A Horizontal Brazil-Nut Effect and Its Reverse

Transport effects in a monolayer consisting of a binary granular mixture, confined in a horizontally vibrating circular dish, are studied experimentally and compared with a reduced theoretical model. Depending on the ratio of the particles’ material density and size, migration of the larger particles occurs either towards the boundary or to the center of the circular container. These directed motions show similarities to the Brazil-nut effect and its reverse form.

Figure 1

Snapshot of 1600 glass spheres (diameter $d=6\mathrm{mm}$, filling fraction $\mu =0.68$) in a swirling dish of diameter $D=29\mathrm{cm}$. After several minutes of horizontal swirling agitation, nine selected intruder particles made of various materials with different sizes are driven either to the center of the container or to its boundary. Shaker amplitude $A=1.91\mathrm{cm}$ and frequency $f=1.67\mathrm{Hz}$.

Figure 2

Temporal evolution of the radial distance $d_{\mathrm{p}}$ from the center of the swirling dish for two different intruder particles. Top: 10 mm polypropylene sphere in 1500 glass beads ($d=6\mathrm{mm}$, filling fraction $\mu =0.64$) migrating to the boundary of the container. Bottom: 10 mm steel ball in 1800 glass beads (filling fraction $\mu =0.77$) being driven to the center of the dish. Black solid lines indicate the results of complementary numerical simulations. The two insets show the corresponding experimental traces of the intruder particles in a comoving frame, with the initial starting positions marked by black circles. Shaker amplitude $A=1.59\mathrm{cm}$ (top) and $A=2.22\mathrm{cm}$ (bottom), and frequency $f=1.67\mathrm{Hz}$ in both cases.

Figure 3

Temporal evolution of the radial distance $d_{\mathrm{p}}$ for two different intruder particles averaged over 10 runs, together with exponential fits. Experimental details as specified in Fig. 2.

Figure 4

Temporal evolution of the radial distance $d_{\mathrm{p}}$ from the center of the swirling dish for a 10 mm steel ball in 1400 glass beads (filling fraction $\mu =0.60$), showing no tendency for supporting any segregation effect. Parameters: $A=1.91\mathrm{cm}$, $f=1.67\mathrm{Hz}$.

Figure 5

Phase diagrams of the critical filling fraction ${\mu }_c$ vs shaker amplitude $A$ for two intruder particles with different material properties as specified in Fig. 2. Green region: polypropylene sphere migrating to the boundary; red: steel ball drifting to the center of the bowl.

Figure 6

Phase space for particle properties. The plot shows the regimes where segregation towards the center (red circles), the boundary (green squares), or a mixed state (blue diamonds) occurs depending on the particle properties. Each symbol represents one experiment. The dashed lines indicate the numerically obtained border lines between the three different regions. Shaker amplitude $A=1.91\mathrm{cm}$ and frequency $f=1.67\mathrm{Hz}$.