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Nonlinear Rheological Properties of Dense Colloidal Dispersions Close to a Glass Transition Under Steady Shear

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High Solid Dispersions

Part of the book series: Advances in Polymer Science ((POLYMER,volume 236))

Abstract

The nonlinear rheological properties of dense colloidal suspensions under steady shear are discussed within a first principles approach. It starts from the Smoluchowski equation of interacting Brownian particles in a given shear flow, derives generalized Green–Kubo relations, which contain the transients dynamics formally exactly, and closes the equations using mode coupling approximations. Shear thinning of colloidal fluids and dynamical yielding of colloidal glasses arise from competition between a slowing down of structural relaxation because of particle interactions, and enhanced decorrelation of fluctuations caused by the shear advection of density fluctuations. The integration through transients (ITT) approach takes account of the dynamic competition, translational invariance enters the concept of wavevector advection, and the mode coupling approximation enables one to explore quantitatively the shear-induced suppression of particle caging and the resulting speed-up of the structural relaxation. Extended comparisons with shear stress data in the linear response and in the nonlinear regime measured in model thermo-sensitive core-shell latices are discussed. Additionally, the single particle motion under shear observed by confocal microscopy and in computer simulations is reviewed and analysed theoretically.

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Notes

  1. 1.

    This effect that flow speeds up the irreversible mixing is one mechanism active when stirring a solution. The non-affine motion even in laminar flow prevents the effect that stirring backwards would reverse the motion of the dissolved constituents.

  2. 2.

    The simplified notation with dimensionless quantities is used in the sections containing formal mainpulations, and in a number of original publications.

  3. 3.

    The MCT shear modulus at short times depends sensitively on the large cut-off k max for hard spheres [57], \(g(t,\dot{\gamma } = 0) = ({n}^{2}{k}_{\mathrm{B}}T/60{\pi }^{2}){ \int \nolimits \nolimits }_{{k}_{\mathrm{min}}}^{{k}_{\mathrm{max}}}\mathrm{d}k\,{k}^{4}{({c\prime}_{k})}^{2}\;{S}_{k}^{2}\,{\Phi }_{k}^{2}(t)\) gives the qualitatively correct [60, 75] short time g { lr}(t → 0) ∼ t − 1 ∕ 2, or high frequency divergence \(G\prime(\omega \gg {D}_{0}/{R}_{\mathrm{H}}^{2}) \sim \sqrt{\omega }\) only for k max → ∞.

  4. 4.

    The loss modulus rises again at very low frequencies, which may indicate that the colloidal glass at this density is metastable and may have a finite lifetime (an ultra-slow process is discussed in [32]).

  5. 5.

    An ultra-slow process causing the metastability of glassy states even without shear may have contributed to restore ergodicity in [32, 33].

  6. 6.

    Except for the introduction of the parameter γc, further quantitatively small, but qualitatively irrelevant, differences exist between the ISHSM defined here and used in Sect. 6.1 according to [45], and that originally defined in [43] and shown in Sect. 5.1; see [45] for discussion.

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Acknowledgment

It is a great pleasure to thank all my colleagues for the enjoyable and fruitful collaboration on this topic. I especially thank Mike Cates for introducing me to rheology, and Matthias Ballauff for his inspiring studies. Kind hospitality in the group of John Brady, where part of this review was written, is gratefully acknowledged. Financial support is acknowledged by the Deutsche Forschungsgemeinschaft in SFB-TR6, SFB 513, IRTG 667, and via grant Fu 309/3.

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  1. Fachbereich Physik, Universität Konstanz, 78457, Konstanz, Germany

    Matthias Fuchs

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  1. Matthias Fuchs
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Correspondence to Matthias Fuchs .

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  1. Chimie Industrielles (ESPCI), CNRS UMR 7167, Ecole Supérieure de Physique et, rue Vauquelin 10, Paris, 75005, France

    Michel Cloitre

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Fuchs, M. (2009). Nonlinear Rheological Properties of Dense Colloidal Dispersions Close to a Glass Transition Under Steady Shear. In: Cloitre, M. (eds) High Solid Dispersions. Advances in Polymer Science, vol 236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/12_2009_30

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