1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
f
Microviscosity, microdiffusivity, and normal stresses in colloidal dispersions
Rent:
Rent this article for
Access full text Article
/content/sor/journal/jor2/56/5/10.1122/1.4722880
1.
1. Barnes, H. A. , F. F. Hutton, and K. Walters, An Introduction to Rheology (Elsevier, Oxford, UK, 1989).
2.
2. Batchelor, G. K. , “Sedimentation in a dilute dispersion of spheres,” J. Fluid Mech. 52(2), 245268 (1972).
http://dx.doi.org/10.1017/S0022112072001399
3.
3. Batchelor, G. K. , “Brownian diffusion of particles with hydrodynamic interaction,” J. Fluid Mech. 74, 129 (1976).
http://dx.doi.org/10.1017/S0022112076001663
4.
4. Batchelor, G. K. , “The effect of Brownian motion on the bulk stress in a suspension of spherical particles,” J. Fluid Mech. 83, 97117 (1977).
http://dx.doi.org/10.1017/S0022112077001062
5.
5. Bausch, A. R. , F. Ziemann, A. A. Boulbitch, K. Jacobson, and E. Sackmann, “Local measurements of viscoelastic parameters of adherent cell surfaces by magnetic bead rheometry,” Biophys. J. 75, 20382049 (1998).
http://dx.doi.org/10.1016/S0006-3495(98)77646-5
6.
6. Bergenholtz, J. , J. F. Brady, and M. Vicic, “The non-Newtonian rheology of dilute colloidal suspensions,” J. Fluid Mech. 456, 239275 (2002).
http://dx.doi.org/10.1017/S0022112001007583
7.
7. Brady, J. F. , “Brownian motion, hydrodynamics, and the osmotic pressure,” J. Chem. Phys. 98, 33353341 (1993).
http://dx.doi.org/10.1063/1.464105
8.
8. Brady, J. F. , and J. F. Morris, “Microstructure of strongly sheared suspensions and its impact on rheology and diffusion,” J. Fluid. Mech. 348, 103139 (1997).
http://dx.doi.org/10.1017/S0022112097006320
9.
9. Brady, J. F. , and M. Vicic, “Normal stresses in colloidal suspensions,” J. Rheol. 39(3), 545566 (1995).
http://dx.doi.org/10.1122/1.550712
10.
10. Breedveld, V. , and D. J. Pine, “Microrheology as a tool for high-throughput screening,” J. Mater. Sci. 38, 44614470 (2003).
http://dx.doi.org/10.1023/A:1027321232318
11.
11. Buscall, R. , and L. R. White, “The consolidation of concentrated suspensions.Part 1. The theory of sedimentation,” J. Chem. Soc., Faraday Trans. 1 83, 873891 (1987).
http://dx.doi.org/10.1039/f19878300873
12.
12. Carnahan, N. F. , and K. E. Starling, “Equation of state for nonattracting rigid spheres,” J. Chem. Phys. 51(2), 635636 (1969).
http://dx.doi.org/10.1063/1.1672048
13.
13. Carpen, I. C. , and J. F. Brady, “Microrheology of colloidal dispersions by Brownian dynamics simulations,” J. Rheol. 49, 14831502 (2005).
http://dx.doi.org/10.1122/1.2085174
14.
14. Crocker, J. C. , “Measurement of the hydrodynamic corrections to the Brownian motion of two colloidal spheres,” J. Chem. Phys. 106, 28372840 (1997).
http://dx.doi.org/10.1063/1.473381
15.
15. Crocker, J. C. , and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” J. Colloid Interface Sci. 179, 298310 (1996).
http://dx.doi.org/10.1006/jcis.1996.0217
16.
16. Crocker, J. C. , J. A. Matteo, A. D. Dinsmore, and A. G. Yodh, “Entropic attraction and repulsion in binary colloids probed with a line optical tweezer,” Phys. Rev. Lett. 82, 43524355 (1999).
http://dx.doi.org/10.1103/PhysRevLett.82.4352
17.
17. Crocker, J. C. , M. T. Valentine, E. R. Weeks, T. Gisler, P. D. Kaplan, A. G. Yodh, and D. A. Weitz, “Two-point microrheology of inhomogeneous soft materials,” Phys. Rev. Lett. 85(4), 888891 (2000).
http://dx.doi.org/10.1103/PhysRevLett.85.888
18.
18. Davis, R. H. , and N. A. Hill, “Hydrodynamic diffusion of a sphere sedimenting through a dilute suspension of neutrally buoyant spheres,” J. Fluid Mech. 236, 513533 (1992).
http://dx.doi.org/10.1017/S0022112092001514
19.
19. DeGroot, S. R. , and P. Mazur, Non-Equilibrium Thermodynamics (Dover, General Publishing Co., Ltd., Ontario, Canada, 1984).
20.
20. Einstein, A. , “Investigations on the theory of the Brownian movement,” Ann. Phys. 19, 371381 (1906).
21.
21. Foss, D. R. , and J. F. Brady, “Brownian dynamics simulation of hard-sphere colloidal dispersions,” J. Rheol. 44(3), 629651 (2000a).
http://dx.doi.org/10.1122/1.551104
22.
22. Foss, D. R. , and J. F. Brady, “Structure, diffusion and rheology of Brownian suspensions by Stokesian dynamics simulation,” J. Fluid Mech. 407, 167200 (2000b).
http://dx.doi.org/10.1017/S0022112099007557
23.
