A foam is not a homogeneous material, but consists of a large number of small air bubbles. The whole is more than the sum of its parts: even though the behavior of a single bubble is easy... Show more A foam is not a homogeneous material, but consists of a large number of small air bubbles. The whole is more than the sum of its parts: even though the behavior of a single bubble is easy to understand, their collective behavior is much more complicated and completely different. The reason for this is that a deformation of the whole is only reflected partially in the deformation of individual bubbles. Instead, a large part of the deformation is reflected in a change in the structure of the foam. In this thesis, we investigate this change in structure. In the first part of this thesis, we use a simple microscopic computer model to simulate the response of a foam when it is deformed by a tiny amount, and measure how far we need to deform the foam until it is irreversibly deformed. In the second part of this thesis, we focus on an experiment, where we measure the response of a two-dimensional foam when it is deformed at the edges. We observe that the response of bubbles in the center of the foam qualitatively depends on how densely the bubbles are packed together. Show less
When soft, repulsive particles, like foam bubbles or emulsion droplets, are sheared, they show interesting scaling behaviour. We develop a simple scaling model that captures the rheological... Show moreWhen soft, repulsive particles, like foam bubbles or emulsion droplets, are sheared, they show interesting scaling behaviour. We develop a simple scaling model that captures the rheological behavior starting from three assumptions that explicitly depend on the microscopic interactions. This model starts from three ingredients: energy conservation, the concept of an effective steady state strain in our flowing system and a constitutive elasticity equation linking the effective strain to the shear stress. Our model allows for non-linear microscopic particle interactions and it predicts that the global rheological behaviour depends on the details of the microscopic interactions between the particles - in contrast to standard critical scaling theory. We test our model in computer simulations of soft, massless particles under steady shear and find that the numerics are broadly consistent with our model. jamming, rheology, foam, critical scaling Show less
Many materials, like foams, emulsions, suspensions and granular media obtain finite rigidity once their constituent particles are brought in contact. Nevertheless, all these materials can be made... Show moreMany materials, like foams, emulsions, suspensions and granular media obtain finite rigidity once their constituent particles are brought in contact. Nevertheless, all these materials can be made to flow by the application of relatively small stresses. By varying thermodynamic (temperature or density) and mechanical (applied stress) variables, one can bring about a transition from a freely flowing to a jammed state. What is the elastic response of foams close to the jamming point? How much can these materials be loaded before they flow? What is their behavior like in the bulk? These problems are of great interest in academics, as well as industrial applications (oil/gas extraction, cosmetics, pharmaceuticals and food processes). I study the transition from the flowing to the non-flowing regime in foams and analyze the non-affine behavior at this critical point. Additionally, whereas the usual rheological approach is to study the shear, I have developed a technique to measure compressive response in a real-world, foam system, taking gravity and temperature fluctuations into account. Show less
This thesis concerns the vibrational properties of different classical disordered condensed matter systems. In the first part we focus on materials that exhibit a rigidity transition as their... Show moreThis thesis concerns the vibrational properties of different classical disordered condensed matter systems. In the first part we focus on materials that exhibit a rigidity transition as their density is increased. By introducing a new method into the field, we were able to look into the localization behavior of vibrational modes of jammed packings of soft spherical particles, both in the localized regime where the localization length is much less and in the regime where it is grater than the linear system size. We also analyze the nature of vibrational modes of jammed packings of soft elliptical particles, where we uncover the change of the structure of the spectrum, compared to the simplest model of sphere packings, due to the rotational degrees of freedom of the particles. In the second part of this thesis we explore the localization properties of collective modes and response to uniform driving of bubble clouds. We find that the response is often very different from that of a typical mode because the frequency response of each mode is sufficiently wide that many modes are excited when the cloud is driven by an ultrasound. Show less
We study the shear flow of two-dimensional foams, i.e., a monolayer of bubbles floating on a soapy solution. We successfully connect local and global flow behaviour
Many disordered materials display a so-called jamming transition between solid-like and fluid-like states. In this thesis, we investigate jamming in granular media by studying granular packings at... Show moreMany disordered materials display a so-called jamming transition between solid-like and fluid-like states. In this thesis, we investigate jamming in granular media by studying granular packings at various distances from the transition. In numerical model systems of spherical particles, the jamming transition has many features of a critical transition. Using the linear response of such packings to external perturbations, we shed new light on their critical behavior. We analyze various scaling relations in terms of the non-affine deformations of the packing, and identify a diverging length scale that determines beyond what scale these systems can be treated as a continuum. This length scale and various other properties are determined primarily by the number of contacts between grains in the system. In the second half of the thesis we investigate force networks in granular media using the recently developed Force Network Ensemble. We discuss the analytical properties of the ensemble, and apply it to study granular media under shear stress, identifying upper bounds on the shear stress that cohesionless granular media can sustain. Show less
