Cooperativity flows and shear-bandings: a statistical field theory approach.

Cooperativity effects have been proposed to explain the non-local rheology in the dynamics of soft jammed systems. Based on the analysis of the free-energy model proposed by L. Bocquet, A. Colin and A. Ajdari, Phys. Rev. Lett., 2009, 103, 036001, we show that cooperativity effects resulting from the non-local nature of the fluidity (inverse viscosity) are intimately related to the emergence of shear-banding configurations. This connection materializes through the onset of inhomogeneous compact solutions (compactons), wherein the fluidity is confined to finite-support subregions of the flow and strictly zero elsewhere. The compacton coexistence with regions of zero fluidity ("non-flowing vacuum") is shown to be stabilized by the presence of mechanical noise, which ultimately shapes up the equilibrium distribution of the fluidity field, the latter acting as an order parameter for the flow-noflow transitions occurring in the material.

Internal dynamics and activated processes in soft-glassy materials.

Plastic rearrangements play a crucial role in the characterization of soft-glassy materials, such as emulsions and foams. Based on numerical simulations of soft-glassy systems, we study the dynamics of plastic rearrangements at the hydrodynamic scales where thermal fluctuations can be neglected. Plastic rearrangements require an energy input, which can be either provided by external sources, or made available through time evolution in the coarsening dynamics, in which the total interfacial area decreases as a consequence of the slow evolution of the dispersed phase from smaller to large droplets/bubbles. We first demonstrate that our hydrodynamic model can quantitatively reproduce such coarsening dynamics. Then, considering periodically oscillating strains, we characterize the number of plastic rearrangements as a function of the external energy-supply, and show that they can be regarded as activated processes induced by a suitable "noise" effect. Here we use the word noise in a broad sense, referring to the internal non-equilibrium dynamics triggered by spatial random heterogeneities and coarsening. Finally, by exploring the interplay between the internal characteristic time-scale of the coarsening dynamics and the external time-scale associated with the imposed oscillating strain, we show that the system exhibits the phenomenon of stochastic resonance, thereby providing further credit to the mechanical activation scenario.

Direct evidence of plastic events and dynamic heterogeneities in soft-glasses.

By using fluid-kinetic simulations of confined and concentrated emulsion droplets, we investigate the nature of space non-homogeneity in soft-glassy dynamics and provide quantitative measurements of the statistical features of plastic events in the proximity of the yield-stress threshold. Above the yield stress, our results show the existence of a finite stress correlation scale, which can be mapped directly onto the cooperativity scale, recently introduced in the literature to capture non-local effects in the soft-glassy dynamics. In this regime, the emergence of a separate boundary (wall) rheology with higher fluidity than the bulk is highlighted in terms of near-wall spontaneous segregation of plastic events. Near the yield stress, where the cooperativity scale cannot be estimated with sufficient accuracy, the system shows a clear increase of the stress correlation scale, whereas plastic events exhibit intermittent clustering in time, with no preferential spatial location. A quantitative measurement of the space-time correlation associated with the motion of the interface of the droplets is key to spot the elastic rigidity of the system.

Growth, competition and cooperation in spatial population genetics.

We study an individual based model describing competition in space between two different alleles. Although the model is similar in spirit to classic models of spatial population genetics such as the stepping stone model, here however space is continuous and the total density of competing individuals fluctuates due to demographic stochasticity. By means of analytics and numerical simulations, we study the behavior of fixation probabilities, fixation times, and heterozygosity, in a neutral setting and in cases where the two species can compete or cooperate. By concluding with examples in which individuals are transported by fluid flows, we argue that this model is a natural choice to describe competition in marine environments.

Heterogeneous diffuse interfaces: a new mechanism for arrested coarsening in binary mixtures. Heterogeneous diffuse interfaces.

We discuss the dynamics of binary fluid mixtures in which surface tension density is allowed to become locally negative within the interface, while still preserving positivity of the overall surface tension (heterogeneous diffuse interface). Numerical simulations of two-dimensional Ginzburg-Landau phase field equations implementing such mechanism and including hydrodynamic motion, show evidence of dynamically arrested domain coarsening. Under specific conditions on the functional form of the surface tension density, dynamical arrest can be interpreted in terms of the collective dynamics of metastable, non-linear excitations of the density field, named compactons, as they are localized to finite-size regions of configuration space and strictly zero elsewhere. Aside from compactons, the heterogeneous diffuse interface scenario appears to provide a robust mechanism for the interpretation of many aspects of soft-glassy behaviour in binary fluid mixtures.

Phase-field model of long-time glasslike relaxation in binary fluid mixtures.

We present a new phase-field model for binary fluids, exhibiting typical signatures of soft-glassy behavior, such as long-time relaxation, aging, and long-term dynamical arrest. The present model allows the cost of building an interface to vanish locally within the interface, while preserving positivity of the overall surface tension. A crucial consequence of this property, which we prove analytically, is the emergence of free-energy minimizing density configurations, hereafter named "compactons," to denote their property of being localized to a finite-size region of space and strictly zero elsewhere (no tails). Thanks to compactness, any arbitrary superposition of compactons still is a free-energy minimizer, which provides a direct link between the complexity of the free-energy landscape and the morphological complexity of configurational space.

Universal intermittent properties of particle trajectories in highly turbulent flows.

We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R{lambda}in[120:740]. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. Parisi-Frisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.

Generalized lattice Boltzmann method with multirange pseudopotential.

