I Thermodynamics, structure and fluctuations 2 A reminder of thermodynamics 36 2.1 State variables and thermodynamic equilibrium 36 2.2 Link with statistical mechanics 42 2.3 Phase coexistence and interfaces 47 2.4 Application 1: scaled particle theory 51 2.5 Application 2: particle insertion 55 2.6 Application 3: critical micellar concentration 57 2.7 Application 4: depletion interactions and solvation forces 62 Further reading 67 3 Equilibrium fluctuations 69 3.1 Gaussian distribution of fluctuations 69 3.2 Density fluctuations in a one-component system 72 3.3 Concentration fluctuations in a mixture 74 3.4 Local order and pair structure 75 3.5 Link with thermodynamics 81 3.6 Static linear response 84 3.7 Application 1: dipole moment fluctuations and dielectric response 85 v vi Contents 3.8 Application 2: determination of the structure from diffraction experiments 3.9 Application 3: form factors of complex objects or molecules 3.10 Application 4: random phase approximation Further reading II Phase transitions 4 Mean field approaches 4.1 Lattice models and mean field treatment 4.2 Landau theory of phase transitions 4.3 Application 1: van der Waals theory of condensation 4.4 Application 2: Flory-Huggins theory of polymer blends 4.5 Application 3: isotropic-nematic transition 4.6 Application 4: freezing 5 Critical fluctuations and scaling 5.1 The correlation length 5.2 Fluctuations and dimensionality 5.3 Scaling ideas 5.4 Application 1: Ginzburg criterion for polymer blends 5.5 Application 2: scaling laws for polymer solutions 5.6 Application 3: finite size scaling III Interfaces and inhomogeneous fluids 6 Macroscopic description of interfaces 6.1 Interfacial tension and excess quantities 6.2 Geometry of curved surfaces 6.3 Wetting phenomena 6.4 Capillary pressure and capillary condensation 6.5 Disjoining pressure and film stability Further reading 7 The density functional approach 7.1 Variational principle 7.2 Some approximate functionals 7.3 Application 1: the fluid-fluid interface 7.4 Application 2: the adsorbed polymer layer 7.5 Application 3: self-assembly of copolymers 7.6 Application 4: electric double-layers 7.7 Application 5: colloid stability Further reading Contents vii 8 Curvature and fluctuations 213 8.1 Fluctuations of interfaces and capillary waves 213 8.2 Membranes and curvature moduli 215 8.3 Fluctuations of membranes 8.4 Steric interactions between membranes 218 Further reading 219 IV Dynamics 9 Phenomenological description of transport processes 9.1 Fluxes, affinities and transport coefficients 220 9.2 Application 1: the diffusion equation 221 9.3 Application 2: spinodal decomposition 224 Further reading 227

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The development of microfluidic devices has recently revived the interest in "old" problems associated with transport at, or across, interfaces. As the characteristic sizes are decreased, the use of pressure gradients to transport fluids becomes problematic, and new, interface driven, methods must be considered. This has lead to new investigations of flow near interfaces, and to the conception of interfaces engineered at various scales to reduce flow friction. In this review, we discuss the present theoretical understanding of flow past solid interfaces at different length scales. We also briefly discuss the corresponding phenomenon of heat transport, and the influence of surface slip on interface driven (e.g. electro-osmotic) flows.

With the important development of microfluidic systems, miniaturization of flow devices has become a real challenge. Microchannels, however, are characterized by a large surface-to-volume ratio, so that surface properties strongly affect flow resistance in submicrometre devices. We present here results showing that the concerted effect of wetting properties and surface roughness may considerably reduce friction of the fluid past the boundaries. The slippage of the fluid at the channel boundaries is shown to be greatly increased by using surfaces that are patterned on the nanometre scale. This effect occurs in the regime where the surface pattern is partially dewetted, in the spirit of the 'superhydrophobic' effects that have been discovered at macroscopic scales. Our results show for the first time that, in contrast to common belief, surface friction may be reduced by surface roughness. They also open the possibility of a controlled realization of the 'nanobubbles' that have long been suspected to play a role in interfacial slippage.

