flat plates. J. Eng. Math. 10:287-303
67. Ma HB, Graham MD. 2005. Theory of shear-induced migration in dilute polymer solutions near solid boundaries. Phys. Fluids 17:083103
68. Macdonald MJ, Muller SJ. 1996. Experimental study of shear-induced migration of polymers in dilute solutions. J. Rheol. 40:259-83 (Pubitemid 126591396)
69. Malevanets A, Kapral R. 1999. Mesoscopic model for solvent dynamics. J. Chem. Phys. 110:8605-13
70. Mark JE, Flory PJ. 1965. The configuration of the polyoxyethylene chain. J. Am. Chem. Soc. 87:1415-23
71. Millan JA, Laradji M. 2009. Cross-stream migration of driven polymer solutions in nanoscale channels: a numerical study with generalized dissipative particle dynamics. Macromolecules 42:803-10
72. Nitsche LC. 1996. Cross-stream migration of bead-spring polymers in nonrectilinear pore flows. AIChE J. 42:613-22 (Pubitemid 126460775)
73. Nitsche LC, Hinch EJ. 1997. Shear-induced lateral migration of Brownian rigid rods in parabolic channel flow. J. Fluid Mech. 332:1-21
74. Odijk T. 2008. Scaling theory of DNA confined in nanochannels and nanoslits. Phys. Rev. E 77:060901
75. Olla P. 1999. Simplified model for red cell dynamics in small blood vessels. Phys. Rev. Lett. 82:453-56 (Pubitemid 129583642)
76. ̈ Ottinger HC. 1996. Stochastic Processes in Polymeric Fluids. New York: Springer
77. Park J, Bricker JM, Butler JE. 2007. Cross-stream migration in dilute solutions of rigid polymers undergoing rectilinear flow near a wall. Phys. Rev. E 76:040801
78. Perkins TT, Smith DE, Larson RG, Chu S. 1995. Stretching of a single tethered polymer in a uniform flow. Science 268:83-87
79. Pham TT, Schiller UD, Prakash JR, Dünweg B. 2009. Implicit and explicit solvent models for the simulation of a single polymer chaininsolution: lattice Boltzmann versus Brownian dynamics.J. Chem. Phys. 131:164114
80. ReisnerW,MortonKJ, RiehnR,WangYM,YuZN,etal.2005.Statics anddynamicsofsingle DNAmolecules confined in nanochannels. Phys. Rev. Lett. 94:196101
81. Ripoll M, Ernst MH, Español P. 2001. Large scale and mesoscopic hydrodynamics for dissipative particle dynamics. J. Chem. Phys. 115:7271-84 (Pubitemid 33028858)
82. Rotne J, Prager S. 1969. Variational treatment of hydrodynamic interaction in polymers. J. Chem. Phys. 50:4831-37
83. Saintillan D, Shaqfeh ESG, Darve E. 2006. Effect of flexibility on the shear-induced migration of short-chain polymers in parabolic channel flow. J. Fluid Mech. 557:297-306 (Pubitemid 44069749)
84. Schiek RL, Shaqfeh ESG. 1997. Cross-streamline migration of slender Brownian fibres in plane Poiseuille flow. J. Fluid Mech. 332:23-39 (Pubitemid 27228380)
85. Segre G, Silberberg A. 1962a. Behaviour of macroscopic rigid spheres in Poiseuille flow, Part 1. Determination of local concentration by statistical analysis of particle passages through crossed light beams. J. Fluid Mech. 14:115-35
86. Segre G, Silberberg A. 1962b. Behaviour of macroscopic rigid spheres in Poiseuille flow, Part 2. Experimental results and interpretation. J. Fluid Mech. 14:136-57
87. Sendner C, Netz RR. 2008. Shear-induced repulsion of a semiflexible polymer from a wall. Europhys. Lett. 81:54006
88. Seo YH, Park OO, Chun MS. 1996. The behavior of velocity enhancement in microcapillary flows of flexible water-soluble polymers. J. Chem. Eng. Jpn. 29:611-19 (Pubitemid 126539305)
89. Shaqfeh ESG. 2005. The dynamics of single-molecule DNA in flow. J. Non-Newton. Fluid Mech. 130:1-28
90. Sierou A, Brady JF. 2001. Accelerated Stokesian dynamics simulations. J. Fluid Mech. 448:115-46 (Pubitemid 33087439)
91. Smart JR, Leighton DT. 1991. Measurement of the drift of a droplet due to the presence of a plane. Phys. Fluids A 3:21-28
92. Smith ER, Snook IK, van Megen W. 1987. Hydrodynamic interactions in Brownian dynamics: I. Periodic boundary conditions for computer simulations. Phys. A 143:441-67
93. Squires TM, Quake SR. 2005. Microfluidics: fluid physics at the nanoliter scale. Rev. Mod. Phys. 77:977-1026 (Pubitemid 43272528)
94. Staben M, Zinchenko AZ, Davis RH. 2003. Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow. Phys. Fluids 15:1711-33 (Pubitemid 36785219)
95. Stein D, van der Heyden FHJ, Koopmans WJA, Dekker C. 2006. Pressure-driven transport of confined DNA polymers in fluidic channels. Proc. Natl. Acad. Sci. USA 103:15853-58 (Pubitemid 44657556)
96. Sugarman JH. 1988. Microcapillary chromatography and radial migration of water-soluble polymers. PhD thesis. Princeton Univ.
