Anti-plane segregation and diffusion in dense, bidisperse granular shear flow

Many dense granular systems are non-monodisperse, consisting of particles of different sizes, and will segregate based on size during flow. This phenomenon is an important aspect of many industrial and geophysical processes, necessitating predictive continuum models. This paper systematically studies a key aspect of the three-dimensional nature of segregation and diffusion in flowing, dense, bidisperse granular mixtures -- namely, segregation and diffusion acting along the direction perpendicular to the plane of shearing, which we refer to as the anti-plane modes of segregation and diffusion. To this end, we consider discrete-element method (DEM) simulations of flows of dense, bidisperse mixtures of frictional spheres in an idealized configuration that isolates anti-plane segregation and diffusion. We find that previously-developed constitutive equations, calibrated to DEM simulation results from flows in which both the segregation and diffusion processes occur within the plane of shearing, do not capture aspects of the anti-plane segregation dynamics. Accordingly, we utilize DEM simulation results to inform and calibrate constitutive equations for the segregation and diffusion fluxes in their anti-plane modes. Predictions of the resulting continuum model for the anti-plane segregation dynamics are tested against additional DEM simulation results across different cases, while parameters such as the shear strain rate and mixture composition are varied, and we find that the calibrated model predictions match well with the DEM simulation results. Finally, we suggest a strategy for generalizing the constitutive forms for the segregation and diffusion fluxes to obtain three-dimensional constitutive equations that account for both the in-plane and anti-plane modes of the segregation and diffusion processes.