23. Freundlich, H. , and W. Seifriz, “Über die elästizitaet von solen und gelen,” Z. Phys. Chem. 104, 233261 (1923).
24.
24. Furst, E. M. , “Applications of laser tweezers in complex fluid rheology,” Curr. Opin. Colloid Interface Sci. 10, 7986 (2005).
http://dx.doi.org/10.1016/j.cocis.2005.04.001
25.
25. Gisler, T. , and D. A. Weitz, “Scaling of the microrheology of semidilute f-actin solutions,” Phys. Rev. Lett. 82, 16061610 (1999).
http://dx.doi.org/10.1103/PhysRevLett.82.1606
26.
26. Gopalakrishnan, V. , K. S. Schweizer, and C. F. Zukoski, “Linking single particle rearrangements to delayed collapse times in transient depletion gels,” J. Phys.: Condens. Matter 18, 1153111550 (2006).
http://dx.doi.org/10.1088/0953-8984/18/50/009
27.
27. Guilford, W. H. , R. C. Lantz, and R. W. Gore, “Locomotive forces produced by single leukocytes in vivo and in vitro,” Am. J. Physio-Cell. Ph. 268(5), C1308C1312 (1995).
28.
28. Habdas, P. , D. Schaar, A. C. Levitt, and E. R. Weeks, “Forced motion of a probe particle near the colloidal glass transition,” Europhys. Lett. 67, 477483 (2004).
http://dx.doi.org/10.1209/epl/i2004-10075-y
29.
29. Heath, J. R. , M. E. Davis, and L. Hood, “Nanomedicine–revolutionizing the fight against cancer,” Sci. Am. 300, 4451 (2009).
http://dx.doi.org/10.1038/scientificamerican0209-44
30.
30. Heyes, D. M. , and J. R. Melrose, “Brownian dynamics simulations of model hard-sphere suspensions,” J. Non-Newtonian Fluid Mech. 46, 128 (1993).
http://dx.doi.org/10.1016/0377-0257(93)80001-R
31.
31. Khair, A. S. , and J. F. Brady, “Microviscoelasticity of colloidal dispersions,” J. Rheol. 49, 14491481 (2005).
http://dx.doi.org/10.1122/1.2085173
32.
32. Khair, A. S. , and J. F. Brady, “Single particle motion in colloidal dispersions: A simple model for active and nonlinear microrheology,” J. Fluid Mech. 557, 73117 (2006).
http://dx.doi.org/10.1017/S0022112006009608
33.
33. Khair, A. S. , and J. F. Brady, “Microrheology of colloidal dispersions: Shape matters,” J. Rheol. 52, 165196 (2008).
http://dx.doi.org/10.1122/1.2821894
34.
34. Lau, A. W. C. , B. D. Hoffman, A. Davies, J. C. Crocker, and T. C. Lubensky, “Microrheology, stress fluctuations, and active behavior of living cells,” Phys. Rev. Lett. 91, 198101 (2003).
http://dx.doi.org/10.1103/PhysRevLett.91.198101
35.
35. LeGrand, A. , and G. Petekidis, “Effects of particle softness on the rheology and yielding of colloidal glasses,” Rheol. Acta 47(5–6), 579590 (2008).
http://dx.doi.org/10.1007/s00397-007-0254-z
36.
36. Levine, A. J. , and T. C. Lubensky, “One- and two-particle microrheology,” Phys. Rev. Lett. 85, 17741778 (2000).
http://dx.doi.org/10.1103/PhysRevLett.85.1774
37.
37. Lindström, S. B. , T. E. Kodger, J. Sprakel, and D. A. Weitz, “Structures, stresses, and fluctuations in the delayed failure of colloidal gels,” Soft Matter 8, 36573664 (2012).
http://dx.doi.org/10.1039/c2sm06723d
38.
38. Lu, Q. , and M. J. Solomon, “Probe size effects on the microrheology of associating polymer solutions,” Phys. Rev. E 66, 061504 (2002).
http://dx.doi.org/10.1103/PhysRevE.66.061504
39.
39. Lukacs, G. L. , P. Haggie, O. Seksek, D. Lechardeur, N. Freedman, and A. S. Verkman, “Size-dependent DNA mobility in cytoplasm and nucleus,” J. Bio. Chem. 275(3), 16251629 (1999).
http://dx.doi.org/10.1074/jbc.275.3.1625
40.
40. MacKintosh, F. C. , and C. F. Schmidt, “Microrheology,” Curr. Opin. Colloid Interface Sci. 4, 300307 (1999).
http://dx.doi.org/10.1016/S1359-0294(99)90010-9
41.
41. Manley, S. , J. M. Skotheim, L. Mahadevan, and D. A. Weitz, “Gravitational collapse of colloidal gels,” Phys. Rev. Lett. 94, 218302 (2005).
http://dx.doi.org/10.1103/PhysRevLett.94.218302
42.
42. Mason, T. G. , and D. A. Weitz, “Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids,” Phys. Rev. Lett. 74(7), 12501253 (1995).
http://dx.doi.org/10.1103/PhysRevLett.74.1250
43.
43. Mason, T. G. , K. Ganesan, J. H. vanZanten, D. Wirtz, and S. C. Kuo, “Particle tracking microrheology of complex fluids,” Phys. Rev. Lett. 79(17), 32823286 (1997).
http://dx.doi.org/10.1103/PhysRevLett.79.3282
44.
44. McQuarrie, D. A. , Statistical Mechanics (Harper and Row, New York, 1976).
45.
45. Meyer, A. , A. Marshall, B. G. Bush, and E. M. Furst, “Laser tweezer microrheology of a colloidal suspension,” J. Rheol. 50, 7792 (2005).
