arXiv subjects

M. E. Cates

Publications and source records attributed to M. E. Cates.

At least 109 records · Page 6Linked to original sources

arXiv2003

Schematic mode coupling theories for shear thinning, shear thickening, and jamming

Mode coupling theory (MCT) appears to explain several, though not all, aspects of the glass transition in colloids (particularly when short-range attractions are present). Developments of MCT, from rational foundations in statistical mechanics, account qualitatively for nonlinear flow behaviour such as the yield stress of a hard-sphere colloidal glass. Such theories so far only predict shear thinning behaviour, whereas in real colloids both shear thinning and shear thickening can be found. The latter observation can, however, be rationalised by postulating an MCT vertex that is not only a decreasing function of strain rate (as found from first principles) but also an increasing function of stress. Within a highly simplified, schematic MCT model this can lead not only to discontinuous shear thickening but also to complete arrest of a fluid phase under the influence of an external stress (`full jamming').

cond-mat.soft↗

arXiv2003

Tensorial Constitutive Models for Disordered Foams, Dense Emulsions, and other Soft Nonergodic Materials

In recent years, the paradigm of `soft glassy matter' has been used to describe diverse nonergodic materials exhibiting strong local disorder and slow mesoscopic rearrangement. As so far formulated, however, the resulting `soft glassy rheology' (SGR) model treats the shear stress in isolation, effectively `scalarizing' the stress and strain rate tensors. Here we offer generalizations of the SGR model that combine its nontrivial aging and yield properties with a tensorial structure that can be specifically adapted, for example, to the description of fluid film assemblies or disordered foams.

cond-mat.soft↗

arXiv2003

Jamming transitions in a schematic model of suspension rheology

We study the steady-state response to applied stress in a simple scalar model of sheared colloids. Our model is based on a schematic (F2) model of the glass transition, with a memory term that depends on both stress and shear rate. For suitable parameters, we find transitions from a fluid to a nonergodic, jammed state, showing zero flow rate in an interval of applied stress. Although the jammed state is a glass, we predict that jamming transitions have an analytical structure distinct from that of the conventional mode coupling glass transition. The static jamming transition we discuss is also distinct from hydrodynamic shear thickening.

cond-mat.soft↗

arXiv2003

A possible new phase of antagonistic nematogens in a disorienting field

A simple model is proposed for nematogenic molecules that favor perpendicular orientations as well as parallel ones. (Charged rods, for example, show this antagonistic tendency.) When a small disorienting field is applied along $z$, a low density phase $N_-$ of nematic order parameter $S_z<0$ coexists with a dense biaxial nematic $N_b$. (At zero field, $N_-$ becomes isotropic and $N_b$ uniaxial.) But at stronger fields, a new phase $N_{+4}$, invariant under $π/2$ rotations around the field axis, appears in between $N_-$ and $N_b$. Prospects for finding the $N_{+4}$ phase experimentally are briefly discussed.

cond-mat.soft↗

arXiv2003

Model fluid in a porous medium: results for a Bethe lattice

We consider a lattice gas with quenched impurities or `quenched-annealed binary mixture' on the Bethe lattice. The quenched part represents a porous matrix in which the (annealed) lattice gas resides. This model features the 3 main factors of fluids in random porous media: wetting, randomness and confinement. The recursive character of the Bethe lattice enables an exact treatment, whose key ingredient is an integral equation yielding the one-particle effective field distribution. Our analysis shows that this distribution consists of two essentially different parts. The first one is a continuous spectrum and corresponds to the macroscopic volume accessible to the fluid, the second is discrete and comes from finite closed cavities in the porous medium. Those closed cavities are in equilibrium with the bulk fluid within the grand canonical ensemble we use, but are inaccessible in real experimental situations. Fortunately, we are able to isolate their contributions. Separation of the discrete spectrum facilitates also the numerical solution of the main equation. The numerical calculations show that the continuous spectrum becomes more and more rough as the temperature decreases, and this limits the accuracy of the solution at low temperatures.

cond-mat.soft↗

arXiv2003

Phase Separation in Binary Fluid Mixtures with Continuously Ramped Temperature

We consider the demixing of a binary fluid mixture, under gravity, which is steadily driven into a two phase region by slowly ramping the temperature. We assume, as a first approximation, that the system remains spatially isothermal, and examine the interplay of two competing nonlinearities. One of these arises because the supersaturation is greatest far from the meniscus, creating inversion of the density which can lead to fluid motion; although isothermal, this is somewhat like the Benard problem (a single-phase fluid heated from below). The other is the intrinsic diffusive instability which results either in nucleation or in spinodal decomposition at large supersaturations. Experimental results on a simple binary mixture show interesting oscillations in heat capacity and optical properties for a wide range of ramp parameters. We argue that these oscillations arise under conditions where both nonlinearities are important.

