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 $0.07 {\rm s^{-1}}$

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)]

A compact 90 kilowatt electric heat source for heating inert gases to 1700 F

Design and fabrication of compact electric heat source for heating inert gase

The electrorheology of suspensions consisting of Na-Fluorohectorite synthetic clay particles in silicon oil

Under application of an electric field greater than a triggering electric field $E_c \sim 0.4$ kV/mm, suspensions obtained by dispersing particles of the synthetic clay fluoro-hectorite in a silicon oil, aggregate into chain- and/or column-like structures parallel to the applied electric field. This micro-structuring results in a transition in the suspensions' rheological behavior, from a Newtonian-like behavior to a shear-thinning rheology with a significant yield stress. This behavior is studied as a function of particle volume fraction and strength of the applied electric field, $E$. The steady shear flow curves are observed to scale onto a master curve with respect to $E$, in a manner similar to what was recently found for suspensions of laponite clay [42]. In the case of Na-fluorohectorite, the corresponding dynamic yield stress is demonstrated to scale with respect to $E$ as a power law with an exponent $\alpha \sim 1.93$, while the static yield stress inferred from constant shear stress tests exhibits a similar behavior with $\alpha \sim 1.58$. The suspensions are also studied in the framework of thixotropic fluids: the bifurcation in the rheology behavior when letting the system flow and evolve under a constant applied shear stress is characterized, and a bifurcation yield stress, estimated as the applied shear stress at which viscosity bifurcation occurs, is measured to scale as $E^\alpha$ with $\alpha \sim 0.5$ to 0.6. All measured yield stresses increase with the particle fraction $\Phi$ of the suspension. For the static yield stress, a scaling law $\Phi^\beta$, with $\beta = 0.54$, is found. The results are found to be reasonably consistent with each other. Their similarities with-, and discrepancies to- results obtained on laponite-oil suspensions are discussed

Statistics of Bubble Rearrangements in a Slowly Sheared Two-dimensional Foam

Many physical systems exhibit plastic flow when subjected to slow steady shear. A unified picture of plastic flow is still lacking; however, there is an emerging theoretical understanding of such flows based on irreversible motions of the constituent ``particles'' of the material. Depending on the specific system, various irreversible events have been studied, such as T1 events in foam and shear transformation zones (STZ's) in amorphous solids. This paper presents an experimental study of the T1 events in a model, two-dimensional foam: bubble rafts. In particular, I report on the connection between the distribution of T1 events and the behavior of the average stress and average velocity profiles during both the initial elastic response of the bubble raft and the subsequent plastic flow at sufficiently high strains

Interplay of internal stresses, electric stresses and surface diffusion in polymer films

We investigate two destabilization mechanisms for elastic polymer films and put them into a general framework: first, instabilities due to in-plane stress and second due to an externally applied electric field normal to the film's free surface. As shown recently, polymer films are often stressed due to out-of-equilibrium fabrication processes as e.g. spin coating. Via an Asaro-Tiller-Grinfeld mechanism as known from solids, the system can decrease its energy by undulating its surface by surface diffusion of polymers and thereby relaxing stresses. On the other hand, application of an electric field is widely used experimentally to structure thin films: when the electric Maxwell surface stress overcomes surface tension and elastic restoring forces, the system undulates with a wavelength determined by the film thickness. We develop a theory taking into account both mechanisms simultaneously and discuss their interplay and the effects of the boundary conditions both at the substrate and the free surface.Comment: 14 pages, 7 figures, 1 tabl

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 [Coussot {\it et al,}, Phys. Rev. Lett. {\bf 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.Comment: typos corrected, figures revised for clarit

Vortex jamming in superconductors and granular rheology

We demonstrate that a highly frustrated anisotropic Josephson junction array(JJA) on a square lattice exhibits a zero-temperature jamming transition, which shares much in common with those in granular systems. Anisotropy of the Josephson couplings along the horizontal and vertical directions plays roles similar to normal load or density in granular systems. We studied numerically static and dynamic response of the system against shear, i. e. injection of external electric current at zero temperature. Current-voltage curves at various strength of the anisotropy exhibit universal scaling features around the jamming point much as do the flow curves in granular rheology, shear-stress vs shear-rate. It turns out that at zero temperature the jamming transition occurs right at the isotropic coupling and anisotropic JJA behaves as an exotic fragile vortex matter : it behaves as superconductor (vortex glass) into one direction while normal conductor (vortex liquid) into the other direction even at zero temperature. Furthermore we find a variant of the theoretical model for the anisotropic JJA quantitatively reproduces universal master flow-curves of the granular systems. Our results suggest an unexpected common paradigm stretching over seemingly unrelated fields - the rheology of soft materials and superconductivity.Comment: 10 pages, 5 figures. To appear in New Journal of Physic

How Dilute are Dilute Solutions in Extensional Flows?

Submitted to J. Rheol.We investigate the concentration-dependence of the characteristic relaxation time of dilute polymer solutions in transient uniaxial elongational flow. A series of monodisperse polystyrene solutions of five different molecular weights (1.8×10^6 ≤ M ≤ 8.3×10^6 g/mol) with concentrations spanning five orders of magnitude were dissolved in two solvents of differing solvent quality (diethyl phthalate and oligomeric styrene). Optical measurements of the rate of filament thinning and the time to break-up in each fluid are used to determine the characteristic relaxation time. A lower sensitivity limit for the measurements was determined experimentally and confirmed by comparison to numerical calculations. Above this sensitivity limit we show that the effective relaxation time of moderately dilute solutions (0.01 ≤ c/c* ≤ 1) in transient extensional flow rises substantially above the fitted value of the relaxation time extracted from small amplitude oscillatory shear flow and above the Zimm relaxation time computed from kinetic theory and intrinsic viscosity measurements. This effective relaxation time exhibits a power-law scaling with the reduced concentration (c/c*) and the magnitude of the exponent varies with the thermodynamic quality of the solvent. This scaling appears to be roughly consistent to that predicted when the dynamics of the partially elongated and overlapping polymer chains are described within the framework of blob theories for semi-dilute solutions.NASA Microgravity Fluid Dynamic