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 suspension's volume fraction and the boundary lubrication friction coefficient control the nature of the shear-thickening transition, both in simulations and experiments.Flow non-linearities attract fundamental interest and have major consequences in a host of practical applications [1,2]. In particular, shear-thickening (ST), a viscosity increase from a constant value (Newtonian flow-Nw) upon increasing shear stress (or rate) at high volume fraction φ, can lead to large-scale processing problems of dense pastes, including cement slurries [3]. Several approaches have been proposed to describe the microscopic origin of shear-thickening [4][5][6][7]. The most common explanation invokes the formation of "hydroclusters", which are responsible for the observed continuous viscosity increase [6,8,9] and which have been observed for Brownian suspensions of moderate volume fractions [10,11]. However, this description no longer holds for bigger particles and denser pastes, where contact networks can develop and transmit positive normal stresses [12]. Moreover, the link between hydroclusters and CST for non-Brownian suspensions is still a matter of debate [13]. Additionally, dense, non-Brownian suspensions can also show sudden viscosity divergence under flow [14][15][16][17] with catastrophic effects, such as pumping failures. In contrast to a continuous viscosity increase at any applied rate, defined as continuous shear-thickening (CST), the appearance of an upper limit of the shear rate defines discontinuous shear-thickening (DST). This CST to DST transition is observed when the volume fraction of the flowing suspension is increased above a critical value, which depends on the system properties, e.g. polydispersity or shape, and on the flow geometry [3,18]. An explanation for its microscopic origin is still lacking [19]. Moreover, experiments have demonstrated that the features of the viscosity increase (slope, critical stress) can be controlled by tuning particle surface properties such as roughness [20] and/or by adsorbing polymers [21,22]. These findings suggest that inter-particle contacts play a crucial role in the macroscopic flow at high volume fractions. A more precise description of these contacts is therefore essential to interpret the rheological behavior.In this paper, we present a unified theoretical framework, supported by both numerical simulations and experimental data, which describes the three flow regimes of rough, frictional, non-Brownian particle suspensions (Nw,CST,DST) and links the Nw-ST (in terms of shear) and the CST-DST transitions (in terms of volume fraction) to the local friction. Our micro...
