Relating Tribology to Rheology in Dense Suspensions

The fascinating behavior of a suspension of cornstarch in water is one of the most popular non-Newtonian fluid experience. Nevertheless, the shear-thickening of dense suspensions is not only a topic of popular interest. It is also an industrial issue because it can lead to large-scale processing problems in a host of practical applications (mining, concrete, food etc) and a challenging scientific question since, despite extensive efforts to describe its microscopic origin, current explanations fail to address the mechanism behind the shear-thickening of non-Brownian suspensions.

The two main features that are not properly described by the existing theories are the dilatancy and the intensity of the shear thickening. Indeed, in such systems networks of contacting particles can develop and transmit positive normal stresses. Moreover, viscosity can suddenly diverge under flow (discontinuous shear-thickening) with dramatic effects.

Previous experiments have demonstrated that the features of the viscosity increase (slope, critical stress) can be controlled by tuning particle surface properties such as roughness and/or by adsorbing polymers. These findings suggest that inter-particle contacts play a crucial role in the macroscopic flow at high volume fractions and that a precise description of these contacts is essential to interpret the rheological behavior.

By applying tribology knowledge to the interaction of one particle with each of its neighbors, we built a simple model, supported by contact-dynamics simulations as well as rheology and friction measurements, which links the transition from continuous to discontinuous shear-thickening in dense granular pastes to distinct lubrication regimes in the particle contacts. In particular we identify a local characteristic number (Sommerfeld number) that determines the transition from Newtonian to shear-thickening flows, and then show that the suspension's volume fraction and the boundary lubrication friction coefficient control the nature of the shear-thickening transition, both in simulations and experiments.

The generality and consistency of our data and of the proposed model sets a global framework in which the tribological (friction) and rheological properties of dense non-colloidal systems are intimately connected. This concept is expected to have an impact on a host of practical applications and relates fundamental issues such as flow localization and minimum local shear rate of granular pastes.

For more detail

N. Fernandez, R. Mani, D. Rinaldi, D. Kadau, M. Mosquet, H. Lombois-Burger, J. Cayer-Barrioz, H.J. Herrmann, D. Spencer, L. Isa, Microscopic mechanism for the shear-thickening of non-Brownian suspensions, accepted for Phys. Rev. Lett., arXiv:1308.1002