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Focus on Imaging Methods in Granular Physics Axelle Amon,1 Philip Born,2 Karen E

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Focus on Imaging Methods in Granular Physics Axelle Amon,1 Philip Born,2 Karen E Focus on Imaging Methods in Granular Physics Axelle Amon,1 Philip Born,2 Karen E. Daniels,3 Joshua A. Dijksman,4 Kai Huang,5 David Parker,6 Matthias Schr¨oter,7 Ralf Stannarius,8 and Andreas Wierschem9 1)Institut de Physique de Rennes, UMR UR1-CNRS 6251, Universit´ede Rennes 1, 35042 Rennes, France 2)Institut f¨urMaterialphysik im Weltraum, Deutsches Zentrum f¨urLuft- und Raumfahrt, 51170 Cologne, Germany 3)Department of Physics, North Carolina State University, Raleigh, NC, 27695 USA 4)Physical Chemistry and Soft Matter, Wageningen University & Research, Wageningen, The Netherlands 5)Experimentalphysik V, Universit¨atBayreuth, 95440 Bayreuth, Germany 6)School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK 7)Institute for Multiscale Simulation, Friedrich-Alexander-Universit¨atErlangen-N¨urnberg (FAU), 91052 Erlangen, Germany. 8)Institut f¨urExperimentelle Physik, Otto-von-Guericke-Universit¨at,39106 Magdeburg, Germany 9)Institute of Fluid Mechanics, Friedrich-Alexander-Universit¨atErlangen-N¨urnberg (FAU), 91058 Erlangen, Germany (Dated: 10 April 2017) Granular materials are complex multi-particle ensembles in which macroscopic properties are largely determined by inter-particle interactions between their numerous constituents. In order to understand and to predict their macroscopic physical behavior, it is necessary to analyze the composition and interactions at the level of individual contacts and grains. To do so requires the ability to image individual particles and their local configurations to high precision. A variety of complementary imaging techniques have been developed for that task. In this introductory paper accompanying the Focus Issue, we provide an overview of these imaging methods and discuss their advantages and drawbacks, as well as their limits of application. I. CURRENT CHALLENGES stress is governed by force chains14. Those force chains sensitively depend on the individual contacts between 15,16 To see a world in a grain of sand, the grains, and the history of loading those contacts . and a heaven in a wild flower. Consequently, local properties of the contacts, such as their typical orientation or the nature of the frictional The poem Auguries of Innocence by William Blake contacts, can modify the mechanical behavior of the sys- illustrates one of the complexities of granular physics: tem. For example, anisotropy in the orientation of those 1 Each grain of sand is unique and the entirety of particle- contacts17, arising due to shear, can have a major impact 2 particle interactions in a sand pile is unpredictable . on the macroscopic response. While walking on a beach, one intermittently experiences On an intermediate scale between the the size of the the transition between a rigid, solid-like state and a fluid- grains and the sample as a whole, it has been shown that like state. One leaves behind the stress loading history the non-affine motion of the system, at the scale of clus- in the form of footprints3,4. Stepping into the water, one ters of typically ten grains, plays a non-negligible role in recognizes the sediments are looser in comparison to the the mechanical response of the system18. This non-affine partially wet sand on the beach and susceptible to the motion seems to control numerous features of amorphous surrounding fluid flow, leading to sand ripples5. materials such as the thickness of shear bands19 or the Continuum descriptions based on empirical as- eddy-like structures in dense flows18. Several nonlocal ef- sumptions can successfully describe rapid flows and arXiv:1703.02928v2 [physics.ins-det] 7 Apr 2017 fects have been observed, particularly in confined flows. sufficiently-dilute granular gases6{8. However, continuum For example, it has been demonstrated that shear bands approaches fail to describe slow dense flows or critical be- generate mechanical noise even deep into the seemingly- havior such as intermittent flows, jamming and pattern static phase20,21. formation9,10. These systems are governed by phenom- ena which are hard to model in continuum descriptions: Therefore, it is of paramount importance for a descrip- strong dissipation at the contacts between the grains due tion of granular matter to be able to make observations to friction11, inelastic deformation12, and cohesion13, etc. on many length scales: from the grain or contact scale, Moreover, the athermal nature of the system does not al- through the mesoscopic effects such as nonlocality and low for the use of statistical physics to connect the micro- shear banding which appear on the ∼ 10 grain scale, scale to the macro-scale. even up to the scale of a full sample that may contain One of the major issues in modeling granular materials billions of grains. arises from the fact that what happens at the scale of a At the grain scale, there are two generic issues making single grain can impact the response of the whole mate- it difficult to extract data