Coexistence of Active and Hydrodynamic Turbulence in Two-Dimensional Active Nematics.

In active nematic liquid crystals, activity is able to drive chaotic spatiotemporal flows referred to as active turbulence. Active turbulence has been characterized through theoretical and experimental work as a low Reynolds number phenomenon. We show that, in two dimensions, the active forcing alone is able to trigger hydrodynamic turbulence leading to the coexistence of active and inertial turbulence. This type of flow develops for sufficiently active and extensile flow-aligning nematics. We observe that the combined effect of an extensile nematic and large values of the flow-aligning parameter leads to a broadening of the elastic energy spectrum that promotes a growth of kinetic energy able to trigger an inverse energy cascade.

Aggregation of discoidal particles due to depletion interaction.

Depletion interactions between colloids of discoidal shape can induce their self-assembly into columnar aggregates. This is an effect of entropic origin with important implications in a range of colloidal systems, particularly in the clustering of erythrocytes that determine the rheological properties of blood. Here, we investigate the equilibrium state reached by discoidal colloids in a solution of smaller depletant particles. We develop a thermodynamic model of depletion-induced aggregation based on self-assembly theory and solve it analytically. We test the validity of the model by using Langevin simulations of a system of discs and depletant particles in which the depletion interaction emerges naturally. In addition, we consider the effect of an attractive interaction between depletant and discoidal particles, which we show induces a re-entrant dependence of aggregation with temperature.

Confinement-controlled rectification in a geometric nanofluidic diode.

Recent experiments with electrolytes driven through conical nanopores give evidence of strong rectified current response. In such devices, the asymmetry in the confinement is responsible for the non-Ohmic response, suggesting that the interplay of entropic and enthalpic forces plays a major role. Here, we propose a theoretical model to shed light on the physical mechanism underlying ionic current rectification. By use of an effective description of the ionic dynamics, we explore the system's response in different electrostatic regimes. We show that the rectification efficiency, as well as the channel selectivity, is driven by the surface-to-bulk conductivity ratio Dukhin length rather than the electrical double layer overlap.

Flow of colloidal suspensions through small orifices.

In this work, we numerically study a dense colloidal suspension flowing through a small outlet driven by a pressure drop using lattice-Boltzmann methods. This system shows intermittent flow regimes that precede clogging events. Several pieces of evidence suggest that the temperature controls the dynamic state of the system when the driving force and the aperture size are fixed. When the temperature is low, the suspension's flow can be interrupted during long time periods, which can be even two orders of magnitude larger than the system's characteristic time (Stokes). We also find that strong thermal noise does not allow the formation of stable aggregate structures avoiding extreme clogging events, but, at the same time, it randomizes the particle trajectories and disturbs the advective particle flow through the aperture. Moreover, examining the particle velocity statistics, we obtain that in the plane normal to the pressure drop the colloids always move as free particles regardless of the temperature value. In the pressure drop direction, at high temperature the colloids experience a simple balance between advective and diffusive transport, but at low temperature the nature of the flow is much more complex, correlating with the occurrence of very long clogging events.

Bistability, Oscillations, and Bidirectional Motion of Ensemble of Hydrodynamically Coupled Molecular Motors.

We analyze the collective behavior of hydrodynamically coupled molecular motors. We show that the local fluxes induced by motor displacement can induce the experimentally observed bidirectional motion of cargoes and vesicles. By means of a mean-field approach we show that sustained oscillations as well as bistable collective motor motion arise even for very large collection of motors, when thermal noise is irrelevant. The analysis clarifies the physical mechanisms responsible for such dynamics by identifying the relevant coupling parameter and its dependence on the geometry of the hydrodynamic coupling as well as on system size. We quantify the phase diagram for the different phases that characterize the collective motion of hydrodynamically coupled motors and show that sustained oscillations can be reached for biologically relevant parameters, hence, demonstrating the relevance of hydrodynamic interactions in intracellular transport.

Mesoscopic non-equilibrium thermodynamic analysis of molecular motors.

