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Journal of Rheology / Volume 50 / Issue 1

J. Rheol. 50, 77 (2006); http://dx.doi.org/10.1122/1.2139098 (16 pages)

Laser tweezer microrheology of a colloidal suspension

Alexander Meyer, Andrew Marshall, Brian G. Bush, and Eric M. Furst

Department of Chemical Engineering, Colburn Laboratory, University of Delaware, Newark, Delaware 19716

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The microrheology of a colloidal suspension is measured using laser tweezers. Suspensions of refractive index-matched fluorinated ethylene propylene (FEP) particles are seeded with index-mismatched polystyrene or silica probe particles. Laser trapped probes are then subjected to steady uniform flows, enabling measurements of the suspension microviscosity as a function of FEP volume fraction and flow velocity. The microrheology results agree with bulk rheology, and both exhibit the same volume fraction dependence of the Krieger-Dougherty relationship for hard spheres. As volume fraction increases, the microrheology more closely agrees with the infinite shear bulk viscosity. In this regime, measurements using small probes exhibit additional shear thinning. Using confocal microscopy and fluorescent poly(methylmethacrylate) dispersions, we demonstrate that the nonlinear microrheology is consistent with the development of an anisotropic nonequilibrium pair distribution function between the probe and bath particles, with a denser region at the leading surface of the probe and a wake trailing it. The nonlinear response and underlying microstructure are in qualitative agreement with recent theory [ T. M. Squires and J. F. Brady, Phys. Fluids 17, 073101 (2005) ].

© 2006 The Society of Rheology

ACKNOWLEDGMENTS

The authors thank John Brady, Todd Squires, and Norman Wagner for helpful discussions and Andrew Hollingsworth, Michael Solomon, and Bill Russel for providing PMMA particles. They also acknowledge supporting experimental instrumentation by John Bishop. Financial support for this work was provided by the National Science Foundation (CTS-0238689).

Article Outline

  1. INTRODUCTION
  2. EXPERIMENTAL METHODS
    1. Materials
    2. Laser tweezer microrheology
    3. Experimental error
    4. Confocal microscopy
    5. Bulk rheology
  3. RESULTS AND DISCUSSION
  4. CONCLUSIONS

KEYWORDS and PACS

Keywords

colloids, suspensions, rheology, laser beam applications, refractive index, polymers, viscosity, radiation pressure

PACS

  • 83.80.Hj

    Suspensions, dispersions, pastes, slurries, colloids

  • 42.62.-b

    Laser applications

  • 82.70.Dd

    Colloids

  • 82.70.Kj

    Emulsions and suspensions

  • 66.20.-d

    Viscosity of liquids; diffusive momentum transport

PUBLICATION DATA

ISSN

0148-6055 (print)  

Publisher

The Society of Rheology

RELATED DATABASES

Web of Science

View this record in Web of Science

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ARTICLE DATA

History
Received 01 Sep 05
Revised 13 Oct 05
Digital Object Identifier
http://dx.doi.org/10.1122/1.2139098

