arXiv subjects

Peter D. Olmsted

Publications and source records attributed to Peter D. Olmsted.

At least 55 records · Page 3Linked to original sources

arXiv2005

Nonlinear dynamics of a shear banding interface

We study numerically the nonlinear dynamics of a shear banding interface in two dimensional planar shear flow, within the non-local Johnson Segalman model. Consistent with a recent linear stability analysis, we find that an initially flat interface is unstable with respect to small undulations for sufficiently small ratio of the interfacial width $\ell$ to cell length $L_x$. The instability saturates in finite amplitude interfacial fluctuations. For decreasing $\ell/L_x$ these undergo a non equilibrium transition from simple travelling interfacial waves with constant average wall stress, to periodically rippling waves with a periodic stress response. When multiple shear bands are present we find erratic interfacial dynamics and a stress response suggesting low dimensional chaos.

cond-mat.soft↗

arXiv2005

Budding and Domain Shape Transformations in Mixed Lipid Films and Bilayer Membranes

We study the stability and shapes of domains with spontaneous curvature in fluid films and membranes, embedded in a surrounding membrane with zero spontaneous curvature. These domains can result from the inclusion of an impurity in a fluid membrane, or from phase separation within the membrane. We show that for small but finite line and surface tensions and for finite spontaneous curvatures, an equilibrium phase of protruding circular domains is obtained at low impurity concentrations. At higher concentrations, we predict a transition from circular domains, or "caplets", to stripes. In both cases, we calculate the shapes of these domains within the Monge representation for the membrane shape. With increasing line tension, we show numerically that there is a budding transformation from stable protruding circular domains to spherical buds. We calculate the full phase diagram, and demonstrate a two triple points, of respectively bud-flat-caplet and flat-stripe-caplet coexistence.

cond-mat.soft↗

arXiv2004

Lateral phase separation in mixtures of lipids and cholesterol systems

In an effort to understand ``rafts'' in biological membranes, we propose phenomenological models for saturated and unsaturated lipid mixtures, and lipid-cholesterol mixtures. We consider simple couplings between the local composition and internal membrane structure, and their influence on transitions between liquid and ``gel'' membrane phases. Assuming that the gel transition temperature of the saturated lipid is shifted by the presence of the unsaturated lipid, and that cholesterol acts as an external field on the chain melting transition, a variety of phase diagrams are obtained. The phase diagrams for binary mixtures of saturated/unsaturated lipids and lipid/cholesterol are in semi-quantitative agreement with the experiments. Our results also apply to regions in the ternary phase diagram of lipid/lipid/cholesterol systems.

cond-mat.soft↗

arXiv2002

Dynamical Coarse-Graining of Highly Fluctuating Membranes under Shear Flow

The effect of strong shear flow on highly fluctuating lamellar systems stabilized by intermembrane collisions via the Helfrich interaction is studied. Advection enters the microscopic equation of motion for a single membrane via a non-linear coupling. Upon coarse-graining the theory for a single bilayer up to the length scale of the collision length, at which a hydrodynamic description applies, an additional dynamical coupling is generated which is of the form of a wavevector-dependent tension that is non-linear in the applied shear rate. This new term has consequences for the effects of strong flow on the stability and dynamics of lamellar surfactant phases.

cond-mat.soft↗

arXiv2002

Kinetics of the shear banding instability in startup flows

Motivated by experiments on wormlike micelles, we study the early stages of the shear banding instability using a two-fluid Johnson-Segalman model. We perform a linear stability analysis for coupled fluctuations in shear rate, micellar strain and concentration about an initially homogeneous state. First we calculate the ``spinodal'' onset of instability in sweeps along the intrinsic constitutive curve. For startup ``quenches'' into the unstable region, the instability usually occurs before the intrinsic constitutive curve can be attained so we analyse the fluctuations with respect to the homogeneous startup flow to find the selected length and time scales at which inhomogeneity first emerges. In the uncoupled limit, fluctuations in shear rate and micellar strain are independent of those in concentration, and are unstable when the intrinsic constitutive curve has negative slope; but no length scale is selected. When coupled to concentration, this instability is enhanced at short length scales; a length scale is selected, as seen experimentally. The unstable region is then broadened. Far from an underlying (zero-shear) demixing instability, the broadening is slight and the instability is still dominated by shear rate and micellar strain. Close to demixing, instability sets in at very low shear rate, where it is demixing triggered by flow.

cond-mat.soft↗

arXiv2002

The Effect of Shear Flow on the Helfrich Interaction in Lyotropic Lamellar Systems

