The effect of confining pressure (overburden) on segregation of granular material is studied in discrete element method (DEM) simulations of horizontal planar shear flow. To mitigate changes to the shear rate due to the changing overburden, a linear with depth variation in the streamwise velocity component is imposed using a simple feedback scheme. Under these conditions, both the rate of segregation and the ultimate degree of segregation in size bidisperse and density bidisperse granular flows decrease with increasing overburden pressure and scale with the overburden pressure normalized by the lithostatic pressure of the particle bed. At overburdens greater than approximately 20 times the lithostatic pressure at the bottom of the bed, the density segregation rate is zero while the size segregation rate is small but nonzero, suggesting that different physical mechanisms drive the two types of segregation. The segregation rate scales close to linearly with the inertial number for both size bidisperse and density bidisperse mixtures under various flow conditions, leading to a proposed pressure dependence term for existing segregation velocity correlations. Surprisingly, particle stiffness has only a minor effect on segregation, although it significantly affects the packing density.
Discrete element method simulations of confined bidisperse granular shear flows elucidate the balance between diffusion and segregation that can lead to either mixed or segregated states, depending on confining pressure. Results indicate that the collisional diffusion is essentially independent of overburden pressure. Because the rate of segregation diminishes with overburden pressure, the tendency for particles to segregate weakens relative to the remixing of particles due to collisional diffusion as the overburden pressure increases. Using a continuum approach that includes a pressure-dependent segregation velocity and a pressure-independent diffusion coefficient, the interplay between diffusion and segregation is accurately predicted for both size and density bidisperse mixtures over a wide range of flow conditions when compared to simulation results. Additional simulations with initially segregated conditions demonstrate that applying a high enough overburden pressure can suppress segregation to the point that collisional diffusion mixes the segregated particles.
We present a method to estimate the segregation parameter, S, a key input in a continuum transport model of particulate flows. S is determined by minimizing the difference between measured and model-predicted concentration profiles. To validate the approach, we conduct discrete element method simulations of size-bidisperse mixtures in quasi-2D bounded heap flow; the resulting data show that S calculated from concentration profiles is consistent with the directly measured value. The method's accuracy depends critically on the velocity profile during filling, but only weakly on the diffusion coefficient. When the velocity profile is nominally spanwise invariant, the error between estimated and measured S is 10%. This method is intended for practical application (described in Part II), so we restrict characterization of the velocity profile to that which can be readily determined experimentally, and explore the sensitivity of concentration profiles to variation of the gap between the sidewalls of the heap.
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