The physical behavior of a class of mesoscopic models for multiphase flows is analyzed in details near interfaces. In particular, an extended pseudopotential method is developed, which permits to tune the equation of state and surface tension independently of each other. The spurious velocity contributions of this extended model are shown to vanish in the limit of high grid refinement and/or high order isotropy. Higher order schemes to implement self-consistent forcings are rigorously computed for 2d and 3d models. The extended scenario developed in this work clarifies the theoretical foundations of the Shan-Chen methodology for the lattice Boltzmann method and enhances its applicability and flexibility to the simulation of multiphase flows to density ratios up to O(100).

Surface roughness-hydrophobicity coupling in microchannel and nanochannel flows.

An approach based on a lattice version of the Boltzmann kinetic equation for describing multiphase flows in nano- and microcorrugated devices is proposed. We specialize it to describe the wetting-dewetting transition of fluids in the presence of nanoscopic grooves etched on the boundaries. This approach permits us to retain the essential supramolecular details of fluid-solid interactions without surrendering--actually boosting--the computational efficiency of continuum methods. The method is used to analyze the importance of conspiring effects between hydrophobicity and roughness on the global mass flow rate of the microchannel. In particular we show that smart surfaces can be tailored to yield very different mass throughput by changing the bulk pressure. The mesoscopic method is also validated quantitatively against the molecular dynamics results of [Cottin-Bizonne, Nat. Mater. 2, 237 (2003)].

Mesoscopic modeling of a two-phase flow in the presence of boundaries: The contact angle.

We present a mesoscopic model, based on the Boltzmann equation, for the interaction between a solid wall and a nonideal fluid. We present an analytic derivation of the contact angle in terms of the surface tension between the liquid-gas, the liquid-solid, and the gas-solid phases. We study the dependency of the contact angle on the two free parameters of the model, which determine the interaction between the fluid and the boundaries, i.e. the equivalent of the wall density and of the wall-fluid potential in molecular dynamics studies. We compare the analytical results obtained in the hydrodynamical limit for the density profile and for the surface tension expression with the numerical simulations. We compare also our two-phase approach with some exact results obtained by E. Lauga and H. Stone [J. Fluid. Mech. 489, 55 (2003)] and J. Philip [Z. Angew. Math. Phys. 23, 960 (1972)] for a pure hydrodynamical incompressible fluid based on Navier-Stokes equations with boundary conditions made up of alternating slip and no-slip strips. Finally, we show how to overcome some theoretical limitations connected with the discretized Boltzmann scheme proposed by X. Shan and H. Chen [Phys. Rev. E 49, 2941 (1994)] and we discuss the equivalence between the surface tension defined in terms of the mechanical equilibrium and in terms of the Maxwell construction.

Double scaling and intermittency in shear dominated flows.

The nature of intermittency in shear dominated flows changes with respect to homogeneous and isotropic conditions since the process of energy transfer is affected by the turbulent kinetic energy production associated with the Reynolds stresses. For these flows, a new form of refined similarity law is able to describe the increased level of intermittency. Ideally a length scale associated with the mean shear separates the two ranges, i.e., the classical Kolmogorov-like inertial range, below, and the shear dominated range, above. In the present paper we give evidence of the coexistence of the two regimes and we support the conjecture that the statistical properties of the dissipation field are practically insensible to the mean shear. This allows for a theoretical prediction of the scaling exponents of structure functions in the shear dominated range based on the known intermittency corrections for isotropic flows. The prediction is found to closely match the available numerical and experimental data. The analysis shows that the larger anisotropic scales of shear turbulence display universality, and determines the modality by which the dissipation field fixes the properties of turbulent fluctuations in the shear dominated range.

Substrate competition in postischemic myocardium. Effect of substrate availability during reperfusion on metabolic and contractile recovery in isolated rat hearts.

Normal myocardium can derive energy for contraction and relaxation from oxidative metabolism of a variety of substrates. This investigation examined the influence of substrate availability early during reperfusion on the substrate pattern of oxidative metabolism and recovery of contractile function. For this purpose, isovolumically beating isolated rat hearts, perfused retrogradely with erythrocyte-supplemented buffer containing 0.4 mmol/L palmitate and 11 mmol/L glucose, were subjected to 40 minutes of no-flow ischemia. Hearts were reperfused with medium containing selected concentrations of palmitate and glucose. The substrate pattern for oxidative metabolism was determined on the basis of myocardial release of 14CO2 after equilibration of the hearts during the initial 15 minutes of reperfusion with either [1-14C]palmitate or [U-14C]glucose. In continuously perfused control hearts, glucose oxidation was largely inhibited by palmitate. During postischemic reperfusion, oxidation of glucose was increased by 59% (P < .05) and 467% (P <.01) in hearts reperfused after the ischemic period with 11 mmol/L glucose plus 0.4 or 1.2 mmol/L palmitate, respectively. Oxidation of palmitate was concomitantly reduced during reperfusion at low (0.4 mmol/L) but not at high (1.2 mmol/L) palmitate concentration. Compared with hearts reperfused with medium containing 0.4 mmol/L palmitate as sole substrate, hearts reperfused with medium containing 11 mmol/L glucose with 0.4 mmol/L palmitate exhibited lower left ventricular diastolic pressure (69 +/- 5 versus 90 +/- 3 mm Hg [mean +/- SEM], P < .05), less release of creatine kinase (31 +/- 5 versus 59 +/- 7 U/g wet wt, P < .05), and better recovery of left ventricular pressure development (26 +/- 9 versus 6 +/- 4 mm Hg, P < .05). Omission of palmitate or increasing the palmitate concentration to 1.2 mmol/L did not significantly alter postischemic myocardial contracture and enzyme release. The findings support the view that glucose oxidation early during reperfusion may be crucial for functional recovery. The results further indicate that interaction of substrates of oxidative metabolism is altered in severely injured postischemic myocardium. Inhibition of glucose oxidation by fatty acids was partially reversed during reperfusion.