97. Tegenfeldt JO, Prinz C, Cao H, Chou S, Reisner WW, et al. 2004a. The dynamics of genomic-length DNA molecules in 100-nm channels. Proc. Natl. Acad. Sci. USA 101:10979-83 (Pubitemid 38989570)
98. Tegenfeldt JO, Prinz C, Cao H, Huang RL, Austin RH, et al. 2004b. Micro-and nanofluidics for DNA analysis. Anal. Bioanal. Chem. 378:1678-92
99. Teraoka I. 1996. Polymer solutions in confining geometries. Prog. Polym. Sci. 21:89-149 (Pubitemid 126403990)
100. Tlusty T. 2006. Screening by symmetry of long-range hydrodynamic interactions of polymers confined in sheets. Macromolecules 39:3927-30 (Pubitemid 44013271)
101. Toukmaji AY, Board JA Jr. 1996. Ewald summation techniques in perspective: a survey. Comput. Phys. Commun. 95:73-92 (Pubitemid 126362827)
102. Usta OB, Butler JE, Ladd AJC. 2006. Flow-induced migration of polymers in dilute solution. Phys. Fluids 18:031703
103. Usta OB, Ladd AJC, Butler JE. 2005. Lattice-Boltzmann simulations of the dynamics of polymer solutions in periodic and confined geometries. J. Chem. Phys. 122:094902
104. Viovy JL. 2000. Electrophoresis of DNA and other polyelectrolytes: physical mechanisms. Rev. Mod. Phys. 72:813-72
105. Wall FT, Seitz WA, Chin JC, De Gennes PG. 1978. Statistics of self-avoiding walks confined to strips and capillaries. Proc. Natl. Acad. Sci. USA 75:2069-70
106. Watari N, Makino M, Kikuchi N, Larson RG, Doi M. 2007. Simulation of DNA motion in a microchannel using stochastic rotation dynamics. J. Chem. Phys. 126:094902
107. Woo NJ, Shaqfeh ESG, Khomami B. 2004a. The effect of confinement on dynamics and rheology of dilute deoxyribose nucleic acid solutions. II. Effective rheology and single chain dynamics. J. Rheol. 48:299-318
108. Woo NJ, Shaqfeh ESG, Khomami B. 2004b. Effect of confinement on dynamics and rheology of dilute DNA solutions. I. Entropic spring force under confinement and a numerical algorithm. J. Rheol. 48:281-98
109. Yamakawa H. 1970. Transport properties of polymer chains in dilute solution: hydrodynamic interaction. J. Chem. Phys. 53:436-43
110. Zhang Y, De Pablo JJ, Graham MD. 2009. Multiple free energy minima in systems of confined tethered polymers-toward soft nanomechanical bistable elements. Soft Matter 5:3694-700
111. Zheng J, Yeung ES. 2002. Anomalous radial migration of single DNA molecules in capillary electrophoresis. Anal. Chem. 74:4536-47 (Pubitemid 35006445)
112. Zheng J, Young ES. 2003. Mechanism for the separation of large molecules based on radial migration in capillary electrophoresis. Anal. Chem. 75:3675-80 (Pubitemid 36962097)