FINAL REPORT FOR DE-FG02-03ER46071 ENTITLED, "UNDERSTANDING FOAM RHEOLOGY FROM THE MICROSCOPIC TO THE MACROSCOPIC SCALE"

This research effort is focused on understanding the mechanical response of foams, and other complex fluids, from the microscopic to the macroscopic level. The research uses a model two-dimensional system: bubble rafts. Bubble rafts are a single layer of gas bubbles with liquid walls that float on a water surface. The work involves studies of the macroscopic response of foam under various conditions of external forcing, mesoscopic studies of bubble motion, and systematic variations of the microscopic details of the system. In addition to characterizing the specific properties of the bubble raft, a second aim of the research is to provide experimental tests of various general theories that have recently been developed to characterize complex fluids. Primarily, the focus is on testing the proposed jamming phase diagram paradigm. This paradigm suggests that a general âjammedâ state of matter exists and is common to a wide range of systems, including foam, colloids, granular matter, glasses, and emulsions. Therefore,we have extended our research in two directions. First, we have included studies of plastic bead rafts. These are systems of plastic beads floating on the air-water interface. The advantage of plastic beads is that they do not pop, so they can be studied for the much longer periods of time required to measure the slow dynamics associated with the jammed state. Also, they allow us to explore a different density regime than the bubbles. Second, to better understand the role of defects in jamming behavior, we have done a few experiments on the impact of defects on domain growth

Viscoelastic shear banding in foam

Shear banding is an important feature of flow in complex fluids. Essentially, shear bands refer to the coexistence of flowing and non-flowing regions in driven material. Understanding the possible sources of shear banding has important implications for a wide range of flow applications. In this regard, quasi-two dimensional flow offers a unique opportunity to study competing factors that result in shear bands. One proposal is the competition between intrinsic dissipation and an external source of dissipation. In this paper, we report on the experimental observation of the transition between different classes of shear-bands that have been predicted to exist in cylindrical geometry as the result of this competition [R. J. Clancy, E. Janiaud, D. Weaire, and S. Hutzlet, Eur. J. Phys. E, {\bf 21}, 123 (2006)]

Impact of boundaries on velocity profiles in bubble rafts

Under conditions of sufficiently slow flow, foams, colloids, granular matter, and various pastes have been observed to exhibit shear localization, i.e. regions of flow coexisting with regions of solid-like behavior. The details of such shear localization can vary depending on the system being studied. A number of the systems of interest are confined so as to be quasi-two dimensional, and an important issue in these systems is the role of the confining boundaries. For foams, three basic systems have been studied with very different boundary conditions: Hele-Shaw cells (bubbles confined between two solid plates); bubble rafts (a single layer of bubbles freely floating on a surface of water); and confined bubble rafts (bubbles confined between the surface of water below and a glass plate on top). Often, it is assumed that the impact of the boundaries is not significant in the ``quasi-static limit'', i.e. when externally imposed rates of strain are sufficiently smaller than internal kinematic relaxation times. In this paper, we directly test this assumption for rates of strain ranging from $10^{-3}$ to $10^{-2} {\rm s^{-1}}$. This corresponds to the quoted quasi-static limit in a number of previous experiments. It is found that the top plate dramatically alters both the velocity profile and the distribution of nonlinear rearrangements, even at these slow rates of strain.Comment: New figures added, revised version accepted for publication in Phys. Rev.

Flow transitions in two-dimensional foams

For sufficiently slow rates of strain, flowing foam can exhibit inhomogeneous flows. The nature of these flows is an area of active study in both two-dimensional model foams and three dimensional foam. Recent work in three-dimensional foam has identified three distinct regimes of flow [S. Rodts, J. C. Baudez, and P. Coussot, Europhys. Lett. {\bf 69}, 636 (2005)]. Two of these regimes are identified with continuum behavior (full flow and shear-banding), and the third regime is identified as a discrete regime exhibiting extreme localization. In this paper, the discrete regime is studied in more detail using a model two dimensional foam: a bubble raft. We characterize the behavior of the bubble raft subjected to a constant rate of strain as a function of time, system size, and applied rate of strain. We observe localized flow that is consistent with the coexistence of a power-law fluid with rigid body rotation. As a function of applied rate of strain, there is a transition from a continuum description of the flow to discrete flow when the thickness of the flow region is approximately 10 bubbles. This occurs at an applied rotation rate of approximately $0.07 {\rm s^{-1}}$