Shear thickening in concentrated suspensions: phenomenology, mechanisms,
  and relations to jamming

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Abstract

Shear thickening is a type of non-Newtonian behavior in which the stress required to shear a fluid increases faster than linearly with shear rate. Many concentrated suspensions of particles exhibit an especially dramatic version, known as Discontinuous Shear Thickening (DST), in which the stress suddenly jumps with increasing shear rate and produces solid-like behavior. The best known example of such counter-intuitive response to applied stresses occurs in mixtures of cornstarch in water. Over the last several years, this shear-induced solid-like behavior together with a variety of other unusual fluid phenomena has generated considerable interest in the physics of densely packed suspensions. In this review, we discuss the common physical properties of systems exhibiting shear thickening, and different mechanisms and models proposed to describe it. We then suggest how these mechanisms may be related and generalized, and propose a general phase diagram for shear thickening systems. We also discuss how recent work has related the physics of shear thickening to that of granular materials and jammed systems. Since DST is described by models that require only simple generic interactions between particles, we outline the broader context of other concentrated many-particle systems such as foams and emulsions, and explain why DST is restricted to the parameter regime of hard-particle suspensions. Finally, we discuss some of the outstanding problems and emerging opportunities.

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Jamming phase diagram for attractive particles.

V. Trappe, V. Prasad, L Cipelletti … (2001)

A wide variety of systems, including granular media, colloidal suspensions and molecular systems, exhibit non-equilibrium transitions from a fluid-like to a solid-like state, characterized solely by the sudden arrest of their dynamics. Crowding or jamming of the constituent particles traps them kinetically, precluding further exploration of the phase space. The disordered fluid-like structure remains essentially unchanged at the transition. The jammed solid can be refluidized by thermalization, through temperature or vibration, or by an applied stress. The generality of the jamming transition led to the proposal of a unifying description, based on a jamming phase diagram. It was further postulated that attractive interactions might have the same effect in jamming the system as a confining pressure, and thus could be incorporated into the generalized description. Here we study experimentally the fluid-to-solid transition of weakly attractive colloidal particles, which undergo markedly similar gelation behaviour with increasing concentration and decreasing thermalization or stress. Our results support the concept of a jamming phase diagram for attractive colloidal particles, providing a unifying link between the glass transition, gelation and aggregation.

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Shear thickening in colloidal dispersions

Norman J Wagner, John Brady (2009)

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Is Open Access

Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder

S Nagel, C. S. O'Hern, L. Silbert … (2003)

We have studied how 2- and 3- dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and applied stress. For each configuration, there is a unique jamming threshold, \(\phi_c\), at which particles can no longer avoid each other and the bulk and shear moduli simultaneously become non-zero. The distribution of \(\phi_c\) values becomes narrower as the system size increases, so that essentially all configurations jam at the same \(\phi\) in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close-packing. In fact, our results provide a well-defined meaning for "random close-packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, Point J, occurring at zero temperature and applied stress and at the random close-packing density, has properties reminiscent of an ordinary critical point. As Point J is approached from higher packing fractions, power-law scaling is found for many quantities. Moreover, near Point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, Point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as Point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. All of these results suggest that Point J may control behavior in its vicinity-perhaps even at the glass transition.