Pattern selection by a granular wave in a rotating drum

The results of an experimental investigation of granular segregation in a thin rotating drum are presented. A mechanism based on the presence of an uphill wave of particles has been found to govern the observed pattern of petals. Specifically we develop a simple model that captures the essential physics of the segregation and yields an algebraic expression that predicts the number of petals in the pattern.

Figure 1

(Color online) (a) core and (b)–(d) petals developed when a mixture of $0.71\mathrm{mm}$ (red/gray) and $0.12\mathrm{mm}$ (white) glass particles is rotated in a thin drum at $0.60,0.20,0.13$, and $0.09\mathrm{rad}∕\mathrm{s}$, respectively. The diameter of the drum is $D=24.5\mathrm{cm}$ and the volume fraction of small particles $\varphi =0.35$.

Figure 2

(Color online) (a) Angular distance between two consecutive petals $\left(\lambda \right)$ versus the rotation frequency $\left(\omega \right)$. The $24.5\mathrm{cm}$ diameter drum is half-filled with $\varphi =0.42$ volume fraction of small particles. (b) The values of the period depending on the frequency of rotation that correspond to the wavelengths of the figure (a) plotted in logarithmic scale and in linear scale (inset).

Figure 3

(Color online) log-log plot of the period versus the frequency of the drum for different volume fractions of small particles and different diameters of the rotating drum. Solid black lines show the different $T_c$ obtained from a fit like that in Fig. 2. The dashed black line is a least squares fit of $T=0.67w^{-0.63}$.

Figure 4

(Color online) The constant period selected by the system versus the radius of the initial core of small particles. Those results have been obtained for different diameters of the drum $\left(D\right)$ and volume fraction of small particles $\left(\varphi \right)$. The solid black line shows a linear fit with $T_c=0.456r_c$.

Figure 5

(Color online) (a) Steady wave at the end of the petal during the small particles deposition. (b) Uphill wave traveling from the end of the petal to the center of the drum. (c) Surface profile after $0.0\mathrm{s}$ $(•)$, $0.2\mathrm{s}$ $(▿)$, $0.4\mathrm{s}$ $(▵)$, $0.6\mathrm{s}$ $(◻)$, and $0.8\mathrm{s}$ $(◆)$ relative to the final flat surface, achieved for $t=0.88\mathrm{s}$ (dot line). $r$ is the distance from the center of the drum.