A Minimal Model for Vorticity and Gradient Banding in Complex Fluids

A general phenomenological reaction-diffusion model for flow-induced phase transitions in complex fluids is presented. The model consists of an equation of motion for a nonconserved composition variable, coupled to a Newtonian stress relations for the reactant and product species. Multivalued reaction terms allow for different homogeneous phases to coexist with each other, resulting in banded composition and shear rate profiles. The one-dimensional equation of motion is evolved from a random initial state to its final steady-state. We find that the system chooses banded states over homogeneous states, depending on the shape of the stress constitutive curve and the magnitude of the diffusion coefficient. Banding in the flow gradient direction under shear rate control is observed for shear-thinning transitions, while banding in the vorticity direction under stress control is observed for shear-thickening transitions.Comment: 11 pages, submitted to Eur Phys J

Two-dimensional perturbations in a scalar model for shear banding

We present an analytical study of a toy model for shear banding, without normal stresses, which uses a piecewise linear approximation to the flow curve (shear stress as a function of shear rate). This model exhibits multiple stationary states, one of which is linearly stable against general two-dimensional perturbations. This is in contrast to analogous results for the Johnson-Segalman model, which includes normal stresses, and which has been reported to be linearly unstable for general two-dimensional perturbations. This strongly suggests that the linear instabilities found in the Johnson-Segalman can be attributed to normal stress effects.Comment: 16 pages, 10 figures, to appear in EPJE, available online first, click DOI or http://www.springerlink.com/content/q1q0187385017628

A non-monotonic constitutive model is not necessary to obtain shear banding phenomena in entangled polymer solutions

In 1975 Doi and Edwards predicted that entangled polymer melts and solutions can have a constitutive instability, signified by a decreasing stress for shear rates greater than the inverse of the reptation time. Experiments did not support this, and more sophisticated theories incorporated Marrucci's idea (1996) of removing constraints by advection; this produced a monotonically increasing stress and thus stable constitutive behavior. Recent experiments have suggested that entangled polymer solutions may possess a constitutive instability after all, and have led some workers to question the validity of existing constitutive models. In this Letter we use a simple modern constitutive model for entangled polymers, the non-stretching Rolie-Poly model with an added solvent viscosity, and show that (1) instability and shear banding is captured within this simple class of models; (2) shear banding phenomena is observable for weakly stable fluids in flow geometries that impose a sufficiently inhomogeneous total shear stress; (3) transient phenomena can possess inhomogeneities that resemble shear banding, even for weakly stable fluids. Many of these results are model-independent.Comment: 5 figure

Perspectives on the viscoelasticity and flow behavior of entangled linear and branched polymers

We briefly review the recent advances in the rheology of entangled polymers and identify emerging research trends and outstanding challenges, especially with respect to branched polymers. Emphasis is placed on the role of well-characterized model systems, as well as the synergy of synthesis-characterization, rheometry and modeling/simulations. The theoretical framework for understanding the observed linear and nonlinear rheological phenomena is the tube model which is critically assessed in view of its successes and shortcomings, whereas alternative approaches are briefly discussed. Finally, intriguing experimental findings and controversial issues that merit consistent explanation, such as shear banding instabilities, multiple stress overshoots in transient simple shear and enhanced steady-state elongational viscosity in polymer solutions, are discussed, whereas future directions such as branch point dynamics and anisotropic monomeric friction are outlined.Comment: 25 pages, accepted for publication in Journal of Physics Condensed Matter (August 2015

Body Weight and Body Image

Health Issue: Body weight is of physical and psychological importance to Canadian women; it is associated with health status, physical activity, body image, and self-esteem. Although the problems associated with overweight and obesity are indeed serious, there are also problems connected to being underweight. Weight prejudice and the dieting industry intensify body image concerns for Canadian women and can have a major negative impact on self-esteem. Key Findings: Women have lower BMIs than men, a lower incidence of being overweight and a higher incidence of being underweight. However, women across all weight categories are more dissatisfied with their bodies. Sixty percent of women are inactive, and women with a BMI of 27 or higher are more likely to be inactive than women with lower BMIs. The data show that women are aware of the health benefits of exercise, but there is a gap between knowledge and practice. When asked about barriers to health improvement, 39.7 % of women cited lack of time and 39.2 % lack of willpower. Data Gaps and Recommendations: Weight prejudice must be made unacceptable and positive body image should be encouraged and diversity valued. Health policies should encourage health

Micro- vs. macro-phase separation in binary blends of poly(styrene)-poly(isoprene) and poly(isoprene)-poly(ethylene oxide) diblock copolymers

In this paper we present an experimentally determined phase diagram of binary blends of the diblock copolymers poly(styrene)-poly(isoprene) and poly(isoprene)-poly(ethylene oxide). At high temperatures, the blends form an isotropic mixture. Upon lowering the temperature, the blend macro-phase separates before micro-phase separation occurs. The observed phase diagram is compared to theoretical predictions based on experimental parameters. In the low-temperature phase the crystallisation of the poly(ethylene oxide) block influences the spacing of the ordered phase

Vorticity Banding During the Lamellar-to-Onion Transition in a Lyotropic Surfactant Solution in Shear Flow

We report on the rheology of a lamellar lyotropic surfactant solution (SDS/dodecane/pentanol/water), and identify a discontinuous transition between two shear thinning regimes which correspond to the low stress lamellar phase and the more viscous shear induced multi-lamellar vesicle, or ``onion'' phase. We study in detail the flow curve, stress as a function of shear rate, during the transition region, and present evidence that the region consists of a shear banded phase where the material has macroscopically separated into bands of lamellae and onions stacked in the vorticity direction. We infer very slow and irregular transformations from lamellae to onions as the stress is increased through the two phase region, and identify distinct events consistent with the nucleation of small fractions of onions that coexist with sheared lamellae.Comment: 10 pages, 10 figure

Undulation instability in a bilayer lipid membrane due to electric field interaction with lipid dipoles

Bilayer lipid membranes [BLMs] are an essential component of all biological systems, forming a functional barrier for cells and organelles from the surrounding environment. The lipid molecules that form membranes contain both permanent and induced dipoles, and an electric field can induce the formation of pores when the transverse field is sufficiently strong (electroporation). Here, a phenomenological free energy is constructed to model the response of a BLM to a transverse static electric field. The model contains a continuum description of the membrane dipoles and a coupling between the headgroup dipoles and the membrane tilt. The membrane is found to become unstable through buckling modes, which are weakly coupled to thickness fluctuations in the membrane. The thickness fluctuations, along with the increase in interfacial area produced by membrane buckling, increase the probability of localized membrane breakdown, which may lead to pore formation. The instability is found to depend strongly on the strength of the coupling between the dipolar headgroups and the membrane tilt as well as the degree of dipolar ordering in the membrane.Comment: 29 pages 8 fig

The Johnson-Segalman model with a diffusion term in Couette flow

We study the Johnson-Segalman (JS) model as a paradigm for some complex fluids which are observed to phase separate, or ``shear-band'' in flow. We analyze the behavior of this model in cylindrical Couette flow and demonstrate the history dependence inherent in the local JS model. We add a simple gradient term to the stress dynamics and demonstrate how this term breaks the degeneracy of the local model and prescribes a much smaller (discrete, rather than continuous) set of banded steady state solutions. We investigate some of the effects of the curvature of Couette flow on the observable steady state behavior and kinetics, and discuss some of the implications for metastability.Comment: 14 pp, to be published in Journal of Rheolog

Lifshitz points in blends of AB and BC diblock copolymers

We consider micro- and macro-phase separation in blends of AB and BC flexible 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