Using an original pressure-imposed shear cell, we study the rheology of dense suspensions. We show that they exhibit a viscoplastic behavior similarly to granular media successfully described by a frictional rheology and fully characterized by the evolution of the friction coefficient μ and the volume fraction ϕ with a dimensionless viscous number I(v). Dense suspension and granular media are thus unified under a common framework. These results are shown to be compatible with classical empirical models of suspension rheology and provide a clear determination of constitutive laws close to the jamming transition.

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Unifying suspension and granular rheology.

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.

https://iopscience.iop.org/article/10.1088/0034-4885/77/4/046602/pdf

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

Foreword 1. Introduction 2. Interactions at the grain level 3. The granular solid: statics and elasticity 4. The granular solid: plasticity 5. Granular gases 6. The granular liquid 7. Immersed granular media 8. Erosion and sediment transport 9. Geomorphology References Index.

Granular Media: Between Fluid and Solid

Particles suspended in a Newtonian fluid raise the viscosity and also generally give rise to a shear-rate dependent rheology. In particular, pronounced shear thickening may be observed at large solid volume fractions. In a recent article [R. Seto et al., Phys. Rev. Lett. 111, 218301 (2013)], we have considered the minimum set of components to reproduce the experimentally observed shear thickening behavior, including discontinuous shear thickening. We have found frictional contact forces to be essential and were able to reproduce the experimental behavior by a simulation including this physical ingredient along with viscous lubrication. In the present article, we thoroughly investigate the effect of friction and express it in the framework of the jamming transition. The viscosity divergence at the jamming transition has been a well known phenomenon in suspension rheology, as reflected in many empirical laws for the viscosity. Friction can affect this divergence, and in particular the jamming packing fraction is reduced if particles are frictional. Within the physical description proposed here, shear thickening is a direct consequence of this effect: As the shear rate increases, friction is increasingly incorporated as more contacts form, leading to a transition from a mostly frictionless to a mostly frictional rheology. This result is significant because it shifts the emphasis from lubrication hydrodynamics and detailed microscopic interactions to geometry and steric constraints close to the jamming transition.

https://sor.scitation.org/doi/pdf/10.1122/1.4890747

Shear thickening, frictionless and frictional rheologies in non-Brownian suspensions

Understanding the behaviour of particles suspended in a fluid has many important applications across a range of fields, including engineering and geophysics. Comprising two main parts, this book begins with the well-developed theory of particles in viscous fluids, i.e. microhydrodynamics, particularly for single- and pair-body dynamics. Part II considers many-body dynamics, covering shear flows and sedimentation, bulk flow properties and collective phenomena. An interlude between the two parts provides the basic statistical techniques needed to employ the results of the first (microscopic) in the second (macroscopic). The authors introduce theoretical, mathematical concepts through concrete examples, making the material accessible to non-mathematicians. They also include some of the many open questions in the field to encourage further study. Consequently, this is an ideal introduction for students and researchers from other disciplines who are approaching suspension dynamics for the first time.

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A physical introduction to suspension dynamics

Levich Institute and Chemical Engineering, City College of New York, New York, New York 10031, USA(Received 10 July 2008; published 9 March 2009)The normal stress exerted by particles in a sheared suspension is measured by analogy with a methodused to measure osmotic pressure in solutions. Particles in a liquid are conﬁned by a ﬁne screen to a gapbetweentwoverticalconcentric cylinders,theinnerofwhichrotates.Pressureintheliquidissensedeitherby a manometer or by a pressure transducer across the screen. The particles are large enough so thatBrownian motion and equilibrium osmotic pressure are vanishingly small. The measured pressure yieldsthe shear-induced particle pressure , the nonequilibrium continuation of equilibrium osmotic pressure.Forvolume fractions 0:3 0:5, is strongly dependent on , and linear in shear rate. Comparisonsof the measured particle pressure with modeling and simulation show good agreement.

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Particle pressure in a sheared suspension: a bridge from osmosis to granular dilatancy.

The isotropic contribution of the particle phase to the bulk stress, or the particle pressure, is studied for Brownian hard sphere suspensions in computationally simulated shear flow. The particle pressure is mechanically defined as the negative mean normal stress exerted by the particles, i.e., Π=−(1∕3)[Σ11+Σ22+Σ33] for a viscometric flow where 1, 2, and 3 refer to the flow, velocity gradient, and vorticity directions, respectively. Analysis is provided to relate the particle pressure to the equilibrium osmotic pressure and to show the relation of Π to particle migration phenomena. Utilizing existing hydrodynamic functions and simulating the flow by the Stokesian Dynamics technique, the particle pressure is evaluated for particle volume fractions in the range 0.1⩽ϕ⩽0.52 for monodisperse spherical particles. The relative strength of Brownian to shearing motion is given by the Peclet number Pe=γa2∕D0, where γ is the shear rate of a simple shear flow, a is the spherical particle radius, and D0=kT∕6πηa wit...

Yevgeny Yurkovetsky

Papers

Particle pressure in a sheared suspension: a bridge from osmosis to granular dilatancy.

Particle pressure in sheared Brownian suspensions