Granular Segregation as a Critical Phenomenon

Abstract

We present the results of an experimental study of patterned segregation in a horizontally shaken shallow layer of a binary mixture of dry particles. An order parameter for the segregated structures is defined and the effect of the variation of the combined filling fraction, C, of the mixture on the observed pattern formation is systematically studied. The surprising result is that there is a critical event associated with the onset of the pattern, at C = 0.647 ± 0.049, which has the characteristics of a second order phase transition, including critical slowing down.PACS numbers: 01.50Pa, 45.70Mg, 64.75.+g, 68.35.Rh, 45.70Qj. Keywords: Experiment, granular, binary mixture, segregation, critical phenomena, pattern formation.Segregation is a counter-intuitive phenomenon where an initially mixed state of dry granular particles separates into its constituent components under excitation [1]. Intriguingly, it does not always happen and the conditions for its occurrence are difficult to predict. Segregation is not only of fundamental interest but it is also of practical importance with applications in areas ranging from industry[2] to geology [3]. In recent years, there has been an upsurge of interest in small scale laboratory studies where vibration [4,5], avalanching in partially filled horizontal rotating drums [6,7] and stratification in vertically poured mixtures [8] have all provided interesting examples of pattern formation.Our focus is on quasi-2-dimensional horizontally driven layers of binary mixtures of particles [9,10] as this gives the practical advantage that any collective behavior is readily visualized and gravity is effectively eliminated. Moreover, the material is in contact with the drive throughout the motion. For this class of binary granular systems a qualitative segregation mechanism has been suggested [11] borrowing the idea of excluded volume depletion from colloidal systems and binary alloys [12]. In a driven 2D binary system of particles of different sizes, the packing fraction of the system is decreased if self-organized clustering of the larger particles occurs. Thereby considerably increasing the number of configurational states of the system. Hence ordered arrangement of the large spheres can increase the total entropy of the system by increasing the mobility of the small particles. This process has been referred to as entropic ordering [1]. We believe that analogous attractive depletion forces are responsible for segregation in our granular system. We show that segregation undergoes a phase transition and occurs only for filling fractions above a critical value with the characteristics of a second order phase transition with critical slowing down.A schematic diagram of the top view of the apparatus is presented in Fig. 1. It consisted of a horizontal smooth rectangular tray, of dimensions (x, y) = 180×90mm with a flatness of less than ±5µm, on which a binary mixture of particles was vibrated longitudinally. The tray, made out of aluminum tool plate, was mounted on a system of four high p...

Stripe Formation in Differentially Forced Binary Systems

“…The wavelengths of the stripes corresponds to the wavelength of sound to within ∼ 10%. Finally we discuss how differential forcing of the two components of a granular mixture may be responsible for the experimental findings of Mullin et al [5]. Mullin et al consider a flat tray which is oscillated in the horizontal plane at a frequency of 12Hz.…”

“…For sufficiently large amplitudes of vibration a mixture of equal sized glass and bronze particles were found to separate into a striped pattern. Sanchez et al proposed that the differential fluid drag on the two components of the mixture is the mechanism responsible for the segregation.Mullin et al [5,6,7] have performed a series of experiments in which they horizontally oscillate a quasi-2 dimensional layer of bronze spheres and poppy seeds. The species are again observed to segregate into a striped pattern.…”

“…Mullin et al [5,6,7] have performed a series of experiments in which they horizontally oscillate a quasi-2 dimensional layer of bronze spheres and poppy seeds. The species are again observed to segregate into a striped pattern.…”

Segregation mechanisms in a numerical model of a binary granular mixture

“…The experimental system used in [1,2] consists of a smooth horizontal tray of dimensions L x = 180mm by L y = 90mm vibrated sinusoidally parallel to its major axis at a frequency of f = 12Hz and amplitude of A = 1.74 ± 0.01mm. The grains are high-precision phosphorbronze spheres (denoted by c in the following) of radius R c = 0.75mm and mass m c = 16.8µg and poppy seeds (denoted by p in the following) of average radius and mass R p = 0.54mm and m p = 0.52µg respectively.…”

Nonequilibrium anisotropic phases, nucleation, and critical behavior in a driven Lennard-Jones fluid

“…This occurs during segregation in driven sheared systems 5,6,7 , flowing fluids 8 , shaken granular matter 9,10 , and non-equilibrium liquid-liquid binary mixtures 11 , and it has been reproduced in computer simulations of driven colloidal 12 and fluid 4,13 systems, for instance. Further examples are the anisotropies observed in both high-temperature superconductors 14,15 and electron gases 16,17 .…”