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

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

Fibrational induction rules for initial algebras

This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs’ elegant algebraic formulation of induction for polynomial data types. Our contribution is to derive, under slightly different assumptions, an induction rule that is generic over all inductive types, polynomial or not. Our induction rule is generic over the kinds of properties to be proved as well: like Hermida and Jacobs, we work in a general fibrational setting and so can accommodate very general notions of properties on inductive types rather than just those of particular syntactic forms. We establish the correctness of our generic induction rule by reducing induction to iteration. We show how our rule can be instantiated to give induction rules for the data types of rose trees, finite hereditary sets, and hyperfunctions. The former lies outside the scope of Hermida and Jacobs’ work because it is not polynomial; as far as we are aware, no induction rules have been known to exist for the latter two in a general fibrational framework. Our instantiation for hyperfunctions underscores the value of working in the general fibrational setting since this data type cannot be interpreted as a set

Supersymmetry solution for finitely extensible dumbbell model

Exact relaxation times and eigenfunctions for a simple mechanical model of polymer dynamics are obtained using supersymmetry methods of quantum mechanics. The model includes the finite extensibility of the molecule and does not make use of the self-consistently averaging approximation. The finite extensibility reduces the relaxation times when compared to a linear force. The linear viscoelastic behaviour is obtained in the form of the ``generalized Maxwell model''. Using these results, a numerical integration scheme is proposed in the presence of a given flow kinematics.Comment: 5 pages, 2 figure

Thermodynamics of polymer adsorption to a flexible membrane

We analyze the structural behavior of a single polymer chain grafted to an attractive, flexible surface. Our model is composed of a coarse-grained bead-and-spring polymer and a tethered membrane. By means of extensive parallel tempering Monte Carlo simulations it is shown that the system exhibits a rich phase behavior ranging from highly ordered, compact to extended random coil structures and from desorbed to completely adsorbed or even partially embedded conformations. These findings are summarized in a pseudophase diagram indicating the predominant class of conformations as a function of the external parameters temperature and polymer-membrane interaction strength. By comparison with adsorption to a stiff membrane surface it is shown that the flexibility of the membrane gives rise to qualitatively new behavior such as stretching of adsorbed conformations

Transition to turbulence in slowly divergent pipe flow

The results of a combined experimental and numerical study of the flow in slowly diverging pipes are presented. Interestingly, an axisymmetric conical recirculation cell has been observed. The conditions for its existence and the length of the cell are simulated for a range of diverging angles and expansion ratios. There is a critical velocity for the appearance of this state. When the flow rate increases further, a subcritical transition for localized turbulence arises. The transition and relaminarization experiments described here quantify the extent of turbulence. The findings suggest that the transition scenario in slowly diverging pipes is a combination of stages similar to those observed in sudden expansions and in straight circular pipe flow.Comment: 8 pages, 5 figure

Elastic Lennard-Jones Polymers Meet Clusters -- Differences and Similarities

We investigate solid-solid and solid-liquid transitions of elastic flexible off-lattice polymers with Lennard-Jones monomer-monomer interaction and anharmonic springs by means of sophisticated variants of multicanonical Monte Carlo methods. We find that the low-temperature behavior depends strongly and non-monotonically on the system size and exhibits broad similarities to unbound atomic clusters. Particular emphasis is dedicated to the classification of icosahedral and non-icosahedral low-energy polymer morphologies.Comment: 9 pages, 17 figure

Gaussian approximation for finitely extensible bead-spring chains with hydrodynamic interaction

The Gaussian Approximation, proposed originally by Ottinger [J. Chem. Phys., 90 (1) : 463-473, 1989] to account for the influence of fluctuations in hydrodynamic interactions in Rouse chains, is adapted here to derive a new mean-field approximation for the FENE spring force. This "FENE-PG" force law approximately accounts for spring-force fluctuations, which are neglected in the widely used FENE-P approximation. The Gaussian Approximation for hydrodynamic interactions is combined with the FENE-P and FENE-PG spring force approximations to obtain approximate models for finitely-extensible bead-spring chains with hydrodynamic interactions. The closed set of ODE's governing the evolution of the second-moments of the configurational probability distribution in the approximate models are used to generate predictions of rheological properties in steady and unsteady shear and uniaxial extensional flows, which are found to be in good agreement with the exact results obtained with Brownian dynamics simulations. In particular, predictions of coil-stretch hysteresis are in quantitative agreement with simulations' results. Additional simplifying diagonalization-of-normal-modes assumptions are found to lead to considerable savings in computation time, without significant loss in accuracy.Comment: 26 pages, 17 figures, 2 tables, 75 numbered equations, 1 appendix with 10 numbered equations Submitted to J. Chem. Phys. on 6 February 200

Two-dimensional turbulence of dilute polymer solutions

We investigate theoretically and numerically the effect of polymer additives on two-dimensional turbulence by means of a viscoelastic model. We provide compelling evidence that at vanishingly small concentrations, such that the polymers are passively transported, the probability distribution of polymer elongation has a power law tail: its slope is related to the statistics of finite-time Lyapunov exponents of the flow, in quantitative agreement with theoretical predictions. We show that at finite concentrations and sufficiently large elasticity the polymers react on the flow with manifold consequences: velocity fluctuations are drastically depleted, as observed in soap film experiments; the velocity statistics becomes strongly intermittent; the distribution of finite-time Lyapunov exponents shifts to lower values, signalling the reduction of Lagrangian chaos.Comment: 4 pages, 5 figure

Shell Model of Two-dimensional Turbulence in Polymer Solutions

We address the effect of polymer additives on two dimensional turbulence, an issue that was studied recently in experiments and direct numerical simulations. We show that the same simple shell model that reproduced drag reduction in three-dimensional turbulence reproduces all the reported effects in the two-dimensional case. The simplicity of the model offers a straightforward understanding of the all the major effects under consideration