Michael Dennin

Shear-induced stress relaxation in a two-dimensional wet foam.

We report on experimental measurements of the flow behavior of a wet, two-dimensional foam under conditions of slow, steady shear. The initial response of the foam is elastic. Above the yield strain, the foam begins to flow. The flow consists of irregular intervals of elastic stretch followed by sudden reductions of the stress, i.e., stress drops. We report on the distribution of the stress drops as a function of the applied shear rate. We also comment on our results in the context of various two-dimensional models of foams.

Folding Langmuir monolayers.

The maximum pressure a two-dimensional surfactant monolayer is able to withstand is limited by the collapse instability towards formation of three-dimensional material. We propose a new description for reversible collapse based on a mathematical analogy between the formation of folds in surfactant monolayers and the formation of Griffith Cracks in solid plates under stress. The description, which is tested in a combined microscopy and rheology study of the collapse of a single-phase Langmuir monolayer (LM) of 2-hydroxy-tetracosanoic acid (2-OH TCA), provides a connection between the in-plane rheology of LMs and reversible folding.

Velocity profiles in slowly sheared bubble rafts

Measurements of average velocity profiles in a bubble raft subjected to slow, steady shear demonstrate the coexistence between a flowing state and a jammed state similar to that observed for three-dimensional foams and emulsions [P. Coussot et al., Phys. Rev. Lett. 88, 218301 (2002)]. For sufficiently slow shear, the flow is generated by nonlinear topological rearrangements. We report on the connection between this short-time motion of the bubbles and the long-time averages. We find that velocity profiles for individual rearrangement events fluctuate, but a smooth, average velocity is reached after averaging over only a relatively few events.

Spatiotemporal Chaos in Electroconvection

Spatiotemporal chaos (STC) near the onset of electroconvection in a nematic liquid crystal is reported. In samples with conductivities greater than 1 × 10−8 per ohm per meter, STC was found to evolve by means of a supercritical Hopf bifurcation from the uniform conduction state. Because this example of STC resulted from nonlinear interactions between only four modes, it provides a realistic opportunity to understand the observed phenomena in terms of a weakly nonlinear theory in the form of four coupled complex Ginzburg-Landau equations derived from the full equations of motion of the system. For smaller conductivities, the pattern immediately above onset consisted of localized pulses of convection that coexisted with the conduction state. The pulses had a unique width in the direction perpendicular to the director (the axis parallel to the average orientation) and had much larger and varying lengths parallel to the director.

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. 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 ten bubbles. This occurs at an applied rotation rate of approximately 0.07 s-1.

Reversible Plastic Events in Amorphous Materials

For crystalline materials, the microscopic origin of plasticity is well understood in terms of the dynamics of topological defects. For amorphous materials, the underlying structural disorder prevents such a description. Therefore identifying and characterizing the microscopic plastic events in amorphous materials remains an important challenge. We show direct evidence for the coexistence of reversible and irreversible plastic events (T1 events) at the microscopic scale in both experiments and simulations of two-dimensional foam. In the simulations, we also demonstrate a link between the reversibility of T1 events and pathways in the potential energy landscape of the system.

Nonlinear stress and fluctuation dynamics of sheared disordered wet foam

A sheared wet foam, which stores elastic energy in bubble deformations, relaxes stress through bubble rearrangements. The intermittency of bubble rearrangements in the foam leads to effectively stochastic drops in stress that are followed by periods of elastic increase. We investigate global characteristics of highly disordered foams over three decades of strain rate and almost two decades of system size. We characterize the behavior using a range of measures: average stress, distribution of stress drops, rate of stress drops, and a normalized fluctuation intensity. There is essentially no dependence on system size. As a function of strain rate, there is a change in behavior around shear rates of 0.07 s(-1).

Effect of subphase Ca++ ions on the viscoelastic properties of Langmuir monolayers

It is known that the presence of cations like Ca++ or Pb++ in the water subphase alters the pressure-area isotherms for fatty acid monolayers. The corresponding lattice constant changes have been studied using x-ray diffraction. Reflection-absorption spectroscopy has been used to probe the chemical composition of the film. We report on the first measurements of the time evolution of the shear viscosity of arachidic acid monolayers in the presence of Ca++ ions in the subphase. We find that the introduction of Ca++ ions to the water subphase results in an increase of the film’s viscosity by at least three orders of magnitude. This increase occurs in three distinct stages. First, there is a rapid change in the viscosity of up to one order of magnitude. This is followed by two periods, with very different time constants, of a relatively slow increase in the viscosity over the next 10 or more hours. The corresponding time constants for this rise decrease as either the subphase pH or Ca++ concentration is incre...

A two-dimensional Couette viscometer for Langmuir monolayers

We have developed an apparatus that is capable of simultaneously measuring the viscosity of Langmuir monolayers and visualizing their flow. It consists of a circular trough with a nearly circular elastic barrier that can be rotated to generate two-dimensional Couette flow. The “inner cylinder” is a Teflon knife-edge disk that is hung by a thin wire. The torque on the inner cylinder is determined by measuring the angular displacement of the disk. A stepper motor controls the barrier rotation. Viscosity can be measured in two different ways: by oscillating the torsion pendulum and by generating Couette flow. The dynamic viscosity range of the apparatus is 10−4<η<103 g/s. Typical shear rates range from 10−4 to 101 s−1. A Brewster angle microscope is mounted on the apparatus. This is used to study various properties of the monolayer such as: velocity profiles, domain shape during shear, domain relaxation after shear, and size distribution of domains.

Rheology of two-dimensional F-actin networks associated with a lipid interface

We report on the surface rheology of cross-linked F-actin networks associated with a lipid monolayer at the air-water interface of a Langmuir monolayer. The rheological measurements are made using a Couette cell. These data demonstrate that the network has a finite elastic modulus that grows as a function of the cross-linking concentration. We also note that under steady-state flow the system behaves as a power-law fluid in which the effective viscosity decreases with imposed shear.