arXiv subjects

S. M. Fielding

Publications and source records attributed to S. M. Fielding.

14 recordsLinked to original sources

arXiv2017

Thickening of viscoelastic flow in a model porous medium

We study numerically two-dimensional creeping viscoelastic flow past a biperiodic square array of cylinders within the Oldroyd B, FENE-CR and FENE-P constitutive models of dilute polymer solutions. Our results capture the initial mild decrease then dramatic upturn ('thickening') seen experimentally in the drag coefficient as a function of increasing Weissenberg number. By systematically varying the porosity of the flow geometry, we demonstrate two qualitatively different mechanisms underpinning this thickening effect: one that operates in the highly porous case of widely spaced obstacles, and another for more densely packed obstacles, with a crossover between these two mechanisms at intermediate porosities. We also briefly consider 2D creeping viscoelastic flow past a linear array of cylinders confined to a channel, where we find that the flow is steady for all Weissenberg numbers explored.

cond-mat.soft↗

arXiv2016

Correlation lengths in hydrodynamic models of active nematics

We examine the scaling with activity of the emergent length scales that control the nonequilibrium dynamics of an active nematic liquid crystal, using two popular hydrodynamic models that have been employed in previous studies. In both models we find that the chaotic spatio-temporal dynamics in the regime of fully developed active turbulence is controlled by a single active scale determined by the balance of active and elastic stresses, regardless of whether the active stress is extensile or contractile in nature. The observed scaling of the kinetic energy and enstropy with activity is consistent with our single-length scale argument and simple dimensional analysis. Our results provide a unified understanding of apparent discrepancies in the previous literature and demonstrate that the essential physics is robust to the choice of model.

cond-mat.soft↗

arXiv2016

Viscoelastic and elastomeric active matter: Linear instability and nonlinear dynamics

We consider a continuum model of active viscoelastic matter, whereby an active nematic liquid-crystal is coupled to a minimal model of polymer dynamics with a viscoelastic relaxation time $τ_C$. To explore the resulting interplay between active and polymeric dynamics, we first generalise a linear stability analysis (from earlier studies without polymer) to derive criteria for the onset of spontaneous heterogeneous flows (strain rate) and/or deformations (strain). We find two modes of instability. The first is a viscous mode, associated with strain rate perturbations. It dominates for relatively small values of $τ_C$ and is a simple generalisation of the instability known previously without polymer. The second is an elastomeric mode, associated with strain perturbations, which dominates at large $τ_C$ and persists even as $τ_C\to\infty$. We explore the novel dynamical states to which these instabilities lead by means of direct numerical simulations. These reveal oscillatory shear-banded states in 1D, and activity-driven turbulence in 2D even in the elastomeric limit $τ_C\to\infty$. Adding polymer can also have calming effects, increasing the net throughput of spontaneous flow along a channel in a new type of "drag-reduction". Finally the effect of including strong, antagonistic coupling between nematic and polymer is examined numerically, revealing a rich array of spontaneously flowing states.

cond-mat.soft↗

arXiv2015

Age dependent modes of extensional necking instability in soft glassy materials

We study the instability to necking of an initially cylindrical filament of soft glassy material subject to extensional stretching. By numerical simulation of the soft glassy rheology model and a simplified fluidity model, and by analytical predictions within a highly generic toy description, we show that the mode of instability is set by the age of the sample relative to the inverse of the applied extensional strain rate. Young samples neck gradually via a liquid-like mode, the onset of which is determined by both the elastic loading and plastic relaxation terms in the stress constitutive equation. Older samples fail at smaller draw ratios via a more rapid mode, the onset of which is determined only by the solid-like elastic loading terms (though plastic effects arise later, once appreciable necking develops). We show this solid-like mode to be the counterpart, for elastoplastic materials, of the Considère mode of necking in strain-rate-independent solids.

cond-mat.soft↗

arXiv2015

Active Viscoelastic Matter: from Bacterial Drag Reduction to Turbulent Solids

A paradigm for internally driven matter is the active nematic liquid crystal, whereby the equations of a conventional nematic are supplemented by a minimal active stress that violates time reversal symmetry. In practice, active fluids may have not only liquid crystalline but also viscoelastic polymer degrees of freedom. Here we explore the resulting interplay by coupling an active nematic to a minimal model of polymer rheology. We find that adding polymer can greatly increase the complexity of spontaneous flow, but can also have calming effects, thereby increasing the net throughput of spontaneous flow along a pipe (a 'drag-reduction' effect). Remarkably, active turbulence can also arise after switching on activity in a sufficiently soft elastomeric solid.

