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Convection and Segregation in Fluidised Granular Systems Exposed to Two-Dimensional Vibration

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Convection and Segregation in Fluidised Granular Systems Exposed to Two-Dimensional Vibration Home Search Collections Journals About Contact us My IOPscience Convection and segregation in fluidised granular systems exposed to two-dimensional vibration This content has been downloaded from IOPscience. Please scroll down to see the full text. 2016 New J. Phys. 18 033005 (http://iopscience.iop.org/1367-2630/18/3/033005) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 197.210.205.92 This content was downloaded on 25/06/2016 at 03:48 Please note that terms and conditions apply. New J. Phys. 18 (2016) 033005 doi:10.1088/1367-2630/18/3/033005 PAPER Convection and segregation in fluidised granular systems exposed to OPEN ACCESS two-dimensional vibration RECEIVED 14 December 2015 C R K Windows-Yule REVISED Multi-Scale Mechanics, Department of Mechanical Engineering, MESA+, University of Twente, PO Box 217, 7500 AE Enschede, 10 February 2016 The Netherlands ACCEPTED FOR PUBLICATION School of Physics and Astronomy, University of Birmingham, Edgbaston, B15 2TT, UK 12 February 2016 PUBLISHED E-mail: [email protected] 2 March 2016 Keywords: granular, convection, segregation, vibrated, phase diagram Original content from this work may be used under the terms of the Creative Abstract Commons Attribution 3.0 licence. Convection and segregation in granular systems not only provide a rich phenomenology of Any further distribution of scientifically interesting behaviours but are also crucial to numerous ‘real-world’ processes ranging this work must maintain attribution to the from important and widely used industrial procedures to potentially cataclysmic geophysical author(s) and the title of phenomena. Simple, small-scale experimental or simulated test systems are often employed by the work, journal citation and DOI. researchers in order to gain an understanding of the fundamental physics underlying the behaviours of granular media. Such systems have been the subject of extensive research over several decades, with numerous system geometries and manners of producing excitation explored. Energy is commonly provided to granular assemblies through the application of vibration—the simplicity of the dynamical systems produced and the high degree of control afforded over their behaviour make vibrated granular beds a valuable canonical system by which to explore a diverse range of phenomena. Although a wide variety of vibrated systems have been explored in the existing literature, the vast majority are exposed to vibration along only a single spatial direction. In this paper, we study highly fluidised systems subjected to strong, multi-directional driving, providing a first insight into the dynamics and behaviours of these systems which may potentially hold valuable new information relevant to important industrial and natural processes. With a particular focus on the processes of convection and segregation, we analyse the various states and phase transitions exhibited by our system, detailing a number of previously unobserved dynamical phenomena and system states. 1. Introduction Assemblies of multiple, individual macroscopic particles, collectively known as granular materials, are ubiquitous in the world around us, playing vital rôles in innumerable industrial and natural processes [1–3]. When exposed to an energy source, granular media are known to demonstrate numerous different physical states, and to exhibit a wide variety of interesting and often surprising dynamical phenomena [4, 5], both with and without parallel in classical, molecular materials. While there exist various manners in which energy may be provided to a granular system [6–8], our focus here is on the provision of energy through vibrational excitation, whereby the particles comprising a granular bed gain energy through collisions with a massive, oscillating surface [9]. The study of vibrated systems is of direct relevance to various industrial processes including, but by no means limited to, the drying [10], mixing [11] and sorting [12] of various materials, the separation of valuable substances from electronic waste [13], and the construction of dampers used in fields ranging from aerospace engineering to architecture [14]. Vibrated granular media also provide valuable canonical systems in which the collisional interactions between particles may be studied on a fundamental level. More recently, these systems have been used to provide easily studied analogues to microscale, nanoscale and even biological systems [15, 16]. These nascent applications hold much promise for future study in a number of diverse fields. © 2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft New J. Phys. 18 (2016) 033005 C R K Windows-Yule However, before the potential of any of the above applications can be fully achieved, there remains much work to be done understanding vibrated granular materials on a fundamental level. Despite the utility and versatility of vibrofluidised granular systems, they remain, on the whole, poorly understood and under- researched as compared to classical, molecular systems. In particular, it is notable that in the vast majority of prior studies, vibration is applied only in one direction; while the application of (mono-directional) vertical and (mono-directional) horizontal vibration has been extensively researched, there exist only a handful of studies in which the effects of two- [17] or three-dimensional [18–21] vibrational excitation are explored. Moreover, these studies deal exclusively with highly dense, weakly excited systems. To the best of the author’s knowledge, there exist no studies investigating the effects of multi-directional driving on more energetic liquid- or gas-like systems. This is surprising as, unlike in molecular systems, the dissipative nature of granular liquids and gases means that the exact manner of energy input may carry numerous consequences [22–24] which are not apparent in classical fluids. In other words, by neglecting the case of strong, multi-directional driving, it is highly probable that the community has thus far overlooked the existence of potentially interesting phenomena unique to these systems. In this paper, we take a first step towards understanding the effects of multi-dimensional driving in the case of energetic, highly fluidised granulates. Specifically, we study a simulated system driven in two spatial dimensions by four oscillating sidewalls. In doing so, we demonstrate numerous novel system states, phase transitions and dynamical behaviours unobserved in unilaterally driven systems and undocumented in the existing literature. We focus in particular on two phenomena of particular relevance to ‘real-world’ systems— granular convection [25, 26] and granular segregation [9, 27]. We present phase diagrams showing the diverse phenomena and physical states exhibited over a wide range of parameter space for both single-component systems and binary mixtures. We demonstrate that the application of multi-dimensional driving allows the state and behaviour of a system to be deliberately manipulated in various manners, of which many are not possible using only a single vibration direction. Nonetheless, our results also provide insight into the convective and segregative behaviours observed in these more conventional systems, in particular the interactions and competition between the various segregation mechanisms present in vibrated beds. The paper is ordered as follows: in the remainder of this section, we provide an introduction to the three topics which form the main focus of our work: granular convection (section 1.1), granular segregation (section 1.2), and the phase behaviour of the systems studied (section 1.3). We then provide details of the simulations from which our data are acquired (section 2) before detailing and analysing our results (section 3). Finally, in section 4 we summarise our major findings and conclusions. 1.1. Sidewall-driven convection The convective motion observed within granular systems can be broadly categorised into two main types: frictionally driven convection [25, 26] in dense systems where contacts are enduring and frictional forces dominate the system’s behaviour, and ‘thermal’ or ‘buoyancy-driven’ convection [28, 29] in systems where collisional interactions predominate. While frictionally driven convection is typically strongly coupled to the specific motion of the vibrating base [30], for thermally convective systems, the vibrating walls can be considered simply as an energy source—thus allowing a much closer analogy to thermodynamic systems. Indeed, it has been shown that thermal convection can be reproduced in simulations [29] and hydrodynamic models [31] where vibrating walls are replaced by a static energy source. Since our current interest lies predominantly in the behaviours of energetic, fluid-like systems we will focus our discussion primarily on thermal convection. Thermal convection is so named due to its dependence on the granular analogue to temperature, Tg, which is related to the fluctuation of particle velocities about a mean value [32]—a greater fluctuating kinetic energy is 1 2 equivalent to a higher ‘granular temperature ’. The granular temperature is defined as Tmvvg0=á-() ñ, where m is the average mass of a particle, (vv- 0) gives the deviation of a given particle velocity, v, from the mean value, v0, and the brackets áñrepresent an ensemble average over all particles within a given volume. Due to the fact that granular materials are inherently dissipative, a granular assembly driven by a single, vertically
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