Micromechanical Origin of Particle Size Segregation

We computationally study the micromechanics of shear-induced size segregation and propose distinct migration mechanisms for individual large and small particles. While small particles percolate through voids without enduring contacts, large particles climb under shear through their crowded neighborhoods with anisotropic contact network. Particle rotation associated with shear is necessary for the upward migration of large particles. Segregation of large particles can be suppressed with inadequate friction, or with no rotation; increasing interparticle friction promotes the migration of large particles, but has little effect on the percolation of small particles.

Figure 1

Basic information. A bidisperse flow (${\mathrm{\Phi }}_l=0.5$) at the (a) initial and (b) final state. The temporal evolution of (c) kinetic energy $E_k$, (d) the degree of segregation $\alpha$, and (e) the distribution of local concentration of large particles (${\varphi }_l$).

Figure 2

Displacement statistics. (a) PDF for small particles in ${\mathrm{\Phi }}_l=0.5$. The solid line is fitted by a normal distribution. (b) PDF for large particles in ${\mathrm{\Phi }}_l=0.5$. The solid line is fitted by a Gaussian mixture distribution, with dashed lines showing the two components. (c) PDFs for large particles with ${\mathrm{\Phi }}_l$ varying in [0.1, 0.9]. Lines are fitted by Gaussian mixture distributions. Inset: ${\alpha }_f$ as a function of ${\mathrm{\Phi }}_l$.

Figure 3

Saturation of segregation. (a) Evolution of $\alpha$ for NG, RG, and MX. (b) Local concentration of large particles ${\varphi }_l$ at the final steady state.

Figure 4

Microstructures. (a) Evolution of coordination number $Z$ for large (solid, blue) and small (dashed, red) particles and a control setup of monodisperse flow (thick black). Inset: contact orientation. (b) Trajectory and (c) connectivity $Z_i$ of a single large (${\mathrm{\Phi }}_l\to 0$, blue) and a single small (${\mathrm{\Phi }}_l\to 1$, red) particle. (d) Evolution of the average normal contact force, $⟨f_n/⟨f_n⟩⟩$, for large (solid, blue) and single small (dashed, red) particles. Inset: stress partitioning for ${\mathrm{\Phi }}_l$ varying from 0.1 (dark markers) to 0.9 (bright markers). The red solid line is a linear fit in log scale with slope 0.9260. (e) Percolation velocity $w_{pI}/\dot{\gamma }\overline{d}$ as a function of local concentration $1-{\varphi }_I$ ($I=l$, $s$). Blue squares and red triangles (with error bars) are the mean values of raw data (gray points) for large and small particles, respectively. Dashed lines are fitted with the means.

Figure 5

Migration mechanism. The neighborhoods of (a) a dropping small particle and (b) a climbing large particle, in the flow of ${\mathrm{\Phi }}_l=0.5$. Arrows represent velocities relative to the focused particle.

Figure 6

Role of friction. (a) Single intruder cases. Square markers: large intruder. Circular markers: small intruder. (b) ${\mathrm{\Phi }}_l=0.5$ cases.