cond-mat.soft↗

arXiv2002

Role of inertia in two-dimensional deformation and breakup of a droplet

We investigate by Lattice Boltzmann methods the effect of inertia on the deformation and break-up of a two-dimensional fluid droplet surrounded by fluid of equal viscosity (in a confined geometry) whose shear rate is increased very slowly. We give evidence that in two dimensions inertia is {\em necessary} for break-up, so that at zero Reynolds number the droplet deforms indefinitely without breaking. We identify two different routes to breakup via two-lobed and three-lobed structures respectively, and give evidence for a sharp transition between these routes as parameters are varied.

cond-mat.soft↗

arXiv2002

A solvable senescence model showing a mortality plateau

We present some analytic results for the steady states of the Penna model of sen escence, generalised to allow genetically identical individuals to die at differ ent ages via an arbitrary survival function. Modelling this with a Fermi functio n (of modest width) we obtain a clear mortality plateau late in life: something that has so far eluded explanation within such mutation accumulation models. This suggests that factors causing variable mortality withi n genetically identical subpopulations, which include environmental effects, may be essential to understanding the mortality plateau seen in many real species.

cond-mat.soft↗

arXiv2002

Arrest and flow of colloidal glasses

I review recent progress in understanding the arrest and flow behaviour of colloidal glasses, based on mode coupling theory (MCT) and related approaches. MCT has had notable recent successes in predicting the re-entrant arrest behaviour of colloids with short range attractions. Developments based upon it offer important steps towards calculating, from rational foundations in statistical mechanics, nonlinear flow parameters such as the yield stress of a colloidal glass. An important open question is why MCT works so well.

cond-mat.soft↗

arXiv2002

Landau Expansion for the Critical Point of a Polydisperse System

The effect of polydispersity on the phase diagram of a simple binary mixture is to split the binodal curve into cloud and shadow curves that cross at the critical point (which, in general, is not at the maximum of either curve). Recent theories of polydispersity have shown, in favorable cases, how to project the (infinite-dimensional) free energy of the polydisperse system into a low dimensional space of `moment densities'. We address here the issue of how to construct a Landau expansion from the projected free energy. For the simplest case where the excess free energy depends on one moment density $ρ_1$ (this includes Flory Huggins theory for length-polydisperse chains) we show that the minimal expansion remains quartic in $ρ_1$ but nonetheless has seven independent coefficients, not two. When this expansion is handled correctly all the peculiar qualitative features of the polydisperse phase diagram are recovered, as are the slopes of the cloud and shadow curves, and the curvature of the cloud. However, to correctly predict the curvature of the shadow, certain fifth order terms must be retained. We also consider the phase diagram on the temperature-pressure plane, where the coexistence line broadens into a region. In general, the critical point lies between the point of maximum temperature and the point of maximum pressure on the perimeter of this region. This behaviour is again captured by the Landau expansion.

cond-mat.stat-mech↗

arXiv2002

Dynamics of Polydisperse Polymer Mixtures

We develop a general analysis of the diffusive dynamics of polydisperse polymers in the presence of chemical potential gradients, within the context of the tube model (with all species entangled). We obtain a set of coupled dynamical equations for the time evolution of the polymeric densities with explicitly derived coefficients. For the case of chemical polydispersity (a set of chains that are identical except for having a continuous spectrum of enthalpic interaction strengths) the coupled equations can be fully solved in certain cases. For these we study the linearised mode spectrum following a quench through the spinodal, with and without a passive (polymeric) solvent. We also study the more conventional case of length polydisperse chains in a poor solvent.

cond-mat.soft↗

arXiv2002

Rheological Chaos in a Scalar Shear-Thickening Model

We study a simple scalar constitutive equation for a shear-thickening material at zero Reynolds number, in which the shear stress σis driven at a constant shear rate \dotγand relaxes by two parallel decay processes: a nonlinear decay at a nonmonotonic rate R(σ_1) and a linear decay at rate λσ_2. Here σ_{1,2}(t) = τ_{1,2}^{-1}\int_0^tσ(t')\exp[-(t-t')/τ_{1,2}] {\rm d}t' are two retarded stresses. For suitable parameters, the steady state flow curve is monotonic but unstable; this arises when τ_2>τ_1 and 0>R'(σ)>-λso that monotonicity is restored only through the strongly retarded term (which might model a slow evolution of material structure under stress). Within the unstable region we find a period-doubling sequence leading to chaos. Instability, but not chaos, persists even for the case τ_1\to 0. A similar generic mechanism might also arise in shear thinning systems and in some banded flows.

