arXiv subjects

Suzanne M. Fielding

Publications and source records attributed to Suzanne M. Fielding.

54 records · Page 3Linked to original sources

arXiv2016

Shear Banding of Soft Glassy Materials in Large Amplitude Oscillatory Shear

We study shear banding in soft glassy materials subject to a large amplitude oscillatory shear flow (LAOS). By numerical simulations of the widely used soft glassy rheology model, supplemented by more general physical arguments, we demonstrate strong banding over an extensive range of amplitudes and frequencies of the imposed shear rate $\dotγ(t)=\dotγ_0\cos(ωt)$, even in materials that do not permit banding as their steady state response to a steady imposed shear flow $\dotγ=\dotγ_0=$const. Highly counterintuitively, banding persists in LAOS even in the limit of zero frequency $ω\to 0$, where one might a priori have expected a homogeneous flow response (consistent with the requirement of homogeneous flow for a strictly zero frequency steady imposed shear flow). We explain this finding in terms of an alternating competition within each cycle between glassy aging and flow rejuvenation. Our predictions have far-reaching implications for the flow behavior of aging yield stress fluids, suggesting a generic expectation of shear banding in flows of even arbitrarily slow time variation.

cond-mat.soft↗

arXiv2016

Shear banding in large amplitude oscillatory shear (LAOStrain and LAOStress) of polymers and wormlike micelles

We investigate theoretically shear banding in large amplitude oscillatory shear (LAOS) of polymers and wormlike micelles. In LAOStrain we find banding at low frequencies and sufficiently high strain rate amplitudes in fluids for which the underlying constitutive curve of shear stress as a function of shear rate is non-monotonic. This is the direct analogue of quasi steady state banding seen in slow strain rate sweeps along the flow curve. At higher frequencies and sufficiently high strain amplitudes we report a different but related phenomenon, which we call `elastic' shear banding. This is associated with an overshoot in the elastic (Lissajous-Bowditch) curve of stress as a function of strain. We suggest that this may arise widely even in fluids that have a monotonic underlying constitutive curve, and so do not show steady state banding under a steadily applied shear flow. In LAOStress we report banding in fluids that shear thin strongly enough to have either a negatively, or weakly positively, sloping region in the underlying constitutive curve, noting again that fluids in the latter category do not display steady state banding in a steadily applied flow. This banding is triggered in each half cycle as the stress magnitude transits the region of weak slope in an upward direction, such that the fluid effectively yields. Our numerics are performed in the Rolie-poly model of polymeric fluids, but we also provide arguments suggesting that our results should apply more widely. Besides banding in the shear rate profile, which can be measured by velocimetry, we also predict banding in the shear and normal stress components, measurable by birefringence. As a backdrop to understanding the new results on shear banding in LAOS, we also briefly review earlier work on banding in other time-dependent protocols, focusing in particular on shear startup and step stress.

cond-mat.soft↗

arXiv2015

Moving contact line dynamics: from diffuse to sharp interfaces

We reconcile two scaling laws that have been proposed in the literature for the slip length associated with a moving contact line in diffuse interface models, by demonstrating each to apply in a different regime of the ratio of the microscopic interfacial width $l$ and the macroscopic diffusive length $l_D= (Mη)^{1/2}$, where $η$ is the fluid viscosity and $M$ the mobility governing intermolecular diffusion. For small $l_D/l$ we find a diffuse interface regime in which the slip length scales as $ξ\sim(l_Dl)^{1/2}$. For larger $l_D/l>1$ we find a sharp interface regime in which the slip length depends only on the diffusive length, $ξ\sim l_D \sim (Mη)^{1/2}$, and therefore only on the macroscopic variables $η$ and $M$, independent of the microscopic interfacial width $l$. We also give evidence that modifying the microscopic interfacial terms in the model's free energy functional appears to affect the value of the slip length only the diffuse interface regime, consistent with the slip length depending only on macroscopic variables in the sharp interface regime. Finally, we demonstrate the dependence of the dynamic contact angle on the capillary number to be in excellent agreement with the theoretical prediction of \cite{Cox1986}, provided we allow the slip length to be rescaled by a dimensionless prefactor. This prefactor appears to converge to unity in the sharp interface limit, but is smaller in the diffuse interface limit. The excellent agreement of results obtained using three independent numerical methods, across several decades of the relevant dimensionless variables, demonstrates our findings to be free of numerical artifacts.

