In our second phase of the project (year two) we build upon the serendipitous finding made in phase one (year one): The significance of the new Pèclet number Pe = γ˙ d/√T extends beyond simply quantifying the relative importance of advection to diffusion, Akin to the definition of the Inertial number (I) and viscous number (Iv), Pe also represents the ratio of microscopic kinetic rearrangement timescale d/√T to the macroscopic shearing timescale (1/γ˙ ). Consequently, kinetic rearrangement—the fundamental driver of mixing—to the definition of the Inertial number (I) and viscous number (Iv), Pe also represents the ratio of microscopic kinetic rearrangement timescale d/√T to the macroscopic shearing is now controlled by the actual relative motion between particles, as opposed to assuming that the microscopic motion (so-called particle fall) is driven by pressure.
So building the new Pèclet-based rheology into a macroscopic-level process model of the rotating drum flow, could yield after suitable scaling, a dimensionless number that fully characterises the local mixing state of the granular assembly. And in terms of the IF- PRI project, the dimensionless number should facilitate robust scaling of the mixing state between different operating conditions.
However, before building the process model and dimensionless number upon a possible “house of cards” we embarked on an extensive testing process of the Pèclet-based rheology via simulation. Within the context of the DEM simulation framework, we treat the DEM outputs as “data” and apply coarse graining to yield the continuum-level stress and strain fields. Using > 200 simulation configurations spanning dry, wet, dense and dilute granular flows, we show that the Mohr-Coulomb friction coefficient µ = τ /σ, where τ is the shear stress and σ the pressure, varies linearly with √Pe for a variable yield stress ratio µs consistent with the different geometric configurations and flow regimes investigated.
µ = cµ√Pe, (1)
where the scaling parameter cµ is dependent on driving conditions, and hence the material contact friction coefficient µc.
The linear collapse of the data according to equation (1) spanned a wider range of the phase space than the µ (I)-rheology, viscoinertial rheology, non-local rheology and extended kinetic theory. We argue that cµ partly encodes the anisotropy of the tangential contact force network, and equation (1) relates this structure anisotropy to the stress ratio. Noting that these anisotropies are also signatures of the granular mixture state, we hypothesise that the most robust mixing rules will emerge from encoding the new Pèclet-based rheology into the formulation of the mixing rules.