CONTENTSFrequently used notations 3 FIG. 1 Overview of amorphous solids. From left to right, top row : cellular phone case made of metallic glass (1); toothpaste (2); mayonnaise (3); coffee foam (4); soya beans (5). Second row : a transmission electron microscopy (TEM) image of a fractured bulk metallic glass (Cu50Zr45Ti5) by X. Tong et. al (Shanghai University, China); TEM image of blend (PLLA/PS) nanoparticles obtained by miniemulsion polymerization, from L. Becker Peres et al. (UFSC, Brazil); emulsion of water droplets in silicon oil observed with an optical microscope by N. Bremond (ESPCI Paris); a soap foam filmed in the lab by M. van Hecke (Leiden University, Netherlands); thin nylon cylinders of different diameters pictured with a camera, from T. Miller et al. (University of Sydney, Australia). The white scale bars are approximate. Just below, a chart of different amorphous materials, classified by the size and the damping regime of their elementary particles. At the bottom: some popular modeling approaches, arranged according to the length scales of the materials for which they were originally developed. STZ stands for the shear transformation zone theory of Langer (2008), and SGR for the soft glassy rheology theory of Sollich et al. (1997).

The nonequilibrium dynamics of a binary Lennard-Jones mixture in a simple shear flow is investigated by means of molecular dynamics simulations. The range of temperature T investigated covers both the liquid, supercooled and glassy states, while the shear rate γ covers both the linear and nonlinear regimes of rheology. The results can be interpreted in the context of a nonequilibrium, schematic mode-coupling theory developed recently, which makes the theory applicable to a wide range of soft glassy materials. The behavior of the viscosity η(T, γ) is first investigated. In the nonlinear regime, strong shear-thinning is obtained, η ∼ γ −α(T ) , with α(T ) ≃ 2/3 in the supercooled regime. Scaling properties of the intermediate scattering functions are studied. Standard 'mode-coupling properties' of factorization and time-superposition hold in this nonequilibrium situation. The fluctuation-dissipation relation is violated in the shear flow in a way very similar to that predicted theoretically, allowing for the definition of an effective temperature T eff for the slow modes of the fluid. Temperature and shear rate dependencies of T eff are studied using density fluctuations as an observable. The observable dependence of T eff is also investigated. Many different observables are found to lead to the same value of T eff , suggesting several experimental procedures to access T eff . It is proposed that a tracer particle of large mass mtr may play the role of an 'effective thermometer'. When the Einstein frequency of the tracers becomes smaller than the inverse relaxation time of the fluid, a nonequilibrium equipartition theorem holds with mtrv 2 z = kBT eff , where vz is the velocity in the direction transverse to the flow. This last result gives strong support to the thermodynamic interpretation of T eff and makes it experimentally accessible in a very direct way.PACS numbers: 64.70.Pf, 05.70.Ln, 83.60.Df L'immense thermomètre reflétait modestement la température du milieu ambiant. Vassili Axionov, L'île de Crimée.

The approach of the elastic continuum limit in small amorphous bodies formed by weakly polydisperse Lennard-Jones beads is investigated in a systematic finite-size study. We show that classical continuum elasticity breaks down when the wavelength of the sollicitation is smaller than a characteristic length of approximately 30 molecular sizes. Due to this surprisingly large effect ensembles containing up to N = 40, 000 particles have been required in two dimensions to yield a convincing match with the classical continuum predictions for the eigenfrequency spectrum of disk-shaped aggregates and periodic bulk systems. The existence of an effective length scale ξ is confirmed by the analysis of the (non-gaussian) noisy part of the low frequency vibrational eigenmodes. Moreover, we relate it to the non-affine part of the displacement fields under imposed elongation and shear. Similar correlations (vortices) are indeed observed on distances up to ξ ≈ 30 particle sizes.

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