cond-mat.soft↗

arXiv2014

Shear banding in soft glassy materials

Many soft materials, including foams, dense emulsions, micro gel bead suspensions, star polymers, dense packing of surfactant onion micelles, and textured morphologies of liquid crystals, share the basic "glassy" features of structural disorder and metastability. These in turn give rise to several notable features in the low frequency shear rheology (deformation and flow properties) of these materials: in particular, the existence of a yield stress below which the material behaves like a solid, and above which it flows like a liquid. In the last decade, intense experimental activity has also revealed that these materials often display a phenomenon known as shear banding, in which the flow profile across the shear cell exhibits macroscopic bands of different viscosity. Two distinct classes of yield stress fluid have been identified: those in which the shear bands apparently persist permanently (for as long as the flow remains applied), and those in which banding arises only transiently during a process in which a steady flowing state is established out of an initial rest state (for example, in a shear startup or step stress experiment). After surveying the motivating experimental data, we describe recent progress in addressing it theoretically, using the soft glassy rheology model and a simple fluidity model. We also briefly place these theoretical approaches in the context of others in the literature, including elasto-plastic models, shear transformation zone theories, and molecular dynamics simulations. We discuss finally some challenges that remain open to theory and experiment alike.

cond-mat.soft↗

arXiv2014

Hydrodynamic suppression of phase separation in active suspensions

We simulate with hydrodynamics a suspension of active disks squirming through a Newtonian fluid. We explore numerically the full range of squirmer area fractions from dilute to close packed and show that "motility induced phase separation" (MIPS), which was recently proposed to arise generically in active matter, and which has been seen in simulations of active Brownian disks, is strongly suppressed by hydrodynamic interactions. We give an argument for why this should be the case and support it with counterpart simulations of active Brownian disks in a parameter regime that provides a closer counterpart to hydrodynamic suspensions than in previous studies.

cond-mat.soft↗

arXiv2013

Shear banding in time-dependent flows of polymers and wormlike micelles

We study theoretically the formation of shear bands in time-dependent flows of polymeric and wormlike micellar surfactant fluids, focussing on the protocols of step shear stress, step shear strain (or in practice a rapid strain ramp), and shear startup, which are commonly studied experimentally. For each protocol we perform a linear stability analysis to provide a fluid-universal criterion for the onset of shear banding, following our recent Letter [Phys. Rev. Lett. 110 (2013) 086001]. In each case this criterion depends only on the shape of the experimentally measured rheological response function for that protocol, independent of the constitutive properties of the material in question. (Therefore our criteria in fact concern all complex fluids and not just the polymeric ones of interest here. A separate manuscript [in preparation] will explore them in a broad class of disordered soft glassy materials including foams, dense emulsions, dense colloids, and microgel bead suspensions.) An important prediction is that pronounced banding can arise transiently in each of these protocols, even in fluids for which the underlying constitutive curve of stress as a function of strain-rate is monotonic and a steadily flowing state is accordingly unbanded. For each protocol we provide numerical results in the rolie-poly and Giesekus models that support our predictions. We comment on the ability of the rolie-poly model to capture the observed experimental phenomenology, and on the failure of the Giesekus model.

cond-mat.soft↗

arXiv2013

Criteria for shear banding in time-dependent flows of complex fluids

Within a highly generalised theoretical framework for the flow properties of complex fluids, we study the onset of shear banding in the three most common time-dependent experimental protocols: step stress, step strain and shear startup. By means of a linear stability analysis we derive a fluid-universal criterion for the onset of banding, separately for each protocol, that depends only on the shape of the experimentally measured time-dependent rheological response function, independent of the constitutive law and internal state variables of the particular fluid in question. Our predictions thus have the same status, in these time-dependent flows, as the widely known criterion for banding in steady state (of negatively sloping shear stress vs. shear rate). We support them with simulations of the rolie-poly model of polymeric fluids, the soft glassy rheology model, and a fluidity model.

cond-mat.soft↗

arXiv2011

Criterion for extensional necking instability in polymeric fluids

We study the linear instability with respect to necking of a filament of polymeric fluid undergoing uniaxial extension. Contrary to the widely discussed Considere criterion, we find the onset of instability to relate closely to the onset of downward curvature in the time (and so strain) evolution of the zz component of the molecular strain, for extension along the z axis. In establishing this result numerically across five of the most widely used models of polymer rheology, and by analytical calculation, we argue it to apply generically. Particularly emphasized is the importance of polymer chain stretching in partially mitigating necking. We comment finally on the relationship between necking and the shape of the underlying steady state constitutive curve for homogeneous extension.

cond-mat.soft↗

arXiv2010

Age-dependent transient shear banding in soft glasses

We study numerically the formation of long-lived transient shear bands during shear startup within two models of soft glasses (a simple fluidity model and an adapted `soft glassy rheology' model). The degree and duration of banding depends strongly on the applied shear rate, and on sample age before shearing. In both models the ultimate steady flow state is homogeneous at all shear rates, consistent with the underlying constitutive curve being monotonic. However, particularly in the SGR case, the transient bands can be extremely long lived. The banding instability is neither `purely viscous' nor `purely elastic' in origin, but is closely associated with stress overshoot in startup flow.

