Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                

Phase-coexisting patterns, horizontal segregation, and controlled convection in vertically vibrated binary granular mixtures

Istafaul Haque Ansari, Nicolas Rivas, and Meheboob Alam
Phys. Rev. E 97, 012911 – Published 26 January 2018
PDFHTMLExport Citation

Abstract

We report patterns consisting of coexistence of synchronous and asynchronous states [for example, a granular gas co-existing with (i) bouncing bed, (ii) undulatory subharmonic waves, and (iii) Leidenfrost-like states] in experiments on vertically vibrated binary granular mixtures in a Hele-Shaw cell. Most experiments have been carried out with equimolar binary mixtures of glass and steel balls of same diameter by varying the total layer height (F) for a range of shaking acceleration (Γ). All patterns as well as the related phase diagram in the (Γ,F) plane have been reproduced via molecular dynamics simulations of the same system. The segregation of heavier and lighter particles along the horizontal direction is shown to be the progenitor of such phase-coexisting patterns as confirmed in both experiment and simulation. At strong shaking we uncover a partial convection state in which a pair of convection rolls is found to coexist with a Leidenfrost-like state. The crucial role of the relative number density of two species on controlling the buoyancy-driven granular convection is demonstrated. The onset of horizontal segregation can be explained in terms of an anisotropic diffusion tensor.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
3 More
  • Received 2 November 2017

DOI:https://doi.org/10.1103/PhysRevE.97.012911

©2018 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Polymers & Soft Matter

Authors & Affiliations

Istafaul Haque Ansari1, Nicolas Rivas2,3, and Meheboob Alam1,*

  • 1Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur PO, Bangalore 560064, India
  • 2Multi-Scale Mechanics, MESA+, University of Twente, Enschede, Netherlands
  • 3Forschungszentrum Jülich GmbH, Helmholtz-Institut Erlangen-Nürnberg für Erneuerbare Energien (IEK-11), Fürther Strasse 248, 90429 Nuremberg, Germany

  • *meheboob@jncasr.ac.in

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 97, Iss. 1 — January 2018

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×

Images

  • Figure 1
    Figure 1

    (a) Phase diagram of patterns in (Γ,F) plane for up-sweeping experiments for Fg=Fs (equimolar mixture) with a shaking amplitude of A/d=3. (See Supplemental Material [27] movies 1 and 2 for a visual inspection of different patterns.) The symbols represent the locations of transitions between two states (e.g., “BB & Gas” and “UW & Gas”) for a specified layer depth F; the vertical dashed line represents an approximate phase boundary between two consecutive F that represent two different states (“Gas & Cluster” and “Gas & LS”); the data for down-sweeping experiments (open grey symbols) for the region of “UW & Gas” patterns are also superimposed; see text for details. (b) Phase diagram from MD simulations; the broken black lines denote the approximate phase boundaries obtained from up-sweeping experiments [same as in (a)]; refer to the text for patterns related to different symbols.

    Reuse & Permissions
  • Figure 2
    Figure 2

    Pixel-intensity profiles (upper panel) for patterns at Γ=3.5 for different F (refer to Fig. 1); the lower panel shows the binary image of the pattern for F=2.5, and thin red box represents the region over which the pixel intensity is vertically averaged to yield the profiles shown in the upper panel.

    Reuse & Permissions
  • Figure 3
    Figure 3

    Emergence of different patterns with increasing filling depth (F) at Γ9. (a) gas and cluster state at F=2.5; (b),(c) undulatory wave (UW) and gas at (b) F=3 and (c) F=4; (d) complete UW at F=5. The dark and light grey particles correspond to steel and glass balls, respectively.

    Reuse & Permissions
  • Figure 4
    Figure 4

    Simulation data for (a) the temporal evolution of horizontal (red line) and vertical (blue line) segregation index: short- and long-time evolutions are in the main panel and the left inset, respectively. Snapshots of particles at (b) t=100τ, (c) 2500τ, (d) 2500τ+τ/2, and (e) 2501τ; filled and open circles refer to steel and glass balls, respectively. Right inset in panel (a) shows the evolution of energy ratio, Es/Eg=msCs2/mgCg2. Parameters are as in experiments of Fig. 3.

    Reuse & Permissions
  • Figure 5
    Figure 5

    Snapshots of granular Leidenfrost states (LS) and horizontal segregation: (a) LS and gas at Γ=50.22 (f=64.5 Hz) and F=4 and (b) complete LS at Γ=50.7 (f=65 Hz) and F=6. (c) Coarse-grained PIV velocity field for the boxed region in (b).

    Reuse & Permissions
  • Figure 6
    Figure 6

    Snapshot (upper panel) and PIV-velocity field (lower panel) of the bouncing-bed (BB) states at Γ=4 and F=4: (a) t=0, (b) τ/2, and (c) τ, with τ=1/f being the time period of harmonic shaking. The horizontal arrow in each snapshot indicates the location of the bottom of the box.

    Reuse & Permissions
  • Figure 7
    Figure 7

    Simulation snapshots of granular Leidenfrost states (LSs) and horizontal segregation: (a) LS and gas at F=4 and (b) complete LS at F=6; other parameter values are as in Figs. 5 and 5, respectively; filled and open circles refer to steel and glass balls, respectively. (c) Simulation data for the evolution of horizontal (upper solid line) and vertical (lower dashed line) segregation indices for parameter values of (b).

    Reuse & Permissions
  • Figure 8
    Figure 8

    Instantaneous snapshot (upper panel) and its coarse-grained PIV velocity field (lower panel) for mixtures of glass and steel balls with (a) 1%, (b) 2%, (c) 5%, and (d) 10% steel balls for Γ50, A/d=3, and F=Fg+Fs=6. The velocity field (lower panel) is calculated within the boxed region (upper panel) of each snapshot.

    Reuse & Permissions
  • Figure 9
    Figure 9

    Effect of relative number fraction of steel balls on the phase diagram of patterns in (Γ,Fs/F) plane for F=Fg+Fs=6 and A/d=3; other details are as in Fig. 1. The vertical dashed line (at Fs/F0.04) represent an approximate phase boundary between two states [“convection” and “LS and convection”; “LS (Leidenfrost state)” and “gas and LS”].

    Reuse & Permissions
  • Figure 10
    Figure 10

    Effect of container length on patterns: (a) L/d=50 (a horizontally segregated state with a “glass-rich” cluster is seen on the right of the container) and (b) L/d=20 (a gaslike nearly homogeneous state) for Γ=7, Fg=Fs=1.5, and A/d=3.

    Reuse & Permissions
×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×