cond-mat.soft↗

arXiv2012

Modeling the Relaxation of Polymer Glasses under Shear and Elongational Loads

Glassy polymers show strain hardening: at constant extensional load, their flow first accelerates, then arrests. Recent experiments under such loading have found this to be accompanied by a striking dip in the segmental relaxation time. This can be explained by a minimal nonfactorable model combining flow-induced melting of a glass with the buildup of stress carried by strained polymers. Within this model, liquefaction of segmental motion permits strong flow that creates polymer-borne stress, slowing the deformation enough for the segmental (or solvent) modes to then re-vitrify. Here we present new results for the corresponding behavior under step-stress shear loading, to which very similar physics applies. To explain the unloading behavior in the extensional case requires introduction of a crinkle factor describing a rapid loss of segmental ordering. We discuss in more detail here the physics of this, which we argue involves non-entropic contributions to the polymer stress, and which might lead to some important differences between shear and elongation. We also discuss some fundamental and possibly testable issues concerning the physical meaning of entropic elasticity in vitrified polymers. Finally we present new results for the startup of steady shear flow, addressing the possible role of transient shear banding.

cond-mat.soft↗

arXiv2011

A Simple Model for the Deformation-Induced Relaxation of Glassy Polymers

Glassy polymers show strain hardening: at constant extensional load, their flow first accelerates, then arrests. Recent experiments have found this to be accompanied by a striking and unexplained dip in the segmental relaxation time. Here we explain such behavior by combining a minimal model of flow-induced liquefaction of a glass, with a description of the stress carried by strained polymers, creating a non-factorable interplay between aging and strain-induced rejuvenation. Under constant load, liquefaction of segmental motion permits strong flow that creates polymer-borne stress. This slows the deformation enough for the segmental modes to re-vitrify, causing strain hardening.

cond-mat.soft↗

arXiv2011

Transient shear banding in entangled polymers: a study using the Rolie-Poly model

Spatially inhomogeneous shear flow occurs in entangled polymer solutions, both as steady state shear banding and transiently after a large step strain or during start up to a steady uniform shear rate. Steady state shear banding is a hallmark of models with a non-monotonic constitutive relation between total shear stress and applied shear rate, but transient banding is sometimes seen in fluids that do not shear band at steady state. We model this behavior using the diffusive Rolie-Poly model in a Newtonian solvent, whose constitutive behavior can be monotonic or non-monotonic depending on the degree of convected constraint release (CCR). We study monotonic constitutive behaviour. Linear stability analysis of start up to a sufficiently high shear rate shows that spatial fluctuations are unstable at early times. There is a strong correlation between this instability and the negative slope of the (time dependent) constitutive curve. If the time integral of the most unstable eigenvalue is sufficiently large then the system exhibits transient shear bands that later vanish in steady state. We show how perturbations, due to fluctuations or the inhomogeneous stresses, can trigger this instability. This transient behavior is similar to recent observations in entangled polymer solutions

cond-mat.soft↗

arXiv2010

Nonlinear dynamics and rheology of active fluids: simulations in two dimensions

We report simulations of a continuum model for (apolar, flow aligning) active fluids in two dimensions. Both free and anchored boundary conditions are considered, at parallel confining walls that are either static or moving at fixed relative velocity. We focus on extensile materials and find that steady shear bands, previously shown to arise ubiquitously in 1D for the active nematic phase at small (or indeed zero) shear rate, are generally replaced in 2D by more complex flow patterns that can be stationary, oscillatory, or apparently chaotic. The consequences of these flow patterns for time-averaged steady-state rheology are examined.

cond-mat.soft↗

arXiv2009

Microchannel flow of a shear-banding fluid: enhanced confinement effect and interfacial instability

Using a micro particle imaging velocity technique, we resolve for the first time the three dimensionnal structure of wormlike shear banding flows in straight microchannels. The study revealed two effects, which should be generic for shear banding flows: the first is a strong amplification of the confinement induced by the edge of the channel, the second is an instability of the interface between the shear bands. A detailed quantitative comparison of our experimental measurements with a theoretical study of the diffusive Johnson Segalman model leads to excellent agreement. Our study clarifies the nature of shear banding flow instabilities, and shows that, despite the challenging complexity of the situation and the uncertainty regarding their molecular structure, shear banding flows in confined geometries are amenable to quantitative modelling, a feature that opens pathways to their practical utilization.

