X-ray Imaging Study Of Dynamic Properties Of Three-dimensional Granular System

Granular materials are ubiquitous in daily life,industry and geotechnical applications.Granular materials can present different states(gas,liquid or solid)under external perturbation such as tapping or shear.These disordered systems form stable structures when unperturbed,but in the presence of external influences they ‘relax',becoming fluid in nature.However,they behave quite differently from traditional continuous medium such as elastic solids and simple liquids.This is since granular materials are by nature many-body systems that out of equilibrium because of the inelastic collisions and nonlinear friction between the particles.Despite the great need for an accurate theoretical description of granular materials for engineering and geotechnical applications,so far there are only empirical macroscopic descriptions of these materials,which lack the descriptions of the microscopic mechanism and cannot work well all the time.It is of fundamental importance to develop a new continuum theory for granular materials starting from the microscopic structure and dynamics.Granular materials usually are optically opaque,therefore,there are huge technical challenges to experimentally determine the dynamic properties of three-dimensional granular systems at particle level.Compared with magnetic resonance imaging or refraction index match imaging,X-ray computed tomography(CT)can record the 3D inner structure of granular systems with high spatial and temporal resolution.In this thesis,to invesitgate the microscopic dynamics of granular materials,we use the CT technique to acquire the positions and orientations of hard ellipsoid particles that are subject to an oscillatory shear in a cell.At the first time,we get the translational and rotational trajectories of all particles in three decades on timescale through algorithms of CT imaging processing and particle tracking.We find that the distribution of the displacements of the ellipsoids is well described by a so-called “Gumbel law"(which is similar to a Gaussian distribution for small displacements but has a heavier tail for larger displacements),with a shape parameter independent of the amplitude of the shear strain and of the time.Despite this universality,the mean squared displacement of an individual ellipsoid does not exhibit the cage effect—the mechanism that slows the dynamics in glass-forming systems,whereby particles are temporarily trapped by their nearest neighbors.Instead,this mean squared displacement follows a power law as a function of time,with an exponent depending on the strain amplitude and time.We assume that these results are related to the presence of two relaxation mechanisms on different length scales—the length scales of surface roughness and of particle size.Meanwhile,dynamical heterogeneities(DH)in translational and rotational degree of freedom are investigated in this system as well.We find that particles translating quickly form the clusters with a size distribution given by a power law with an exponent,which is independent of the strain amplitude.Identical behavior is found for particles that are translating slowly,rotating quickly or rotating slowly,indicating that the dynamics is system universal,in qualitative agreement with the findings about the van Hove function.The geometrical properties of these four different types of clusters are the same as those of random clusters.Surprisingly,these clusters are formed already at time scales that are much shorter than the ?-relaxation time,in stark contrast to the behavior found in glass-forming systems.It shows that the energy landscape of granular materials has a structure that is very different from the one of thermal glass-formers,since the former has a roughness on a length scale which is much smaller than the size of the particles.It can be expected that it is this particle inherent disorder that gives rise to the DH,in contrast to the case of thermal systems,in which the variations of the local packing are the cause for the DH.Different cluster types are considerably correlated/ anti-correlated,indicating a significant coupling between translational and rotational degrees of freedom.Our experiments demonstrate that the relaxation dynamics of such "frictional" systems is qualitatively different from that of "thermal" systems and that granular materials are "marginal solids",i.e.stable if unperturbed but fluid under the slightest external perturbation.The mechanism that leads to this behavior is very general which indicates that these frictional out-of-equilibrium systems obey a new class of microscopic dynamics and therefore a new continuum theory for granular materials should be developed.