The effective temperature

This review presents the effective temperature notion as defined from the deviations from the equilibrium fluctuation-dissipation theorem in out of equilibrium systems with slow dynamics. The thermodynamic meaning of this quantity is discussed in detail. Analytic, numeric and experimental measurements are surveyed. Open issues are mentioned.Comment: 58 page

Nonlinear rheological properties of dense colloidal dispersions close to a glass transition under steady shear

The nonlinear rheological properties of dense colloidal suspensions under steady shear are discussed within a first principles approach. It starts from the Smoluchowski equation of interacting Brownian particles in a given shear flow, derives generalized Green-Kubo relations, which contain the transients dynamics formally exactly, and closes the equations using mode coupling approximations. Shear thinning of colloidal fluids and dynamical yielding of colloidal glasses arise from a competition between a slowing down of structural relaxation, because of particle interactions, and enhanced decorrelation of fluctuations, caused by the shear advection of density fluctuations. The integration through transients approach takes account of the dynamic competition, translational invariance enters the concept of wavevector advection, and the mode coupling approximation enables to quantitatively explore the shear-induced suppression of particle caging and the resulting speed-up of the structural relaxation. Extended comparisons with shear stress data in the linear response and in the nonlinear regime measured in model thermo-sensitive core-shell latices are discussed. Additionally, the single particle motion under shear observed by confocal microscopy and in computer simulations is reviewed and analysed theoretically.Comment: Review submited to special volume 'High Solid Dispersions' ed. M. Cloitre, Vol. xx of 'Advances and Polymer Science' (Springer, Berlin, 2009); some figures slightly cu

Phase coexistence in a monolayer of active particles induced by Marangoni flows

Thermally or chemically active colloids generate thermodynamic gradients in the solution in which they are immersed and thereby induce hydrodynamic flows that affect their dynamical evolution. Here we study a mean-field model for the many-body dynamics of a monolayer of active particles located at a fluid-fluid interface. In this case, the activity of the particles creates long-ranged Marangoni flows due to the response of the interface, which compete with the direct interaction between the particles. For the most interesting case of a $r^{-3}$ soft repulsion that models the electrostatic or magnetic interparticle forces, we show that an "onion-like" density distribution will develop within the monolayer. For a sufficiently large average density, two-dimensional phase transitions (freezing from liquid to hexatic, and melting from solid to hexatic) should be observable in a radially stratified structure. Furthermore, the analysis allows us to conclude that, while the activity may be too weak to allow direct detection of such induced Marangoni flows, it is relevant as a collective effect in the emergence of the experimentally observable spatial structure of phase coexistences noted above. Finally, the relevance of these results for potential experimental realizations is critically discussed.Comment: 11 page

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

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

Flow-Induced Helical Coiling of Semiflexible Polymers in Structured Microchannels

The conformations of semiflexible (bio)polymers are studied in flow through geometrically structured microchannels. Using mesoscale hydrodynamics simulations, we show that the polymer undergoes a rod-to-helix transition as it moves from the narrow high-velocity region into the wide low-velocity region of the channel. The transient helix formation is the result of a non-equilibrium and non-stationary buckling transition of the semiflexible polymer, which is subjected to a compressive force originating from the fluid-velocity variation in the channel. The helix properties depend on the diameter ratio of the channel, the polymer bending rigidity, and the flow strength.Comment: Accepted in Phys. Rev. Let

Role of hydrodynamic flows in chemically driven droplet division

We study the hydrodynamics and shape changes of chemically active droplets. In non-spherical droplets, surface tension generates hydrodynamic flows that drive liquid droplets into a spherical shape. Here we show that spherical droplets that are maintained away from thermodynamic equilibrium by chemical reactions may not remain spherical but can undergo a shape instability which can lead to spontaneous droplet division. In this case chemical activity acts against surface tension and tension-induced hydrodynamic flows. By combining low Reynolds-number hydrodynamics with phase separation dynamics and chemical reaction kinetics we determine stability diagrams of spherical droplets as a function of dimensionless viscosity and reaction parameters. We determine concentration and flow fields inside and outside the droplets during shape changes and division. Our work shows that hydrodynamic flows tends to stabilize spherical shapes but that droplet division occurs for sufficiently strong chemical driving, sufficiently large droplet viscosity or sufficiently small surface tension. Active droplets could provide simple models for prebiotic protocells that are able to proliferate. Our work captures the key hydrodynamics of droplet division that could be observable in chemically active colloidal droplets

Blood crystal: emergent order of red blood cells under wall-confined shear flow

Driven or active suspensions can display fascinating collective behavior, where coherent motions or structures arise on a scale much larger than that of the constituent particles. Here, we report experiments and numerical simulations revealing that red blood cells (RBCs) assemble into regular patterns in a confined shear flow. The order is of pure hydrodynamic and inertialess origin, and emerges from a subtle interplay between (i) hydrodynamic repulsion by the bounding walls which drives deformable cells towards the channel mid-plane and (ii) intercellular hydrodynamic interactions which can be attractive or repulsive depending on cell-cell separation. Various crystal-like structures arise depending on RBC concentration and confinement. Hardened RBCs in experiments and rigid particles in simulations remain disordered under the same conditions where deformable RBCs form regular patterns, highlighting the intimate link between particle deformability and the emergence of order. The difference in structuring ability of healthy (deformable) and diseased (stiff) RBCs creates a flow signature potentially exploitable for diagnosis of blood pathologies

Out of equilibrium dynamics of classical and quantum complex systems

Equilibrium is a rather ideal situation, the exception rather than the rule in Nature. Whenever the external or internal parameters of a physical system are varied its subsequent relaxation to equilibrium may be either impossible or take very long times. From the point of view of fundamental physics no generic principle such as the ones of thermodynamics allows us to fully understand their behaviour. The alternative is to treat each case separately. It is illusionary to attempt to give, at least at this stage, a complete description of all non-equilibrium situations. Still, one can try to identify and characterise some concrete but still general features of a class of out of equilibrium problems - yet to be identified - and search for a unified description of these. In this report I briefly describe the behaviour and theory of a set of non-equilibrium systems and I try to highlight common features and some general laws that have emerged in recent years.Comment: 36 pages, to be published in Compte Rendus de l'Academie de Sciences, T. Giamarchi e

Thermostat for non-equilibrium multiparticle collision dynamics simulations

Multiparticle collision dynamics (MPC), a particle-based mesoscale simulation technique for com- plex fluid, is widely employed in non-equilibrium simulations of soft matter systems. To maintain a defined thermodynamic state, thermalization of the fluid is often required for certain MPC variants. We investigate the influence of three thermostats on the non-equilibrium properties of a MPC fluid under shear or in Poiseuille flow. In all cases, the local velocities are scaled by a factor, which is either determined via a local simple scaling approach (LSS), a Monte Carlo-like procedure (MCS), or by the Maxwell-Boltzmann distribution of kinetic energy (MBS). We find that the various scal- ing schemes leave the flow profile unchanged and maintain the local temperature well. The fluid viscosities extracted from the various simulations are in close agreement. Moreover, the numerically determined viscosities are in remarkably good agreement with the respective theoretically predicted values. At equilibrium, the calculation of the dynamic structure factor reveals that the MBS method closely resembles an isothermal ensemble, whereas the MCS procedure exhibits signatures of an adi- abatic system at larger collision-time steps. Since the velocity distribution of the LSS approach is non-Gaussian, we recommend to apply the MBS thermostat, which has been shown to produce the correct velocity distribution even under non-equilibrium conditions.Comment: 12 pages, 5 figures in Phys. Rev. E, 201