with any imaging technique. rial. In static piles and dense flows, the distribution of First, our most advanced imaging technologies have been 2 developed to act as extensions for our eyes, which op- acts at the level of the contacts between the grains. erate in the visible spectrum. However, most granular This overview article, as well as the following focus is- materials are opaque in this range of wavelengths. Even sue on imaging granular particles, aims to provide guid- if the particles were transparent, their refractive index ance and orientation concerning the experimental tech- would not generically match that of the most common niques which help to face all these challenges. interstitial fluids (air or water), leading to multiple scat- tering. Second, a large volume of raw data is required to analyze a complete granular system: even just a simple II. ACQUIRING PARTICLE POSITIONS, sugar cube contains on the order of 105 individual grains. ORIENTATIONS, & SHAPES To identify the center of mass and orientation of each of these grains, it is necessary to identify its spatial extent To acquire particle positions, orientations and shapes, using several thousand voxels (3D pixels). As a conse- a two-step process is necessary. First, an image is made quence, several gigabytes of data need to be collected of a particle and its immediate surroundings. Second, the to analyze a single static packing of grains. Moreover, required particle information is extracted through data trying to describe any kind of dynamics will compound analysis of those images. For both steps, there are multi- the problem by requiring a sufficiently high frame rate to ple methods to chose from; in this Focus Issue, we discuss collect that data. both steps in some detail. There are a number of ways to address opacity issue, To image a particle, some contrast between the parti- even with visible light. A common technique is to per- cle and their surrounding medium is required. The most form quasi-two-dimensional (Q2D) experiments, allow- obvious method to detect particles is to use the visible ing for the complete tracking of particle positions22,23 part of the electromagnetic spectrum. In this range, it as well as the particle-particle interactions24. Another suffices to use standard cameras to obtain digital images option is to restrict the data collection to the surface of a collection of particles. The only difference between of the granular system, with the disadvantage that bulk 2D and 3D imaging is whether each configuration is rep- properties can differ significantly from the behavior at resented as a single 2D image or as a stack 2D slices. Due the surface25{30. If the volume fraction of the particles to both absorption and scatter, however, the visible spec- is sufficiently low, stereo-camera or volumetric methods trum has limited penetration into most materials. Since can be used to capture three-dimensional (3D) dynam- the time of the first packing experiments by Bernal45, ics31{33. If the particles are optically-transparent, there one solution has been to create 3D images by physically exist two additional options. Where the interstitial liquid disassembling the packing and taking an image at each can be chosen freely, index matching provides a means step. This method is still used in the present day for for to acquire 3D data34. Alternatively, it is possible to em- sufficiently slow flows46. brace the multiple scattering effects, and use coherent To avoid such destructive methods, and considerably light to gather information from the resulting speckle pat- improve the data collection rate, modern experiments tern35. Finally, we can abandon the range of visible light commonly use transparent granular media. For optical entirely, and instead use penetrating radiation to obtain transmission through a pile of transparent glass marbles, data from the bulk of the sample. A variety of such meth- however, scatter remains a significant limitation in go- ods are extensively covered in this focus edition, covering ing deeper than a few particles inward from the bound- terahertz electromagnetic radiation36, radar37, positron ary. The solution is to reduce the scatter by immersing emission38, nuclear magnetic resonance39, and X-ray to- the solid particles in an index-matched medium. To ob- mography40. tain the necessary image contrast, at least one of the two Several solutions also exist for the data-bandwidth is- phases must be stained with a fluorescent dye. Thus, by sue, which are common to the various methods. Limiting illuminating a cross section of the medium with a sheet the analysis to 2D or the surface of a 3D system is an of light (usually via a laser), the fluorescent response of effective way to decrease the number of particles under the dyed material within the sheet is captured by the analysis, at the expense of ignoring the bulk behavior. camera. By moving the light sheet with respect to the To access the bulk, it is possible to restrict the analysis sample and recording a series of slices, a 3D image of the to quasi-static systems in which the driving is stopped medium can be created.
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