This work discusses the flow of granular materials (e.g. sand). Even though a single particle is a simple object, the collective behavior of billions of particles can be very complex. In a... Show moreThis work discusses the flow of granular materials (e.g. sand). Even though a single particle is a simple object, the collective behavior of billions of particles can be very complex. In a surprisingly large amount of cases, it is not exactly known how a granular material behaves, and this while these kinds of materials are omnipresent in everyday life, industry, and nature Similar to materials such as water, which can occur as ice, liquid water and vapor, sand can also exist in different phases of matter. If you for instance walk on the beach, sand behaves like a solid, but if you pour it out of your shoes afterwards, it flows like a liquid. This thesis is dedicated to experiments where we investigate what happens when you try to "liquefy" sand by weakly vibrating it. We use an experimental setup which enables us to study how much stress is required to make sand flow, depending on the desired flow rate and the amount of vibrations. These experiments reveal several physical principles that turn out to be important towards understanding the unique behavior of these kinds of materials Show less
In this thesis, we study energy transport and fluctuations in simple models of fragile matter : a unique state of matter that has a vanishingly small window of linear response since one or both of... Show moreIn this thesis, we study energy transport and fluctuations in simple models of fragile matter : a unique state of matter that has a vanishingly small window of linear response since one or both of its elastic moduli (shear and bulk) are nearly zero. As a consequence, even the tiniest perturbations travel as nonlinear waves. In addition, most models of fragile matter have an amorphous structure. It is the interaction of the non-linear waves with the underlying disorder and the resulting fluctuations, that constitutes the unifying theme explored in this thesis. There are at least two seemingly distinct sources of fragility: a local source stemming from the strongly non-linear interaction potential between particles so that one can not expand around a potential minimum to define a spring constant, and a second, global source, whereby the collective response of the sample can be considered weakly linear. As a model of the first kind, we consider a two dimensional packing of soft frictionless elastic disks that are just touching their nearest neighbours. The interaction potential between elastic disks is given by the nonlinear Hertz law that has no harmonic part. Consequently, for a packing in this state, the bulk modulus is vanishingly small and the smallest compressions imparted at the edges leads to nonlinear solitary like waves. As a model of the second kind, we consider a two dimensional random network of harmonic springs where each node has on average around four nearest neighbours. Here, despite the contact interaction being harmonic, the network has a vanishingly small shear modulus. Consequently, even the tiniest shear strains elicit non-linear waves. There are many important similarities and differences between the nature of non-linear waves and the role played by disorder in the two models described above, which we are gradually beginning to understand. Show less
This thesis explores how rheology and statistical mechanics can be used to describe driven granular materials. Chapter 1 is an overview of the current knowledge of slow granular flows. In Chapter 2... Show moreThis thesis explores how rheology and statistical mechanics can be used to describe driven granular materials. Chapter 1 is an overview of the current knowledge of slow granular flows. In Chapter 2 we characterize the liquid-like behaviour of a granular system excited by flow in a split-bottom geometry. In Chapter 3 we describe the fluctuations experienced by an object floating in our granular liquid and compare these fluctuations to the Brownian motion of particles in a thermal system. In Chapter 4 we characterize the motion of objects moving in a granular system excited by oscillatory flow. Finally, in Chapter 5, we describe both the microscopic and macroscopic motion of pucks on an air hockey table. We find the the system exhibits equipartition of rotational and translational energy and that the system can be described by van der Waals' equation of state. Show less
