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Register a new userShear thickening in non-Brownian suspensions: an excluded volume effect
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Francesco Picano
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Shear thickening appears as an increase of the viscosity of a dense suspension with the shear rate, sometimes sudden and violent at high volume fraction. Its origin for noncolloidal suspension with non-negligible inertial effects is still debated. Here we consider a simple shear flow and demonstrate that fluid inertia causes a strong microstructure anisotropy that results in the formation of a shadow region with no relative flux of particles. We show that shear thickening at finite inertia can be explained as an increase of the effective volume fraction when considering the dynamically excluded volume due to these shadow regions
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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, R. Mari, J. F. Morris, and M. M. Denn., 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 (DST). 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.
A consensus is emerging that discontinuous shear thickening (DST) in dense suspensions marks a transition from a flow state where particles remain well separated by lubrication layers, to one dominated by frictional contacts. We show here that reasonable assumptions about contact proliferation predict two distinct types of DST in the absence of inertia. The first occurs at densities above the jamming point of frictional particles; here the thickened state is completely jammed and (unless particles deform) cannot flow without inhomogeneity or fracture. The second regime shows strain- rate hysteresis and arises at somewhat lower densities where the thickened phase flows smoothly. DST is predicted to arise when finite-range repulsions defer contact formation until a characteristic stress level is exceeded.
We propose a simple model, supported by contact-dynamics simulations as well as rheology and friction measurements, that links the transition from continuous to discontinuous shear-thickening in dense granular pastes to distinct lubrication regimes in the particle contacts. We identify a local Sommerfeld number that determines the transition from Newtonian to shear-thickening flows, and then show that the suspensions volume fraction and the boundary lubrication friction coefficient control the nature of the shear-thickening transition, both in simulations and experiments.
Dynamic particle-scale numerical simulations are used to show that the shear thickening observed in dense colloidal, or Brownian, suspensions is of a similar nature to that observed in non-colloidal suspensions, i.e., a stress-induced transition from a flow of lubricated near-contacting particles to a flow of a frictionally contacting network of particles. Abrupt (or discontinuous) shear thickening is found to be a geometric rather than hydrodynamic phenomenon; it stems from the strong sensitivity of the jamming volume fraction to the nature of contact forces between suspended particles. The thickening obtained in a colloidal suspension of purely hard frictional spheres is qualitatively similar to experimental observations. However, the agreement cannot be made quantitative with only hydrodynamics, frictional contacts and Brownian forces. Therefore the role of a short-range repulsive potential mimicking the stabilization of actual suspensions on the thickening is studied. The effects of Brownian and repulsive forces on the onset stress can be combined in an additive manner. The simulations including Brownian and stabilizing forces show excellent agreement with experimental data for the viscosity $eta$ and the second normal stress difference $N_2$.
We investigated the transient relaxation of a Discontinuous Shear Thickening suspension of cornstarch in water. We performed 2 types of relaxation experiments starting from a steady shear in a parallel plate rheometer, followed by either stopping the top plate rotation and measuring the transient torque relaxation, or removing the torque on the plate and measuring the transient tool rotation. We found that at low weight fraction $phi_{eff}<58.8pm0.4%$, the suspensions exhibited a relaxation behavior consistent with a generalized Newtonian fluid. However, for larger weight fraction $58.8% < phi_{eff} < 61.0%$, near the liquid-solid transition $phi_c=61.0pm0.7%$, we found relaxation behaviors different from the generalized Newtonian model. The relaxation time in this range scales with the inverse of the critical shear rate at the onset of shear thickening. In this range the relaxation time was the same in both stress and rate controlled experiments, rather than the viscosity calculated from the relaxation time which is expected to be intrinsic material parameter in the generalized Newtonian model. The discrepancy between the measured relaxation times and the generalized Newtonian prediction was found to be up to $10^4$, and extrapolations diverge in the limit of $phi_c$ as the generalized Newtonian prediction approaches 0. At the highest weight fractions, the relaxation time scales were measured to be on the order of $sim 1$ s. The fact that this timescale is resolvable by the naked eye may be important to understanding some of the dynamic phenomenon commonly observed in these systems. We also showed that using the critical shear rate $dotgamma_c$ at the onset of shear thickening to characterize the effective weight fraction can more precisely characterize material properties near the critical point $phi_c$, allowing us to resolve this transition so close to $phi_c$.
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