We show that the kinetics of a molecular motor fueled by ATP and operating between a deactivated and an activated state can be derived from the principles of non-equilibrium thermodynamics applied to the mesoscopic domain. The activation by ATP, the possible slip of the motor, as well as the forward stepping carrying a load are viewed as slow diffusion along a reaction coordinate. Local equilibrium is assumed in the reaction coordinate spaces, making it possible to derive the non-equilibrium thermodynamic description. Using this scheme, we find expressions for the velocity of the motor, in terms of the driving force along the spacial coordinate, and for the chemical reaction that brings about activation, in terms of the chemical potentials of the reactants and products which maintain the cycle. The second law efficiency is defined, and the velocity corresponding to maximum power is obtained for myosin movement on actin. Experimental results fitting with the description are reviewed, giving a maximum efficiency of 0.45 at a myosin headgroup velocity of 5 × 10(-7) m s(-1). The formalism allows the introduction and test of meso-level models, which may be needed to explain experiments.

Theory of wetting-induced fluid entrainment by advancing contact lines on dry surfaces.

We report on the onset of fluid entrainment when a contact line is forced to advance over a dry solid of arbitrary wettability. We show that entrainment occurs at a critical advancing speed beyond which the balance between capillary, viscous, and contact-line forces sustaining the shape of the interface is no longer satisfied. Wetting couples to the hydrodynamics by setting both the morphology of the interface at small scales and the viscous friction of the front. We find that the critical deformation that the interface can sustain is controlled by the friction at the contact line and the viscosity contrast between the displacing and displaced fluids, leading to a rich variety of wetting-entrainment regimes. We discuss the potential use of our theory to measure contact-line forces using atomic force microscopy and to study entrainment under microfluidic conditions exploiting colloid-polymer fluids of ultralow surface tension.

Influence of the feeding mechanism on deposits of square particles.

In a previous paper [Hidalgo et al., Phys. Rev. Lett. 103, 118001 (2009)] it was shown that square particles deposited in a silo tend to align with a diagonal parallel to the gravity, giving rise to a deposit with very particular properties. Here we explore, both experimentally and numerically, the effect on these properties of the filling mechanism. In particular, we modify the volume fraction of the initial configuration from which the grains are deposited. Starting from a very dilute case, increasing the volume fraction results in an enhancement of the disorder in the final deposit characterized by a decrease of the final packing fraction and a reduction of the number of particles oriented with their diagonal in the direction of gravity. However, for very high initial volume fractions, the final packing fraction increases again. This result implies that two deposits with the same final packing fraction can be obtained from very different initial conditions. The structural properties of such deposits are analyzed, revealing that, although the final volume fraction is the same, their micromechanical properties notably differ.

Stress distribution of faceted particles in a silo after its partial discharge.

We present experimental and numerical results of the effect that a partial discharge has on the morphological and micro-mechanical properties of non-spherical, convex particles in a silo. The comparison of the particle orientation after filling the silo and its subsequent partial discharge reveals important shear-induced orientation, which affects stress propagation. For elongated particles, the flow induces an increase in the packing disorder which leads to a reduction of the vertical stress propagation developed during the deposit generated prior to the partial discharge. For square particles, the flow favors particle alignment with the lateral walls promoting a behavior opposite to the one of the elongated particles: vertical force transmission, parallel to gravity, is induced. Hence, for elongated particles the flow developed during the partial discharge of the silo leads to force saturation with depth whereas for squares the flow induces hindering of the force saturation observed during the silo filling.

Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case.

In this paper, we consider a simple reaction-diffusion system, namely, a binary fluid mixture with an association-dissociation reaction between two species. We study fluctuations at hydrodynamic spatiotemporal scales when this mixture is driven out of equilibrium by the presence of a temperature gradient, while still being far away from any chemical instability. This study extends the analysis in our first paper on the subject [J. M. Ortiz de Zárate, J. V. Sengers, D. Bedeaux, and S. Kjelstrup, J. Chem. Phys. 127, 034501 (2007)], where we considered fluctuations in a non-isothermal reaction-diffusion system but still close to equilibrium. The present extension is based on mesoscopic non-equilibrium thermodynamics that we recently developed [D. Bedeaux, I. Pagonabarraga, J. M. Ortiz de Zárate, J. V. Sengers, and S. Kjelstrup, Phys. Chem. Chem. Phys. 12, 12780 (2010)] to derive the law of mass action and fluctuation-dissipation theorems for the random contributions to the dissipative fluxes in the nonlinear macroscopic description. Just as for non-equilibrium fluctuations close to equilibrium, we again find an enhancement of the intensity of the concentration fluctuations in the presence of a temperature gradient. The non-equilibrium concentration fluctuations are in both cases spatially long ranged, with an intensity depending on the wave number q. The intensity exhibits a crossover from a ∝q(-4) to a ∝q(-2) behavior depending on whether the corresponding wavelength is smaller or larger than the penetration depth of the reacting mixture. This opens a possibility to distinguish between diffusion- or activation-controlled regimes of the reaction experimentally. The important conclusion overall is that non-equilibrium fluctuations in non-isothermal reaction-diffusion systems are always long ranged.