cond-mat.soft↗

arXiv2008

Shearing active gels close to the isotropic-nematic transition

We study numerically the rheological properties of a slab of active gel close o the isotropic-nematic transition. The flow behavior shows strong dependence on sample size, boundary conditions, and on the bulk constitutive curve, which, on entering the nematic phase, acquires an activity-induced discontinuity at the origin. The precursor of this within the metastable isotropic phase for contractile systems ({\em e.g.,} actomyosin gels) gives a viscosity divergence; its counterpart for extensile ({\em e.g.,} {\em B. subtilis}) suspensions admits instead a shear-banded flow with zero apparent viscosity.

cond-mat.soft↗

arXiv2007

The interplay between boundary conditions and flow geometries in shear banding: hysteresis, band configurations, and surface transitions

We study shear banding flows in models of wormlike micelles or polymer solutions, and explore the effects of different boundary conditions for the viscoelastic stress. These are needed because the equations of motion are inherently non-local and include ``diffusive'' or square-gradient terms. Using the diffusive Johnson-Segalman model and a variant of the Rolie-Poly model for entangled micelles or polymer solutions, we study the interplay between different boundary conditions and the intrinsic stress gradient imposed by the flow geometry. We consider prescribed gradient (Neumann) or value (Dirichlet) of the viscoelastic stress tensor at the boundary, as well as mixed boundary conditions in which an anchoring strength competes with the gradient contribution to the stress dynamics. We find that hysteresis during shear rate sweeps is suppressed if the boundary conditions favor the state that is induced by the sweep. For example, if the boundaries favor the high shear rate phase then hysteresis is suppressed at the low shear rate edges of the stress plateau. If the boundaries favor the low shear rate state, then the high shear rate band can lie in the center of the flow cell, leading to a three-band configuration. Sufficiently strong stress gradients due to curved flow geometries, such as that of cylindrical Couette flow, can convert this to a two-band state by forcing the high shear rate phase against the wall of higher stress, and can suppress the hysteresis loop observed during a shear rate sweep.

cond-mat.soft↗

arXiv2006

Linear instability of planar shear banded flow of both diffusive and non-diffusive Johnson-Segalman fluids

We consider the linear stability of shear banded planar Couette flow of the Johnson-Segalman fluid, with and without the addition of stress diffusion to regularise the equations. In particular, we investigate the effect of two-dimensional perturbations representing undulations along the interface between shear bands. We demonstrate analytically that, for the linear stability problem, the limit in which diffusion tends to zero is mathematically equivalent to a pure (non-diffusive) Johnson-Segalman model with a material interface between the shear bands, provided the wavelength of perturbations being considered is long relative to the (short) diffusion lengthscale. For no diffusion, we find that the flow is unstable to long waves for almost all arrangements of the two shear bands. Weak diffusion provides a small stabilising effect, rendering extremely long waves marginally stable. However, the basic long-wave instability mechanism is not affected by this, and where there would be instability as wavenumber k tends to 0 in the absence of diffusion, we observe instability for moderate to long waves even with diffusion. This paper is the first full analytical investigation into an instability first documented in the numerical study of Physical Review Letters 95 (2005) 134501 cond-mat/0501518. We discuss the relevance of this work to recent experimental observations of complex dynamics seen in shear-banded flows.

cond-mat.soft↗

arXiv1999

Ageing and Rheology in Soft Materials

We study theoretically the role of ageing in the rheology of soft materials. We define several generalized rheological response functions suited to ageing samples (in which time translation invariance is lost). These are then used to study ageing effects within a simple scalar model (the "soft glassy rheology" or SGR model) whose constitutive equations relate shear stress to shear strain among a set of elastic elements, with distributed yield thresholds, undergoing activated dynamics governed by a "noise temperature", $x$. (Between yields, each element follows affinely the applied shear.) For $1<x<2$ there is a power-law fluid regime in which transients occur, but no ageing. For $x<1$, the model has a macroscopic yield stress. So long as this yield stress is not exceeded, ageing occurs, with a sample's apparent relaxation time being of order its own age. The (age-dependent) linear viscoelastic loss modulus $G''(ω,t)$ rises as frequency is {\em lowered}, but falls with age $t$, so as to always remain less than $G'(ω,t)$ (which is nearly constant). Significant ageing is also predicted for the stress overshoot in nonlinear shear startup and for the creep compliance. Though obviously oversimplified, the SGR model may provide a valuable paradigm for the experimental and theoretical study of rheological ageing phenomena in soft solids.

cond-mat.soft↗