  1. Almog, Y., and H. Brenner, "Non-continuum anomalies in the apparent viscosity experienced by a test sphere moving through an otherwise quiescent suspension," Phys. Fluids 9, 16–22 (1997)PHFLE6000009000001000016000001. [ISI]
  2. Banchio, A. J., G. Nagele, and J. Bergenholtz, "Viscoelasticity and generalized Stokes-Einstein relations of colloidal dispersions," J. Chem. Phys. 111, 8721–8740 (1999)JCPSA6000111000018008721000001.
  3. Bergenholtz, J., J. F. Brady, and M. Vicic, "The non-Newtonian rheology of dilute colloidal suspensions," J. Fluid Mech. 456, 239–275 (2002).
  4. Brady, J. F., "Computer simulation of viscous suspensions," Chem. Eng. Sci. 56, 2921–2926 (2001). [ISI]
  5. Campbell, A. I., and P. Bartlett, "Fluorescent hard-sphere polymer colloids for confocal microscopy," J. Colloid Interface Sci. 256, 325–330 (2002).
  6. Chae, B. S., and E. M. Furst, "Probe surface chemistry dependence and local polymer network structure in F-actin microrheology," Langmuir 21, 3084–3089 (2005). [ISI] [MEDLINE]
  7. Chen, D. T., E. R. Weeks, J. C. Crocker, M. F. Islam, R. Verma, J. Gruber, A. J. Levine, T. C. Lubensky, and A. G. Yodh, "Rheological microscopy: Local mechanical properties from microrheology," Phys. Rev. Lett. 90, 108301 (2003). [MEDLINE]
  8. Crocker, J. C., and D. G. Grier, "Methods of digital video microscopy for colloidal studies," J. Colloid Interface Sci. 179, 298–310 (1996).
  9. Foss, D. R., and J. F. Brady, "Structure, diffusion and rheology of Brownian suspensions by stokesian dynamics simulation," J. Fluid Mech. 407, 167–200 (2000).
  10. Gardel, M., M. Valentine, J. Crocker, A. Bausch, and D. Weitz, "Microrheology of entangled F-actin solutions," Phys. Rev. Lett. 91, 158302 (2003). [MEDLINE]
  11. Habdas, P., D. Scharr, A. C. Levitt, and E. R. Weeks, "Forced motion of a probe particle near the colloidal glass transition," Europhys. Lett. 67, 477–483 (2004). [ISI]
  12. Happel, J., and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1965).
  13. Horn, F. M., W. Richtering, J. Bergenholtz, N. Willenbacher, and N. J. Wagner, "Hydrodynamic and colloidal interactions in concentrated charge-stabilized polymer dispersions," J. Colloid Interface Sci. 225, 166–178 (2000). [ISI] [MEDLINE]
  14. Khair, A. S., and J. F. Brady, J. Rheol. 49, 1449–1481 (2005)JORHD2000049000006001449000001.
  15. Larson, R. G., The Structure and Rheology of Complex Fluids (Oxford University Press, New York, 1999).
  16. Le Goff, L., F. Amblard, and E. M. Furst, "Motor-driven dynamics in actin-myosin networks," Phys. Rev. Lett. 88, 018101 (2002). [ISI] [MEDLINE]
  17. Mason, T. G., "Estimating the viscoelastic moduli of complex fluids using the generalized Stokes-Einstein equation," Rheol. Acta 39, 371–378 (2000).
  18. Mason, T. G., T. Gisler, K. Kroy, E. Frey, and D. A. Weitz, "Rheology of F-actin solutions determined from thermally driven tracer motion," J. Rheol. 44, 917–928 (2000)JORHD2000044000004000917000001. [ISI]
  19. Mason, T. G., and D. A. Weitz, "Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids," Phys. Rev. Lett. 74, 1250–1253 (1995). [MEDLINE]
  20. Pantina, J. P., and E. M. Furst, "Directed assembly and rupture mechanics of colloidal aggregates," Langmuir 20, 3940–3946 (2004). [ISI] [MEDLINE]
  21. Papir, Y. S., and I. M. Krieger, "Rheological studies on dispersions of uniform colloidal spheres. 2. Dispersions in nonaqueous media," J. Colloid Interface Sci. 34, 126–130 (1970). [Inspec] [ISI]
  22. Rasband, W. S., ImageJ (U.S. National Institutes of Health, Bethesda, MD 1997–2005)
    URL http://rsb.info.nih.gov/ij/
  23. Russel, W. B., D. A. Saville, and W. R. Schowalter, Colloidal Dispersions (Cambridge University Press, Cambridge, 1989).
  24. Schnurr, B., F. Gittes, F. MacKintosh, and C. Schmidt, "Determining microscopic viscoelasticity in flexible and semiflexible polymer networks from thermal fluctuations," Macromolecules 30, 7781–7792 (1997).
  25. Simmons, R. M., J. T. Finer, S. Chu, and J. A. Spudich, "Quantitative measurements of force and displacement using an optical trap," Biophys. J. 70, 1813–1822 (1996). [Inspec] [ISI] [MEDLINE]
  26. Squires, T. M., and J. F. Brady, "A simple paradigm for active and nonlinear microrheology," Phys. Fluids 17, 073101 (2005)PHFLE6000017000007073101000001. [ISI]
  27. Valentine, M., P. Kaplan, D. Thota, J. Crocker, T. Gisler, R. Prud'homme, M. Beck, and D. Weitz, "Investigating the microenvironments of inhomogeneous soft materials with multiple particle tracking," Phys. Rev. E 64, 061506 (2001).
  28. Valentine, M. T., L. E. Dewalt, and H. D. Ou-Yang, "Forces on a colloidal particle in a polymer solution: a study using optical tweezers," J. Phys.: Condens. Matter 8, 9477–9482 (1996).
  29. Velegol, D., and F. Lanni, "Cell traction forces on soft biomaterials. I. Microrheology of type I collagen gels," Biophys. J. 81, 1786–1792 (2001). [Inspec] [ISI] [MEDLINE]
  30. Yamada, S., D. Wirtz, and S. C. Kuo, "Mechanics of living cells measured by laser tracking microrhology," Biophys. J. 78, 1736–1747 (2000). [Inspec] [ISI] [MEDLINE]
  31. 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, 2210–2216 (1994). [MEDLINE]

