We investigate the hydrodynamic friction properties of superhydrophobic surfaces and quantify their superlubricating potential. On such surfaces, the contact of the liquid with the solid roughness is minimal, while most of the interface is a liquid-gas one, resulting in strongly reduced friction. We obtain scaling laws for the effective slip length at the surface in terms of the generic surface characteristics ͑roughness length scale, depth, solid fraction of the interface, etc.͒. These predictions are successfully compared to numerical results in various geometries ͑grooves, posts or holes͒. This approach provides a versatile framework for the description of slip on these composite surfaces. Slip lengths up to 100 m are predicted for an optimized patterned surface.

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 γ. 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 γ≲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.

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 super-hydrophobic 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 at the composite interface. Comparison between the two approaches shows that they 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.

Stress-induced fluidization of a simple yield stress fluid, namely a carbopol microgel, is addressed through extensive rheological measurements coupled to simultaneous temporally and spatially resolved velocimetry. These combined measurements allow us to rule out any bulk fracture-like scenario during the fluidization process such as that suggested in [Caton et al., Rheol Acta, 2008, 47, 601-607]. On the contrary, we observe that the transient regime from solidlike to liquidlike behaviour under a constant shear stress σ successively involves creep deformation, total wall slip, and shear banding before a homogeneous steady state is reached. Interestingly, the total duration τ f of this fluidization process scales as τ f ∝ 1/(σ − σc) β , where σc stands for the yield stress of the microgel, and β is an exponent which only depends on the microgel properties and not on the gap width or on the boundary conditions. Together with recent experiments under imposed shear rate [Divoux et al., Phys. Rev. Lett., 2010, 104, 208301], this scaling law suggests a route to rationalize the phenomenological Herschel-Bulkley (HB) power-law classically used to describe the steady-state rheology of simple yield stress fluids. In particular, we show that the steady-state HB exponent appears as the ratio of the two fluidization exponents extracted separately from the transient fluidization processes respectively under controlled shear rate and under controlled shear stress.

We report a large amount of experimental data on the stress overshoot phenomenon which takes place during start-up shear flows in a simple yield stress fluid, namely a carbopol microgel. A combination of classical rheological measurements and ultrasonic velocimetry makes it possible to get physical insights on the transient dynamics of both the stress σ(t) and the velocity field across the gap of a rough cylindrical Couette cell during the start-up of shear under an applied shear ratė γ. (i) At small strains (γ < 1), σ(t) increases linearly and the microgel undergoes homogeneous deformation. (ii) At a time tm, the stress reaches a maximum value σm which corresponds to the failure of the microgel and to the nucleation of a thin lubrication layer at the moving wall. (iii) The microgel then experiences a strong elastic recoil and enters a regime of total wall slip while the stress slowly decreases. (iv) Total wall slip gives way to a transient shear-banding phenomenon, which occurs on timescales much longer than that of the stress overshoot and has been described elsewhere [Divoux et al., Phys. Rev. Lett., 2010, 104, 208301]. This whole sequence is very robust to concentration changes in the explored range (0.5 ≤ C ≤ 3% w/w). We further demonstrate that the maximum stress σm and the corresponding strain γm =γtm both depend on the applied shear rateγ and on the waiting time tw between preshear and shear start-up: they remain roughly constant as long asγ is smaller than some critical shear rateγw ∼ 1/tw and they increase as weak power laws ofγ forγ >γw. Finally, by changing the boundary conditions from rough to smooth, we show that there exists a critical shear rateγs fixed by the wall surface roughness below which slip at both walls allows for faster stress relaxation and for stress fluctuations strongly reminiscent of stick-slip. Interestingly, the value ofγs is observed to coincide with the shear rate below which the flow curve displays a kink attributed to wall slip. PACS numbers:The transient response of complex materials to the application of an external shear deformation is of huge importance not only for the practical use of such materials but also during the processing stage. The archetypal experiment used for transient rheological characterization is a "start-up experiment" where a constant shear rateγ is applied from rest and the subsequent stress response is monitored until steady-state is reached. A host of widely different systems from soft and hard condensed matter have been reported to present a non-monotonic stress response during start-up experiments. Roughly, the stress σ versus time t first increases linearly, reaches a maximum value denoted σ m at a time t m and then decreases towards it steady-state value. This temporal sequence is usually referred to as a stress overshoot. It has been reported experimentally for both amorphous materials, such as amorphous polymers [1][2][3] and metallic glasses [4,5], and for soft glassy materials, namely emulsions [6][7][8][9], foams [10,11], microgels [12,13]...

In this paper, we probe the influence of confinement on the flows of a polymer microgel, namely Carbopol. We compare its bulk rheological behavior, measured with a rheometer and well described by a Hershel-Bulkley law, to velocity profiles measured in rough microchannels, obtained with a particle tracking velocimetry technique. We show a strong disagreement between the bulk prediction for the velocity profiles and the measured ones in the microchannels. Velocity profiles in confined conditions are successfully analyzed within the framework of a non-local fluidity model introduced recently (J. Goyon et al. Nature, 454, 84 (2008)). This allows to determine a cooperativity length ξ, whose order of magnitude compares with the structure size of the microgel. Moreover, we measure flow curves using a rheometer for different gap conditions and also show that this set of data exhibit a strong effect of the confinement on the measured rheological properties. This is again characterized by a typical length of the same order as the cooperativity length scale ξ. We thus evidence confinement effects with two complementary experiments which both give the same typical length for the rearrangements in the flows.

We study monolayers formed at an air-water interface on a Langmuir trough by telechelic poly(ethylene oxide) polymers end capped with hydrophobic alkane groups (C12 and C16). The pressurearea isotherms show two plateaus: the first plateau at low coverage already exists for nontelechelic PEO and is attributed to the formation of loops in the solution; after this plateau, the pressure rises stongly as the hydrophobic groups anchor the polymers on the surface, which leads to the formation of a grafted polymer layer; the second plateau at high density is due to a dissolution of the polymer chains in the bulk water. Starting from a monolayer at high density, we also study experimentally the relaxation of the surface pressure with time due to the dissolution of the polymer. A theoretical approach of this problem based on polymer brush theory is proposed. Both the static properties of the layer and the desorption kinetics are calculated. The model accounts well for the shape of the isotherms and for the relaxation kinetics. It gives a good interpretation of the role of various parameters such as the compression velocity, the molecular weight, and the hydrophobicity of the chain ends. The anchoring energy of the hydrophobic groups is determined by comparison with experiments.

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 breaks 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.