We study the effect of shear flow on the entropic Helfrich interaction in lyotropic surfactant smectic fluids. Arguing that flow induces an effective anisotropic surface tension in bilayers due to a combination of intermonolayer friction, bilayer collisions and convection, we calculate the reduction in fluctuations and hence the renormalised change in effective compression modulus and steady-state layer spacing. We demonstrate that non-permeable or slowly permeating membranes can be susceptible to a undulatory instability of the Helfrich-Hurault type, and speculate that such an instability could be one source of a transition to multilamellar vesicles.

cond-mat.soft↗

arXiv2002

Early stages of the shear banding instability in wormlike micelles

We study the early stages of the shear banding instability in semidilute wormlike micelles using the non-local Johnson-Segalman model with a two-fluid coupling of the concentration (phi) to the shear rate (gamma_dot) and micellar strain (tensor{W}). We calculate the ``spinodal'' limit of stability for sweeps along the homogeneous intrinsic flow curve. For startup ``quenches'' into the unstable region, the instability in general occurs before the homogeneous startup flow can attain the intrinsic flow curve. We predict the selected time and length scales at which inhomogeneity first emerges. In the ``infinite drag'' limit, fluctuations in the mechanical variables (gamma_dot and \tensor{W}) are independent of those in phi, and are unstable when the slope of the intrinsic flow curve is negative; but no length scale is selected. For finite drag, the mechanical instability is enhanced by coupling to phi and a length scale is selected, in qualitative agreement with recent experiments. For systems far from an underlying zero-shear demixing instability this enhancement is slight, while close to demixing the instability sets in at low shear rates and is essentially demixing triggered by flow.

cond-mat.soft↗

arXiv1999

Effects of Non-local Stress on the Determination of Shear Banding Flow

We analyze the steady planar shear flow of the modified Johnson-Segalman model, which has an added non-local term. We find that the new term allows for unambiguous selection of the stress at which two ``phases'' coexist, in contrast to the original model. For general differential constitutive models we show the singular nature of stress selection in terms of a saddle connection between fixed points in the equivalent dynamical system. The result means that stress selection is unique under most conditions for space non-local models Finally, illustrated by simple models, we show that stress selection generally depends on the form of the non-local terms (weak universality).

cond-mat.soft↗

arXiv1999

Two-state shear diagrams for complex fluids in shear flow

The possible ``phase diagrams'' for shear-induced phase transitions between two phases are collected. We consider shear-thickening and shear-thinning fluids, under conditions of both common strain rate and common stress in the two phases, and present the four fundamental shear stress vs. strain-rate curves and discuss their concentration dependence. We outline how to construct more complicated phase diagrams, discuss in which class various experimental systems fall, and sketch how to reconstruct the phase diagrams from rheological measurements.

cond-mat.soft↗

arXiv1999

Phase Separation of Rigid-Rod Suspensions in Shear Flow

We analyze the behavior of a suspension of rigid rod-like particles in shear flow using a modified version of the Doi model, and construct diagrams for phase coexistence under conditions of constant imposed stress and constant imposed strain rate, among paranematic, flow-aligning nematic, and log-rolling nematic states. We calculate the effective constitutive relations that would be measured through the regime of phase separation into shear bands. We calculate phase coexistence by examining the stability of interfacial steady states and find a wide range of possible ``phase'' behaviors.

cond-mat.soft↗

arXiv1999

Dynamics and flow-induced phase separation in polymeric fluids

The past few years have seen many advances in our understanding of the dynamics of polymeric fluids. These include improvements on the successful reptation theory; an emerging molecular theory of semiflexible chain dynamics; and an understanding of how to calculate and classify ``phase diagrams'' for flow-induced transitions. Experimentalists have begun mapping out the phase behavior of wormlike micelles, a ``living'' polymeric system, in flow: these systems undergo transitions into shear-thinning or shear-thickening phases, whose variety is remarkably rich and poorly understood. Polymeric ideas must be extended to include the delicate charge and composition effects which conspire to stabilize the micelles and are strongly influenced by flow.

cond-mat.soft↗

arXiv1999

Phase Coexistence of Complex Fluids in Shear Flow

We present some results of recent calculations of rigid rod-like particles in shear flow, based on the Doi model. This is an ideal model system for exhibiting the generic behavior of shear-thinning fluids (polymer solutions, wormlike micelles, surfactant solutions, liquid crystals) in shear flow. We present calculations of phase coexistence under shear among weakly-aligned (paranematic) and strongly-aligned phases, including alignment in the shear plane and in the vorticity direction (log-rolling). Phase coexistence is possible, in principle, under conditions of both common shear stress and common strain rate, corresponding to different orientations of the interface between phases. We discuss arguments for resolving this degeneracy. Calculation of phase coexistence relies on the presence of inhomogeneous terms in the dynamical equations of motion, which select the appropriate pair of coexisting states. We cast this condition in terms of an equivalent dynamical system, and explore some aspects of how this differs from equilibrium phase coexistence.

