Phase-field model of long-time glass-like relaxation in binary fluid mixtures

We present a new phase-field model for binary fluids exhibiting typical signatures of self-glassiness, such as long-time relaxation, ageing and long-term dynamical arrest. The present model allows the cost of building an interface to become locally zero, while preserving global positivity of the overall surface tension. An important consequence of this property, which we prove analytically, is the emergence of compact configurations of fluid density. Owing to their finite-size support, these "compactons" can be arbitrarily superposed, thereby providing a direct link between the ruggedness of the free-energy landscape and morphological complexity in configurational space. The analytical picture is supported by numerical simulations of the proposed phase-field equation.Comment: 5 Pages, 6 Figure

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 \& A. Ajdari ({\em Phys. Rev. Lett.} {\bf 103}, 036001 (2009)), 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. Compactons 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.Comment: 33 pages, 10 figure

On the impact of controlled wall roughness shape on the flow of a soft-material

We explore the impact of geometrical corrugations on the near-wall flow properties of a soft-material driven in a confined rough microchannel. By means of numerical simulations, we perform a quantitative analysis of the relation between the flow rate $\Phi$ and the wall stress $\sigma_w$ for a number of setups, by changing both the roughness values as well as the roughness shape. Roughness suppresses the flow, with the existence of a characteristic value of $\sigma_w$ at which flow sets in. Just above the onset of flow, we quantitatively analyze the relation between $\Phi$ and $\sigma_w$. While for smooth walls a linear dependency is observed, steeper behaviours are found to set in by increasing wall roughness. The variation of the steepness, in turn, depends on the shape of the wall roughness, wherein gentle steepness changes are promoted by a variable space localization of the roughness

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 {\it 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 cooperative 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 long-range amorphous order at the yield stress threshold

Mesoscopic lattice Boltzmann modeling of soft-glassy systems: theory and simulations

A multi-component lattice Boltzmann model recently introduced (R. Benzi et al. Phys. Rev. Lett 102, 026002 (2009)) to describe some dynamical behaviors of soft-flowing materials is theoretically analyzed. Equilibrium and transport properties are derived within the framework of a continuum free-energy formulation, and checked against numerical simulations. Due to the competition between short-range inter-species repulsion and mid-range intra-species attraction, the model is shown to give rise to a very rich configurational dynamics of the density field, exhibiting numerous features of soft-flowing materials, such as long-time relaxation due to caging effects, enhanced viscosity and structural arrest, ageing under moderate shear and shear-thinning flow above a critical shear threshold.Comment: 25 pages, 17 figures, submitted to Journal of chemical physics

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.Comment: 21 Pages, 9 figure

Stochastic resonance in soft-glassy materials

Flow in soft-glasses occurs via a sequence of reversible elastic deformations and local irreversible plastic rearrangements. Yield events in the material cause kicks adding up to an effectively thermal noise, an intuition that has inspired the development of phenomenological models aiming at explaining the main features of soft-glassy rheology. In this letter, we provide a specific scenario for such mechanical activation, based on a general paradigm of non-equilibrium statistical mechanics, namely {\it stochastic resonance}. By using mesoscopic simulations of emulsion droplets subject to an oscillatory strain, we characterize the response of the system and highlight a resonance-like behavior in the plastic rearrangements. This confirms that the synchronization of the system response to an external time-dependent load is triggered by the mechanical noise resulting from disordered configurations (polydispersity)