http://dx.doi.org/10.1122/1.2139098
46.
46. Morris, J. F. , and J. F. Brady, “Self diffusion in sheared suspensions,” J. Fluid. Mech. 312, 223252 (1996).
http://dx.doi.org/10.1017/S002211209600198X
47.
47. Olsen, B. D. , J. A. Kornfield, and D. A. Tirrell, “Yielding behavior in injectable hydrogels from telechelic proteins,” Macromolecules 43(21), 90949099 (2010).
http://dx.doi.org/10.1021/ma101434a
48.
48. Perrin, J-.B. , “Mouvement Brownian et réalité moléculaire (Brownian motion and the molecular reality),” Ann. Chim. Phys. 18, 5114 (1909).
49.
49. Petekidis, G. , D. Vlassopoulous, and P. N. Pusey, “Yielding and flow of sheared colloidal glasses,” J. Phys.: Condens. Matter 16(8), S3955S3963 (2004).
http://dx.doi.org/10.1088/0953-8984/16/38/013
50.
50. Poon, W. C. K. , L. Starrs, S. P. Meeker, A. Moussad, R. M. L. Evans, P. N. Pusey, and M. M. Robins, “Delayed sedimentation of transient gels in colloid-polymer mixtures: Dark-field observation, rheology and dynamic light scattering studies,” Faraday Discuss. 112, 143154 (1999).
http://dx.doi.org/10.1039/a900664h
51.
51. Potanin, A. A. , and W. B. Russel, “Fractal model of consolidation of weakly aggregated colloidal dispersions,” Phys. Rev. E 53, 37023709 (1996).
http://dx.doi.org/10.1103/PhysRevE.53.3702
52.
52. Rallison, J. M. , and E. J. Hinch, “The effect of particle interactions on dynamic light scattering from a dilute suspension,” J. Fluid Mech. 167, 131168 (1986).
http://dx.doi.org/10.1017/S0022112086002768
53.
53. Saltzman, E. J. , and K. S. Schweizer, “Activated hopping and dynamical fluctuation effects in hard sphere suspensions and fluids,” J. Chem. Phys. 125(4), 044509104450919 (2006).
http://dx.doi.org/10.1063/1.22177739
54.
54. Sami, S. , “Stokesian dynamics simulation of Brownian suspensions in extensional flow,” Ph.D. thesis, California Institute of Technology, 1996.
55.
55. Schultz, K. M. , and E. M. Furst, “High-throughput rheology in a microfluidic device,” Lab Chip 11, 38023809 (2011).
http://dx.doi.org/10.1039/c1lc20376b
56.
56. Sprakel, J. , S. B. Lindström, T. E. Kodger, and D. A. Weitz, “Stress enhancement in the delayed yielding of colloidal gels,” Phys. Rev. Lett. 106, 248303 (2011).
http://dx.doi.org/10.1103/PhysRevLett.106.248303
57.
57. Squires, T. M. , “Nonlinear microrheology: Bulk stresses versus direct interactions,” Langmuir 24, 11471159 (2008).
http://dx.doi.org/10.1021/la7023692
58.
58. Squires, T. M. , and J. F. Brady, “A simple paradigm for active and nonlinear microrheology,” Phys. Fluids 17, 073101 (2005).
http://dx.doi.org/10.1063/1.1960607
59.
59. Sriram, I. , R. DePuit, T. M. Squires, and E. M. Furst, “Small amplitude active oscillatory microrheology of a colloidal suspension,” J. Rheol. 53, 357381 (2009).
http://dx.doi.org/10.1122/1.3058438
60.
60. Suh, J. , D. Wirtz, and J. Hanes, “Efficient active transport of gene nanocarriers to the cell nucleus,” Proc. Natl. Acad. Sci. U.S.A. 100(7), 37383882 (2003).
http://dx.doi.org/10.1073/pnas.0636277100
61.
61. Verkman, A. S. , “Solute and macromolecule diffusion in cellular aqueous compartments,” Trends Biochem. Sci. 27, 2733 (2002).
http://dx.doi.org/10.1016/S0968-0004(01)02003-5
62.
62. Wilson, L. G. , A. W. Harrison, A. B. Schofield, J. Arlt, and W. C. K. Poon, “Passive and active microrheology of hard-sphere colloids,” J. Phys. Chem. 113, 38063812 (2009).
http://dx.doi.org/10.1021/jp8079028
63.
63. Zia, R. N. , “Individual particle motion in colloids: Microviscosity, microdiffusivity, and normal stresses,” Ph.D. thesis, California Institute of Technology, 2011.
64.
64. Zia, R. N. , and J. F. Brady, “Single particle motion in colloids: Force-induced diffusion,” J. Fluid Mech. 658, 188210 (2010).
http://dx.doi.org/10.1017/S0022112010001606
65.
65. Zia, R. N. , and J. F. Brady, “Stress development, relaxation, and memory in colloidal dispersions: Transient nonlinear microrheology,” J. Rheol. (submitted).
66.
66. Ziemann, F. , J. Radler, and E. Sackmann, “Local measurements of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer,” Biophys. J. 66, 22102216 (1994).
http://dx.doi.org/10.1016/S0006-3495(94)81017-3
http://aip.metastore.ingenta.com/content/sor/journal/jor2/56/5/10.1122/1.4722880
Loading
/content/sor/journal/jor2/56/5/10.1122/1.4722880
Loading