cond-mat.soft↗

arXiv2001

Jamming, hysteresis and oscillation in scalar models for shear thickening

We investigate shear thickening and jamming within the framework of a family of spatially homogeneous, scalar rheological models. These are based on the `soft glassy rheology' model of Sollich et al. [Phys. Rev. Lett. 78, 2020 (1997)], but with an effective temperature x that is a decreasing function of either the global stress σor the local strain l. For appropiate x=x(σ), it is shown that the flow curves include a region of negative slope, around which the stress exhibits hysteresis under a cyclically varying imposed strain rate \gd. A subclass of these x(σ) have flow curves that touch the \gd=0 axis for a finite range of stresses; imposing a stress from this range {\em jams} the system, in the sense that the strain γcreeps only logarithmically with time t, γ(t)\sim\ln t. These same systems may produce a finite asymptotic yield stress under an imposed strain, in a manner that depends on the entire stress history of the sample, a phenomenon we refer to as history--dependent jamming. In contrast, when x=x(l) the flow curves are always monotonic, but we show that some x(l) generate an oscillatory strain response for a range of steady imposed stresses. Similar spontaneous oscillations are observed in a simplified model with fewer degrees of freedom. We discuss this result in relation to the temporal instabilities observed in rheological experiments and stick--slip behaviour found in other contexts, and comment on the possible relationship with `delay differential equations' that are known to produce oscillations and chaos.

cond-mat.soft↗

arXiv2001

Rheological instability in a simple shear thickening model

We study the strain response to steady imposed stress in a spatially homogeneous, scalar model for shear thickening, in which the local rate of yielding Γ(l) of mesoscopic `elastic elements' is not monotonic in the local strain l. Despite this, the macroscopic, steady-state flow curve (stress vs. strain rate) is monotonic. However, for a broad class of Γ(l), the response to steady stress is not in fact steady flow, but spontaneous oscillation. We discuss this finding in relation to other theoretical and experimental flow instabilities. Within the parameter ranges we studied, the model does not exhibit rheo-chaos.

cond-mat.soft↗

arXiv2001

Ring-Driven Shear Thickening in Wormlike Micelles?

The shear-thickening behaviour of wormlike micelles, at concentrations just below overlap, remains unexplained. In some cases it has recently been confirmed that very slow relaxations must be present even in the quiescent state -- for example, the shear thickening properties can depend on earlier thermal cycling. We present a speculative scenario based on the presence, just below the (apparent) overlap threshold, of large rings whose linking and delinking kinetics control the shear thickening process. Equilibration between rings and open chains in turn controls the slow relaxations.

cond-mat.soft↗

arXiv2001

A practical density functional for polydisperse polymers

The Flory Huggins equation of state for monodisperse polymers can be turned into a density functional by adding a square gradient term, with a coefficient fixed by appeal to RPA (random phase approximation). We present instead a model nonlocal functional in which each polymer is replaced by a deterministic, penetrable particle of known shape. This reproduces the RPA and square gradient theories in the small deviation and/or weak gradient limits, and can readily be extended to polydisperse chains. The utility of the new functional is shown for the case of a polydisperse polymer solution at coexistence in a poor solvent.

cond-mat.soft↗

arXiv2001

Binary fluid demixing: The crossover region

By performing lattice Boltzmann simulations of a binary mixture, we scrutinize the dynamical scaling hypothesis for the spinodal decomposition of binary mixtures for the crossover region, i.e. the region of parameters in the growth curve where neither inertia nor viscous forces dominate the coarsening process. Our results give no evidence for a breakdown of scaling in this region, as might arise if the process were limited by molecular scale physics at the point of fluid pinch-off between domains. A careful data analysis allows us to refine previous estimates on the width of the crossover region which is somewhat narrower than previously reported.

cond-mat.soft↗

arXiv2001

Osmotic Stabilisation of Concentrated Emulsions and Foams

In the absence of coalescence, coarsening of emulsions (and foams) is controlled by molecular diffusion of dispersed phase between droplets/bubbles. Studies of dilute emulsions have shown how the osmotic pressure of a trapped species within droplets can ``osmotically stabilise'' the emulsion. Webster and Cates (Langmuir, 1998, 14, 2068-2079) gave rigorous criteria for osmotic stabilisation of mono- and polydisperse emulsions, in the dilute regime. We consider here whether analogous criteria exist for the osmotic stabilisation of mono- and polydisperse concentrated emulsions and foams, and suggest that the pressure differences driving coarsening are small compared to the mean Laplace pressure. An exact calculation confirms this for a monodisperse 2D model, finding a bubble's pressure as P_i = P + Pi + P_i^G, with P, Pi the atmospheric and osmotic pressures, and P_i^G a ``geometric pressure'' that reduces to the Laplace pressure only for a spherical bubble. For Princen's 2D emulsion model, P_i^G is only 5% larger in the dry limit than the dilute limit. We conclude that osmotic stabilisation of dense systems typically requires a pressure of trapped molecules in each droplet that is comparable to the Laplace pressures the same droplets would have if spherical, as opposed to the much larger Laplace pressures present in the system. We study coarsening of foams and concentrated emulsions when there is insufficient of the trapped species present. Rate-limiting mechanisms are considered, their applicability and associated droplet growth rates discussed. In a concentrated foam or emulsion, a finite yield threshold for droplet rearrangement may be enough to prevent coarsening of the remainder.

cond-mat.soft↗