2. Frictional transition model

2.1 Rheology of an ideal suspension: dimensional analysis

To understand rheo-thickening, it's useful first to consider the case of an ideal suspension made up of hard, non-Brownian spheres immersed in a Newtonian fluid (figure 5 a). In this type of system, particles interact via hydrodynamic forces (drag, lubrication) and solid contact forces (non-interpenetration, solid friction). A dimensional analysis argument can be used to show that the rheology of such a suspension is, like that of a suspending fluid, purely Newtonian. Indeed, the variables on which the behavior of this suspension depends are the particle diameter d, the viscosity of the suspending fluid ${\eta }_{\text{f }}$...