Influence of boundary conditions on yielding in a soft glassy material

The yielding behavior of a sheared Laponite suspension is investigated within a 1 mm gap under two different boundary conditions. No-slip conditions, ensured by using rough walls, lead to shear localization as already reported in various soft glassy materials. When apparent wall slip is allowed using a smooth geometry, the sample is shown to break up into macroscopic solid pieces that get slowly eroded by the surrounding fluidized material up to the point where the whole sample is fluid. Such a drastic effect of boundary conditions on yielding suggests the existence of some macroscopic characteristic length that could be connected to cooperativity effects in jammed materials under shear.Comment: 4 pages, 5 figure

Shear-induced fragmentation of Laponite suspensions

Simultaneous rheological and velocity profile measurements are performed in a smooth Couette geometry on Laponite suspensions seeded with glass microspheres and undergoing the shear-induced solid-to-fluid (or yielding) transition. Under these slippery boundary conditions, a rich temporal behaviour is uncovered, in which shear localization is observed at short times, that rapidly gives way to a highly heterogeneous flow characterized by intermittent switching from plug-like flow to linear velocity profiles. Such a temporal behaviour is linked to the fragmentation of the initially solid sample into blocks separated by fluidized regions. These solid pieces get progressively eroded over time scales ranging from a few minutes to several hours depending on the applied shear rate $\dot{\gamma}$. The steady-state is characterized by a homogeneous flow with almost negligible wall slip. The characteristic time scale for erosion is shown to diverge below some critical shear rate $\dot{\gamma}^\star$ and to scale as $(\dot{\gamma}-\dot{\gamma}^\star)^{-n}$ with $n\simeq 2$ above $\dot{\gamma}^\star$. A tentative model for erosion is discussed together with open questions raised by the present results.Comment: 19 pages, 13 figures, submitted to Soft Matte

Yielding dynamics of a Herschel-Bulkley fluid: a critical-like fluidization behaviour

The shear-induced fluidization of a carbopol microgel is investigated during long start-up experiments using combined rheology and velocimetry in Couette cells of varying gap widths and boundary conditions. As already described in [Divoux et al., {\it Phys. Rev. Lett.}, 2010, {\bf 104}, 208301], we show that the fluidization process of this simple yield stress fluid involves a transient shear-banding regime whose duration $\tau_f$ decreases as a power law of the applied shear rate \gp. Here we go one step further by an exhaustive investigation of the influence of the shearing geometry through the gap width $e$ and the boundary conditions. While slip conditions at the walls seem to have a negligible influence on the fluidization time $\tau_f$, different fluidization processes are observed depending on \gp and $e$: the shear band remains almost stationary for several hours at low shear rates or small gap widths before strong fluctuations lead to a homogeneous flow, whereas at larger values of \gp or $e$, the transient shear band is seen to invade the whole gap in a much smoother way. Still, the power-law behaviour appears as very robust and hints to critical-like dynamics. To further discuss these results, we propose (i) a qualitative scenario to explain the induction-like period that precedes full fluidization and (ii) an analogy with critical phenomena that naturally leads to the observed power laws if one assumes that the yield point is the critical point of an underlying out-of-equilibrium phase transition.Comment: 16 pages, 14+2 figures, published in Soft Matte

Transient Shear Banding in a Simple Yield Stress Fluid

We report a large set of experimental data which demonstrates that a simple yield stress fluid, i.e. which does not present aging or thixotropy, exhibits transient shear banding before reaching a steady state characterized by a homogeneous, linear velocity profile. The duration of the transient regime decreases as a power law with the applied shear rate $\dot\gamma$. This power law behavior, observed here in carbopol dispersions, does not depend on the gap width and on the boundary conditions for a given sample preparation. For $\dot\gamma\lesssim 0.1$ s$^{-1}$, heterogeneous flows could be observed for as long as 10$^5$ s. These local dynamics account for the ultraslow stress relaxation observed at low shear rates.Comment: 4 pages, 4 figure

Yield stress and elasticity influence on surface tension measurements

We have performed surface tension measurements on carbopol gels of different concentrations and yield stresses. Our setup, based on the force exerted by a capillary bridge on two parallel plates, allows to measure an effective surface tension of the complex fluid and to investigate the influence of flow history. More precisely the effective surface tension measured after stretching the bridge is always higher than after compressing it. The difference between the two values is due to the existence of a yield stress in the fluid. The experimental observations are successfully reproduced with a simple elasto-plastic model. The shape of successive stretching-compression cycles can be described by taking into account the yield stress and the elasticity of the gel. We show that the surface tension $\gamma_{LV}$ of yield stress fluids is the mean of the effective surface tension values only if the elastic modulus is high compared to the yield stress. This work highlights that thermodynamical quantities measurements are challenged by the fluid out-of-equilibrium state implied by jamming, even at small scales where the shape of the bridge is driven by surface energy. Therefore setups allowing deformation in opposite directions are relevant for measurements on yield stress fluids.Comment: 12 pages, 16 figures in Soft Matter 201

Dynamics of simple liquids at heterogeneous surfaces : Molecular Dynamics simulations and hydrodynamic description

In this paper we consider the effect of surface heterogeneity on the slippage of fluid, using two complementary approaches. First, MD simulations of a corrugated hydrophobic surface have been performed. A dewetting transition, leading to a super-hydrophobic state, is observed for pressure below a ``capillary'' pressure. Conversely a very large slippage of the fluid on this composite interface is found in this superhydrophobic state. Second, we propose a macroscopic estimate of the effective slip length on the basis of continuum hydrodynamics, in order to rationalize the previous MD results. This calculation allows to estimate the effect of a heterogeneous slip length pattern on the composite interface. Comparison between the two approaches are in good agreement at low pressure, but highlights the role of the exact shape of the liquid-vapor interface at higher pressure. These results confirm that small variations in the roughness of a surface can lead to huge differences in the slip effect. On the basis of these results, we propose some guidelines to design highly slippery surfaces, motivated by potential applications in microfluidics.Comment: submitted to EPJ

Plastic Response of a 2D Lennard-Jones amorphous solid: Detailed analysis of the local rearrangements at very slow strain-rate

We analyze in details the atomistic response of a model amorphous material submitted to plastic shear in the athermal, quasistatic limit. After a linear stress-strain behavior, the system undergoes a noisy plastic flow. We show that the plastic flow is spatially heterogeneous. Two kinds of plastic events occur in the system: quadrupolar localized rearrangements, and shear bands. The analysis of the individual motion of a particle shows also two regimes: a hyper-diffusive regime followed by a diffusive regime, even at zero temperature

Scaling laws for slippage on superhydrophobic fractal surfaces

We study the slippage on hierarchical fractal superhydrophobic surfaces, and find an unexpected rich behavior for hydrodynamic friction on these surfaces. We develop a scaling law approach for the effective slip length, which is validated by numerical resolution of the hydrodynamic equations. Our results demonstrate that slippage does strongly depend on the fractal dimension, and is found to be always smaller on fractal surfaces as compared to surfaces with regular patterns. This shows that in contrast to naive expectations, the value of effective contact angle is not sufficient to infer the amount of slippage on a fractal surface: depending on the underlying geometry of the roughness, strongly superhydrophobic surfaces may in some cases be fully inefficient in terms of drag reduction. Finally, our scaling analysis can be directly extended to the study of heat transfer at fractal surfaces, in order to estimate the Kapitsa surface resistance on patterned surfaces, as well as to the question of trapping of diffusing particles by patchy hierarchical surfaces, in the context of chemoreception