cond-mat.soft↗

arXiv1998

Lifshitz points in blends of AB and BC diblock copolymers

We consider micro- and macro- phase separation in blends of AB and BC diblock copolymers. We show that, depending on architecture, a number of phase diagram topologies are possible. Microphase separation or macrophase separation can occur, and there are a variety of possible Lifshitz points. Because of the rich parameter space, Lifshitz points of multiple order are possible. We demonstrate Lifshitz points of first and second order, and argue that, in principle, up to 5th order Lifshitz points are possible.

cond-mat.soft↗

arXiv1998

Spinodal-assisted crystallization in polymer melts

Recent experiments in some polymer melts quenched below the melting temperature have reported spinodal kinetics in small-angle X ray scattering before the emergence of crystalline structure. To explain these observations we propose that the coupling between density and chain conformation induces a liquid-liquid binodal within the equilibrium liquid--crystalline solid coexistence region. A simple phenomenological theory is developed to illustrate this idea, and several experimentally testable consequences are discussed. Shear is shown to enhance the kinetic role of the hidden binodal.

cond-mat.soft↗

arXiv1998

Strong-Segregation Theory of Bicontinuous Phases in Block Copolymers

We compute phase diagrams for $A_nB_m$ starblock copolymers in the strong-segregation regime as a function of volume fraction $ϕ$, including bicontinuous phases related to minimal surfaces (G, D, and P surfaces) as candidate structures. We present the details of a general method to compute free energies in the strong segregation limit, and demonstrate that the gyroid G phase is the most nearly stable among the bicontinuous phases considered. We explore some effects of conformational asymmetry on the topology of the phase diagram.

cond-mat.soft↗

arXiv1997

Coexistence and Phase Separation in Sheared Complex Fluids

We demonstrate how to construct dynamic phase diagrams for complex fluids that undergo transitions under flow, in which the conserved composition variable and the broken-symmetry order parameter (nematic, smectic, crystalline, etc.) are coupled to shear rate. Our construction relies on a selection criterion, the existence of a steady interface connecting two stable homogeneous states. We use the (generalized) Doi model of lyotropic nematic liquid crystals as a model system, but the method can be easily applied to other systems, provided non-local effects are included.

cond-mat.soft↗

arXiv1996

Instability and front propagation in laser-tweezed lipid bilayer tubules

We study the mechanism of the `pearling' instability seen recently in experiments on lipid tubules under a local applied laser intensity. We argue that the correct boundary conditions are fixed chemical potentials, or surface tensions Σ, at the laser spot and the reservoir in contact with the tubule. We support this with a microscopic picture which includes the intensity profile of the laser beam, and show how this leads to a steady-state flow of lipid along the surface and gradients in the local lipid concentration and surface tension (or chemical potential). This leads to a natural explanation for front propagation and makes several predictions based on the tubule length. While most of the qualitative conclusions of previous studies remain the same, the `ramped' control parameter (surface tension) implies several new qualitative results. We also explore some of the consequences of front propagation into a noisy (due to pre-existing thermal fluctuations) unstable medium.

cond-mat.soft↗

arXiv1995

Mean-Field Nematic--Smectic-{\sl A} Transition in a Random Polymer Network

Liquid crystal elastomers present a rich combination of effects associated with orientational symmetry breaking and the underlying rubber elasticity. In this work we focus on the effect of the network on the nematic--smectic-{\sl A} transition, exploring the additional translational symmetry breaking in these elastomers. We incorporate the crosslinks as a random field in a microscopic picture, thus expressing the degree to which the smectic order is locally frozen with respect to the network. We predict a modification of the NA transition, notably that it can be treated at the mean-field level (type-I system), due to the coupling with elastic degrees of freedom. There is a shift in the transition temperature $T_{\scriptscriptstyle NA}$, a suppression of the Halperin-Lubensky-Ma (HLM) effect (thus recovering the mean-field continuous transition to the smectic state), and a new tri-critical point, depending on the conditions of network formation. When the nematic phase possesses `soft elasticity', the NA transition becomes of first order due to the coupling with soft phonons in the network. We also discuss the microscopic origin of phenomenological long-wavelength coupling between smectic phase and elastic strain.

cond-mat↗