Data & Media loading...

Loading

Article metrics loading...

/content/sor/journal/jor2/56/5/10.1122/1.4722880
2012-06-20
2014-08-27

Abstract

In active, nonlinear microrheology, a Brownian “probe” particle is driven through a complex fluid and its motion tracked in order to infer the mechanical properties of the embedding material. In the absence of external forcing, the probe and background particles form an equilibrium microstructure that fluctuates thermally. Probe motion through the medium distorts the microstructure; the character of this deformation, and hence its influence on probe motion, depends on the strength with which the probe is forced, , compared to thermal forces, , defining a Péclet number, , where is the thermal energy and is the characteristic microstructural length scale. Recent studies showed that the mean probe speed can be interpreted as the effective material viscosity, whereas fluctuations in probe velocity give rise to an anisotropic force-induced diffusive spread of its trajectory. The viscosity and diffusivity can thus be obtained by two simple quantities—mean and mean-square displacement of the probe. The notion that diffusive flux is driven by stress gradients leads to the idea that the stress can be related directly to the microdiffusivity, and thus the anisotropy of the diffusion tensor reflects the presence of normal stress differences in nonlinear microrheology. In this study, a connection is made between diffusion and stress gradients, and a relation between the particle-phase stress and the diffusivity and viscosity is derived for a probe particle moving through a colloidal dispersion. This relation is shown to agree with two standard micromechanical definitions of the stress, suggesting that the normal stresses and normal stress differences can be measured in nonlinear microrheological experiments if both the mean and mean-square motion of the probe are monitored. Owing to the axisymmetry of the motion about a spherical probe, the second normal stress difference is zero, while the first normal stress difference is linear in for and vanishes as for . The expression obtained for stress-induced migration can be viewed as a generalized nonequilibrium Stokes–Einstein relation. A final connection is made between the stress and an “effective temperature” of the medium, prompting the interpretation of the particle stress as the energy density, and the expression for osmotic pressure as a “nonequilibrium equation of state.”

Loading

Full text loading...

/deliver/fulltext/sor/journal/jor2/56/5/1.4722880.html;jsessionid=4npigikogh4ut.x-aip-live-03?itemId=/content/sor/journal/jor2/56/5/10.1122/1.4722880&mimeType=html&fmt=ahah&containerItemId=content/sor/journal/jor2
true
true
This is a required field
Please enter a valid email address
This feature is disabled while Scitation upgrades its access control system.
This feature is disabled while Scitation upgrades its access control system.
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Microviscosity, microdiffusivity, and normal stresses in colloidal dispersions
http://aip.metastore.ingenta.com/content/sor/journal/jor2/56/5/10.1122/1.4722880
10.1122/1.4722880
SEARCH_EXPAND_ITEM