Controlled drop emission by wetting properties in driven liquid filaments.

The controlled formation of micrometre-sized drops is of great importance to many technological applications. Here we present a wetting-based destabilization mechanism of forced microfilaments on either hydrophilic or hydrophobic stripes that leads to the periodic emission of droplets. The drop emission mechanism is triggered above the maximum critical forcing at which wetting, capillarity, viscous friction and gravity can balance to sustain a stable driven contact line. The corresponding critical filament velocity is predicted as a function of the static wetting angle, which can be tuned through the substrate behaviour, and shows a strong dependence on the filament size. This sensitivity explains the qualitative difference in the critical velocity between hydrophilic and hydrophobic stripes, and accounts for previous experimental results of splashing solids. We demonstrate that this mechanism can be used to control independently the drop size and emission period, opening the possibility of highly monodisperse and flexible drop production techniques in open microfluidic geometries.

Mesoscopic non-equilibrium thermodynamics of non-isothermal reaction-diffusion.

We show how the law of mass action can be derived from a thermodynamic basis, in the presence of temperature gradients, chemical potential gradients and hydrodynamic flow. The solution gives the law of mass action for the forward and the reverse contributions to the net chemical reaction. In addition we derive the fluctuation-dissipation theorem for the fluctuating contributions to the reaction rate, heat flux and mass fluxes. All these results arise without any other assumptions than those which are common in mesoscopic non-equilibrium thermodynamics; namely quasi-stationary transport across a high activation energy barrier, and local equilibrium along the reaction coordinate. Arrhenius-type behaviour of the kinetic coefficients is recovered. The thermal conductivity, Soret coefficient and diffusivity are significantly influenced by the presence of a chemical reaction. We thus demonstrate how chemical reactions can be fully reconciled with non-equilibrium thermodynamics.

Hydrodynamic interaction between two trapped swimming model micro-organisms.

We present a theoretical study of the behaviour of two active particles under the action of harmonic traps kept at a fixed distance away from each other. We classify the steady configurations the squirmers develop as a function of their self-propelling velocity and the active stresses the swimmers induce around them. We have further analyzed the stability of such configurations, and have found that the ratio between their self-propelling velocity and the apolar flow generated through active stresses determines whether collinear parallel squirmers or perpendicularly swimming particles moving away from each other are stable. Therefore, there is a close connection between the stable configurations and the active mechanisms leading to the particle self-propulsion. The trap potential does not affect the stability of the configurations; it only modifies some of their relevant time scales. We have also observed the development of characteristic frequencies which should be observable. Finally, we show that the development of the hydrodynamic flows induced by the active particles may be relevant even when its time scale orders of magnitude smaller than the other present characteristic time scales and may destabilize the stable configurations.

Recent advances in the modelling and simulation of electrokinetic effects: bridging the gap between atomistic and macroscopic descriptions.

Electrokinetic phenomena are of great practical importance in fields as diverse as micro-fluidics, colloid science and oil exploration. However, the quantitative prediction of electrokinetic effects was until recently limited to relatively simple geometries that allowed the use of analytical theories. In the past decade, there has been a rapid development in the use of numerical methods that can be used to model electrokinetic phenomena in complex geometries or, more generally, under conditions where the existing analytical approaches fail. The present paper discusses these recent developments, with special emphasis on the advent of coarse-grained models that make it possible to bridge the gap between a purely atomistic and macroscopic descriptions.

Arrested phase separation in reproducing bacteria creates a generic route to pattern formation.

