Microscopic structure and dynamics study of granular segregation mechanism by cyclic shear

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Science Advances  17 Feb 2021:
Vol. 7, no. 8, eabe8737
DOI: 10.1126/sciadv.abe8737
  • Fig. 1 Experimental setup and convection pattern.

    (A) Experimental setup. (B) Tracers’ height trajectories as a function of shear cycle number t. (C) Flow pattern of convection. (D) Flow pattern of tracer particles (D = 12-mm) at steady state.

  • Fig. 2 Snapshots of different tracer particles at their respective steady states.

    (A to F) Snapshots of particle positions of (A) 8-, (B) 10-, (C) 12-, (D) 14-, (E) 16-, and (F) 24-mm tracers at steady states. (G) Maximal penetration depth of tracer particles. The maximal depth that different-size tracers can reach calculated by convection flux analysis (blue line) and the experimentally observed results, which are averaged among hundreds of tracer particles for consecutive 1500 shear cycles (red symbols). (H) Probability distribution functions (PDF) of tracer particles as a function of depth at steady states.

  • Fig. 3 Height trajectories and segregation speeds of tracer particles.

    (A) Heights of the COMs for different-size particles as a function of shear cycle number t. Inset: All curves can be fitted by H/d = A exp(− t0/t) + C, where t0 is the intrinsic time scale of different-size particles to reach the steady states. All curves can collapse after rescaling with t0. (B) Average speeds of the COMs vCOM (red, left axis) and the average normalized speeds v/〈vnei〉 (blue, right axis) for different-size particles. (C and D) Height trajectories of 16 D = 12-mm and 4 D = 24-mm tracer particles as a function of shear cycle number t. The top and bottom insets show the absolute (red) and relative (blue) height trajectories of the tracer particles before and after subtraction of the neighboring particles’ vertical displacements.

  • Fig. 4 Up-down asymmetry of Z and ϕ around the tracer particles, global density gradient, and the pair correlation function of tracer particles.

    (A) PDF of contact number in the upper and lower hemispheres for 8-, 12-, and 24-mm tracers. (B) Average volume fraction distribution of background particles within 4d distance to 8-, 12-, and 24-mm tracers that show the up-down asymmetry. (C) Average volume fraction ϕ of the system as a function of depth. (D) Pair correlation function between 200 12-mm tracers.

  • Fig. 5 Arching effect and fluidization around tracers within one cycle.

    (A) (i and ii) Relative volume fraction ϕrela around the tracer at γ = 0 and γ = 0.33. (iii) Variation of ϕrela around the tracer Δϕrela = ϕrela, γ = 0.33 − ϕrela, γ = 0 between γ = 0.33 and γ = 0 during the first one-fourth shear cycle. (B) (i) Complex bridge structure containing the tracer when the system is sheared rightward. The orientation of the complex bridge structure is defined as the orientation of the principal axis of its inertia tensor with the maximum eigenvalue. θbridge is the angle between the orientation of the bridge structure and z axis on the xz plane. (ii) Schematic diagram of rightward shear. (iii) Evolution of θbridge during the first half shear cycle. When shear is reversed, θbridge changes its direction from BD (θbridge > 0) to AC (θbridge < 0). (C) (i) Background particles around the tracer at the initial state (5- and 6-mm particles are colored by red and blue). (ii) Same particles as the left panel after 30 shear cycles. The green arrows represent the preferred directions that particles flow relative to the tracer. (iii) Trajectory of the tracer particle acquired at the interval of half shear cycle. The zigzag shape demonstrates the asymmetric arch effect due to shear.

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