Theory for size segregation in flowing granular mixtures based on computation of forces on a single large particle

We measure the upward force acting on a single, unconstrained, large particle in a granular medium of small particles flowing over inclined plane using discrete element method (DEM) simulation. Based on the computed force, we obtain an expression for the flux of large particles in a binary mixture of large and small particles and predict the equilibrium concentration profile and the velocity profile of the flowing layer. The theoretical predictions are in very good agreement with the DEM simulation results for a wide range of concentrations of large particles and inclination angles.

Figure 1

(a) Two-dimensional schematic of the simulation setup for obtaining the force on the large size intruder particles. (b) Variation of $y$ position of the intruder ($d_L=2d_S$) with time for $m_L=4$ (black) and $m_L=16$ (green). (c) Variation of the average $y$ position of the intruder with time for different masses. (d) Mass of the intruder shows a linear variation with $\eta d_L{v}_L$ for the two size ratios ($r=2$ and $r=1.5$) considered in this study. All the results are reported for $\theta ={25}^{\circ }$.

Figure 2

Concentration ($f_L$) of large particles for a $50\%$ large (size ratio 1.5) binary mixture for chute flow. Symbols represent DEM simulations results and lines represent predictions from theory. (a) Results for chute inclination $\theta ={25}^{\circ }$. Dashed, dotted, and solid lines show predictions for a constant, linear and quadratic variation of $\alpha \left(f_L\right)$. (b) Results for $\theta ={23}^{\circ }$ and $\theta ={29}^{\circ }$. Solid line in the inset shows the quadratic variation of $\alpha \left(f_L\right)/{\alpha }_0$.

Figure 3

Concentration ($f_L$) of large particles for different total concentration ($f_T$) of large particles for a binary mixture at inclination $\theta ={25}^{\circ }$. Symbols (connected with broken line) represent DEM simulations results and solid lines represent predictions from Eq. (7). (a) Results for size ratio $r=1.5$ and (b) $r=2$.

Figure 4

Velocity ($v_x$) variation of a binary mixture (a) at different inclinations with $50\%$ large ($r=1.5$) particles and (b) at two different overall compositions ($f_T$) at $\theta ={25}^{\circ }$. Solid lines are theoretical predictions from momentum balance equations.