Start-up inertia as an origin for heterogeneous flow.

For quite some time nonmonotonic flow curve was thought to be a requirement for shear banded flows in complex fluids. Thus, in simple yield stress fluids shear banding was considered to be absent. Recent spatially resolved rheological experiments have found simple yield stress fluids to exhibit shear banded flow profiles. One proposed mechanism for the initiation of such transient shear banding process has been a small stress heterogeneity rising from the experimental device geometry. Here, using computational fluid dynamics methods, we show that transient shear banding can be initialized even under homogeneous stress conditions by the fluid start-up inertia, and that such mechanism indeed is present in realistic experimental conditions.

Geometrical model for martensitic phase transitions: Understanding criticality and weak universality during microstructure growth.

A simple model for the growth of elongated domains (needle-like) during a martensitic phase transition is presented. The model is purely geometric and the only interactions are due to the sequentiality of the kinetic problem and to the excluded volume, since domains cannot retransform back to the original phase. Despite this very simple interaction, numerical simulations show that the final observed microstructure can be described as being a consequence of dipolar-like interactions. The model is analytically solved in 2D for the case in which two symmetry related domains can grow in the horizontal and vertical directions. It is remarkable that the solution is analytic both for a finite system of size L×L and in the thermodynamic limit L→∞, where the elongated domains become lines. Results prove the existence of criticality, i.e., that the domain sizes observed in the final microstructure show a power-law distribution characterized by a critical exponent. The exponent, nevertheless, depends on the relative probabilities of the different equivalent variants. The results provide a plausible explanation of the weak universality of the critical exponents measured during martensitic transformations in metallic alloys. Experimental exponents show a monotonous dependence with the number of equivalent variants that grow during the transition.

Apparent wall slip in non-Brownian hard-sphere suspensions.

We analyze apparent wall slip, the reduction of particle concentration near the wall, in hard-sphere suspensions at concentrations well below the jamming limit utilizing a continuum level diffusion model. The approach extends a constitutive equation proposed earlier with two additional potentials describing the effects of gravitation and wall-particle repulsion. We find that although both mechanisms are shear independent by nature, due to the shear-rate-dependent counter-balancing particle migration fluxes, the resulting net effect is non-linearly shear dependent, causing larger slip at small shear rates. In effect, this shows up in the classically measured flow curves as a mild shear thickening regime at the transition from small to intermediate shear rates.

Dynamic hysteresis in the rheology of complex fluids.

Recently, rheological hysteresis has been studied systematically in a wide range of complex fluids combining global rheology and time-resolved velocimetry. In this paper we present an analysis of the roles of the three most fundamental mechanisms in simple-yield-stress fluids: structure dynamics, viscoelastic response, and spatial flow heterogeneities, i.e., time-dependent shear bands. Dynamical hysteresis simulations are done analogously to rheological ramp-up and -down experiments on a coupled model which incorporates viscoelasticity and time-dependent structure evolution. Based on experimental data, a coupling between hysteresis measured from the local velocity profiles and that measured from the global flow curve has been suggested. According to the present model, even if transient shear banding appears during the shear ramps, in typical narrow-gap devices, only a small part of the hysteretic response can be attributed to heterogeneous flow. This results in decoupling of the hysteresis measured from the local velocity profiles and the global flow curve, demonstrating that for an arbitrary time-dependent rheological response this proposed coupling can be very weak.

Avalanches in compressed porous SiO(2)-based materials.

The failure dynamics in SiO(2)-based porous materials under compression, namely the synthetic glass Gelsil and three natural sandstones, has been studied for slowly increasing compressive uniaxial stress with rates between 0.2 and 2.8 kPa/s. The measured collapsed dynamics is similar to Vycor, which is another synthetic porous SiO(2) glass similar to Gelsil but with a different porous mesostructure. Compression occurs by jerks of strain release and a major collapse at the failure point. The acoustic emission and shrinking of the samples during jerks are measured and analyzed. The energy of acoustic emission events, its duration, and waiting times between events show that the failure process follows avalanche criticality with power law statistics over ca. 4 decades with a power law exponent ɛ≃ 1.4 for the energy distribution. This exponent is consistent with the mean-field value for the collapse of granular media. Besides the absence of length, energy, and time scales, we demonstrate the existence of aftershock correlations during the failure process.