cond-mat.soft↗

arXiv2009

Viscoelastic Taylor-Couette instability of shear banded flow

We study numerically shear banded flow in planar and curved Couette geometries. Our aim is to explain two recent observations in shear banding systems of roll cells stacked in the vorticity direction, associated with an undulation of the interface between the bands. Depending on the degree of cell curvature and on the material's constitutive properties, we find either (i) an instability of the interface between the bands driven by a jump in second normal stress across it; or (ii) a bulk viscoelastic Taylor Couette instability in the high shear band driven by a large first normal stress within it. Both lead to roll cells and interfacial undulations, but with a different signature in each case. Our work thereby suggests a different origin for the roll cells in each of the recent experiments.

cond-mat.soft↗

arXiv2009

Shear banding and interfacial instability in planar Poiseuille flow

Motivated by the need for a theoretical study in a planar geometry that can easily be implemented experimentally, we study the pressure driven Poiseuille flow of a shear banding fluid. After discussing the "basic states" predicted by a one dimensional calculation that assumes a flat interface between the bands, we proceed to demonstrate such an interface to be unstable with respect to the growth of undulations along it. We give results for the growth rate and wavevector of the most unstable mode that grows initially, as well as for the ultimate flow patterns to which the instability leads. We discuss the relevance of our predictions to the present state of the experimental literature concerning interfacial instabilities of shear banded flows, in both conventional rheometers and microfluidic channels.

cond-mat.soft↗

arXiv2007

The need for inertia in nonequilibrium steady states of sheared binary fluids

We study numerically phase separation in a binary fluid subject to an applied shear flow in two dimensions, with full hydrodynamics. To do so, we introduce a mixed finite-differencing/spectral simulation technique, with a transformation to render trivial the implementation of Lees-Edwards sheared periodic boundary conditions. For systems with inertia, we reproduce the nonequilibrium steady states reported in a recent lattice Boltzmann study. The domain coarsening that would occur in zero shear is arrested by the applied shear flow, which restores a finite domain size set by the inverse shear rate. For inertialess systems, in contrast, we find no evidence of nonequilibrium steady states free of finite size effects: coarsening persists indefinitely until the typical domain size attains the system size, as in zero shear. We present an analytical argument that supports this observation, and that furthermore provides a possible explanation for a hitherto puzzling property of the nonequilibrium steady states with inertia.

cond-mat.stat-mech↗

arXiv2007

Vorticity structuring and Taylor-like velocity rolls triggered by gradient shear bands

We suggest a novel mechanism by which vorticity structuring and Taylor-like velocity rolls can form in complex fluids, triggered by the linear instability of one dimensional gradient shear banded flow. We support this with a numerical study of the diffusive Johnson-Segalman model. In the steady vorticity structured state, the thickness of the interface between the bands remains finite in the limit of zero stress diffusivity, presenting a possible challenge to the accepted theory of shear banding.

cond-mat.soft↗

arXiv2007

Rheology of giant micelles

Giant micelles are elongated, polymer-like objects created by the self-assembly of amphiphilic molecules (such as detergents) in solution. Giant micelles are typically flexible, and can become highly entangled even at modest concentrations. The resulting viscoelastic solutions show fascinating flow behaviour (rheology) which we address theoretically in this article at two levels. First, we summarise advances in understanding linear viscoelastic spectra and steady-state nonlinear flows, based on microscopic constitutive models that combine the physics of polymer entanglement with the reversible kinetics of self-assembly. Such models were first introduced two decades ago, and since then have been shown to explain robustly several distinctive features of the rheology in the strongly entangled regime, including extreme shear-thinning. We then turn to more complex rheological phenomena, particularly involving spatial heterogeneity, spontaneous oscillation, instability, and chaos. Recent understanding of these complex flows is based largely on grossly simplified models which capture in outline just a few pertinent microscopic features, such as coupling between stresses and other order parameters such as concentration. The role of `structural memory' (the dependence of structural parameters such as the micellar length distribution on the flow history) in explaining these highly nonlinear phenomena is addressed. Structural memory also plays an intriguing role in the little-understood shear-thickening regime, which occurs in a concentration regime close to but below the onset of strong entanglement, and which is marked by a shear-induced transformation from an inviscid to a gelatinous state.

cond-mat.soft↗

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↗

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

Interrupted coarsening in a driven kinetically constrained Ising chain

We introduce a driven version of the 1D kinetically constrained spin chain. In its original undriven version, this model shows anomalous coarsening following a quench to a low temperature, with an equilibration time that diverges as exp(1/T^2) for T\to 0. We show that driving of constant rate gamma_dot interrupts coarsening and stabilises the chain in a state analogous to that of a coarsening chain of age 1/gamma_dot. We present an analytical theory for this steady state, and demonstrate it to be in excellent agreement with our simulation results.

cond-mat.stat-mech↗

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↗