Figures (click on thumbnails to view enlargements)

FIG.1
Scanning electron micrograph of the FEP bath particles. The average particle diameter is 157±20 nm.

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FIG.2
The laser tweezer experimental geometry. An index-mismatched probe particle is held far from the sample interface (>100 μm) using an optical trap. By translating the microscope stage, a uniform flow of the index-matched bath suspension is generated past the probe. The displacement Δx of the probe center from the equilibrium trap position, measured using video microscopy, gives the corresponding drag force. Note that the schematic is not to scale.

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FIG.3
The drag force on a 3.2 μm PS probe particle in a suspension of FEP plotted as a function of fluid velocity. The slope of the force increases with the FEP volume fraction for ϕ = 0.08 (solid triangle), 0.16 (open triangle), 0.23 (solid square), and 0.31 (open circle).

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FIG.4
The drag force on a 2.25 μm silica probe particle in a suspension of FEP plotted as a function of fluid velocity for ϕ = 0.02 (closed circle), 0.04 (open square), 0.16 (closed triangle), 0.19 (open triangle), 0.28 (solid square), and 0.31 (open circle).

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FIG.5
The drag force on a 1.0 μm PS probe particle in a suspension of FEP plotted as a function of the velocity for ϕ = 0.08 (inverted triangle), 0.16 (triangle), and 0.23 (closed square). The line for ϕ = 0.23 is fit to the first half of the points and shows nonlinear behavior at high velocities.

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FIG.6
The relative microviscosity ηr,micro = ηmicro/ηs using laser tweezer microrheology and relative viscosity ηr from bulk rheology (open circles) are plotted vs the FEP volume fraction ϕ. Measurements are shown for probe particles of various sizes and chemistries, including 3.2 μm PS (solid squares), 2.25 μm silica (solid diamonds), 1.1 μm PS (solid circles), 1.0 μm PS (solid inverted triangle) and 2.8 μm PS (solid upright triangle). The solid line is the Krieger-Dougherty equation with an effective diameter deff = 0.18 μm, effective packing fraction ϕm = 0.62, and intrinsic viscosity [η] = 2.46. The dashed line is an estimate of the high-shear relative viscosity using ϕm = 0.71.

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FIG.7
The relative viscosity is plotted as a function of the Peclet number for 1.0 μm (closed symbols) and 3.2 μm (open symbols) PS probe particles in FEP at volume fractions ϕ = 0.08 (inverted triangles), 0.16 (triangles), and 0.23 (squares). The error bars reflect the accuracy of the laser tweezer force measurements, but do not take into account sample-to-sample variations, which can shift each series of data as much as ±0.2.

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FIG.8
The microviscosity (squares) compared with the macroviscosity (diamonds) for ϕ = 0.23 FEP. The solid and open squares represent 1.0 and 2.8 μm probes, respectively. (a) The macroviscosity is plotted vs Pe, while the microviscosity is plotted vs Pemicro. The dashed line is an estimate of ηr∞ based on the Krieger-Dougherty equation with ϕm = 0.71. (b) Shifting Pemicro by a factor 1/β collapses the data onto a master curve.

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FIG.9
Averaged confocal frames showing the structure of a dilute PMMA suspension (2ab = 1 μm, ϕ = 0.04) flowing past a stationary, optically trapped 2 μm melamine probe. The bright ring around the melamine particle is due to attached PMMA particles, giving an effective probe diameter of 4 μm. The flow is from left to right for Pemicro = 50 (a), 150 (b), and 300 (c). The scale bar is 10 μm.

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FIG.10
Intensity profiles from confocal imaging taken along the flow centerlines for Pemicro = 50 (circles), 150 (squares), and 300 (triangles). The flow is directed from the left to the right. The two largest peaks in each case are the attached PMMA particles. The inset shows the upstream profile in greater detail.

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