Rheology dynamics of aggregating colloidal suspensions.

We study a colloidal model based on population balances in the context of complex fluid rheology. Two typical particle microstructure kinetics, orthokinetic, collisions due to shear, and perikinetic, collisions due to Brownian motion, are found to appear at continuum as different flow behaviors - those having monotonic and non-monotonic flow curves, respectively. Solving the colloidal model together with the 1D Stokes equation for laminar, incompressible flow with Couette boundary conditions, allows bridging the gap between the rheological experiments and the microstructural modeling. The analysis of such a model reveals that orthokinetic particle suspensions have a uniquely defined, continuous steady state shear profile, whereas suspensions in which also perikinetic collisions are present, the steady state can be shear banded and non-unique. Thus, the shear banded configurations at a steady state are found to depend on the initial conditions and the collision kinetics of the system. At high shear rates all the studied cases show continuous shear profiles.

Evolution of the average avalanche shape with the universality class.

A multitude of systems ranging from the Barkhausen effect in ferromagnetic materials to plastic deformation and earthquakes respond to slow external driving by exhibiting intermittent, scale-free avalanche dynamics or crackling noise. The avalanches are power-law distributed in size, and have a typical average shape: these are the two most important signatures of avalanching systems. Here we show how the average avalanche shape evolves with the universality class of the avalanche dynamics by employing a combination of scaling theory, extensive numerical simulations and data from crack propagation experiments. It follows a simple scaling form parameterized by two numbers, the scaling exponent relating the average avalanche size to its duration and a parameter characterizing the temporal asymmetry of the avalanches. The latter reflects a broken time-reversal symmetry in the avalanche dynamics, emerging from the local nature of the interaction kernel mediating the avalanche dynamics.

Statistical similarity between the compression of a porous material and earthquakes.

It has long been stated that there are profound analogies between fracture experiments and earthquakes; however, few works attempt a complete characterization of the parallels between these so separate phenomena. We study the acoustic emission events produced during the compression of Vycor (SiO(2)). The Gutenberg-Richter law, the modified Omori's law, and the law of aftershock productivity hold for a minimum of 5 decades, are independent of the compression rate, and keep stationary for all the duration of the experiments. The waiting-time distribution fulfills a unified scaling law with a power-law exponent close to 2.45 for long times, which is explained in terms of the temporal variations of the activity rate.

Transient shear banding in time-dependent fluids.

We study the dynamics of shear-band formation and evolution using a simple rheological model. The description couples the local structure and viscosity to the applied shear stress. We consider in detail the Couette geometry, where the model is solved iteratively with the Navier-Stokes equation to obtain the time evolution of the local velocity and viscosity fields. It is found that the underlying reason for dynamic effects is the nonhomogeneous shear distribution, which is amplified due to a positive feedback between the flow field and the viscosity response of the shear thinning fluid. This offers a simple explanation for the recent observations of transient shear banding in time-dependent fluids. Extensions to more complicated rheological systems are considered.

Work distributions in the T=0 random field Ising model.

We perform a numerical study of the three-dimensional random-field Ising model at T=0. We compare work distributions along metastable trajectories obtained with the single-spin flip dynamics with the distribution of the internal energy change along equilibrium trajectories. The goal is to investigate the possibility of extending the Crooks fluctuation theorem [G. E. Crooks, Phys. Rev. E. 60, 2721 (1999)] to zero temperature when, instead of the standard ensemble statistics, one considers the ensemble generated by the quenched disorder. We show that a simple extension of Crooks fails close to the disordered induced equilibrium phase transition due to the fact that work and internal energy distributions are very asymmetric.