We present a generic mechanism by which reproducing microorganisms, with a diffusivity that depends on the local population density, can form stable patterns. For instance, it is known that a decrease of bacterial motility with density can promote separation into bulk phases of two coexisting densities; this is opposed by the logistic law for birth and death that allows only a single uniform density to be stable. The result of this contest is an arrested nonequilibrium phase separation in which dense droplets or rings become separated by less dense regions, with a characteristic steady-state length scale. Cell division predominates in the dilute regions and cell death in the dense ones, with a continuous flux between these sustained by the diffusivity gradient. We formulate a mathematical model of this in a case involving run-and-tumble bacteria and make connections with a wider class of mechanisms for density-dependent motility. No chemotaxis is assumed in the model, yet it predicts the formation of patterns strikingly similar to some of those believed to result from chemotactic behavior.

Condensation transition in polydisperse hard rods.

We study a mass transport model, where spherical particles diffusing on a ring can stochastically exchange volume v, with the constraint of a fixed total volume V= sum(i=1) (N)v(i), N being the total number of particles. The particles, referred to as p-spheres, have a linear size that behaves as v(i) (1/p) and our model thus represents a gas of polydisperse hard rods with variable diameters v(i) (1/p). We show that our model admits a factorized steady state distribution which provides the size distribution that minimizes the free energy of a polydisperse hard-rod system, under the constraints of fixed N and V. Complementary approaches (explicit construction of the steady state distribution on the one hand; density functional theory on the other hand) completely and consistently specify the behavior of the system. A real space condensation transition is shown to take place for p>1; beyond a critical density a macroscopic aggregate is formed and coexists with a critical fluid phase. Our work establishes the bridge between stochastic mass transport approaches and the optimal polydispersity of hard sphere fluids studied in previous articles.

Dynamics of gravity driven three-dimensional thin films on hydrophilic-hydrophobic patterned substrates.

We investigate numerically the dynamics of unstable gravity driven three-dimensional thin liquid films on hydrophilic-hydrophobic patterned substrates. We explore longitudinally striped and checkerboard arrangements. Simulations show that for longitudinal stripes, the thin film can be guided preferentially on the hydrophilic stripes, while fingers develop on adjacent hydrophobic stripes if the width of the stripes is large enough. On checkerboard patterns, the film develops as a finger on hydrophobic domains, while it spreads laterally to cover the hydrophilic domains, providing a mechanism to tune the growth rate of the film. By means of kinematical arguments, we quantitatively predict the growth rate of the contact line on checkerboard arrangements, providing a first step toward potential techniques that control thin film growth in experimental setups.

Accurate simulation dynamics of microscopic filaments using "caterpillar" Oseen hydrodynamics.

Microscopic semiflexible filaments suspended in a viscous fluid are widely encountered in biophysical problems. The classic example is the flagella used by microorganisms to generate propulsion. Simulating the dynamics of these filaments numerically is complicated because of the coupling between the motion of the filament and that of the surrounding fluid. An attractive idea is to simplify this coupling by modeling the fluid motion by using Stokeslets distributed at equal intervals along the model filament. We show that, with an appropriate choice of the hydrodynamic radii, one can recover accurate hydrodynamic behavior of a filament with a finite cross section without requiring an explicit surface. This is true, however, only if the hydrodynamic radii take specific values and that they differ in the parallel and perpendicular directions leading to a caterpillarlike hydrodynamic shape. Having demonstrated this, we use the model to compare with analytic theory of filament deformation and rotation in the small deformation limit. Generalization of the methodology, including application to simulations using the Rotne-Prager tensor, is discussed.

Negative fluctuation-dissipation ratios in the backgammon model.

We analyze fluctuation-dissipation relations in the backgammon model: a system that displays glassy behavior at zero temperature due to the existence of entropy barriers. We study local and global fluctuation relations for the different observables in the model. For the case of a global perturbation we find a unique negative fluctuation-dissipation ratio that is independent of the observable and which diverges linearly with the waiting time. This result suggests that a negative effective temperature can be observed in glassy systems even in the absence of thermally activated processes.

Avalanche dynamics of fiber bundle models.

We present a detailed analytical and numerical study of the avalanche distributions of the continuous damage fiber bundle model (CDFBM). Linearly elastic fibers undergo a series of partial failure events which give rise to a gradual degradation of their stiffness. We show that the model reproduces a wide range of mechanical behaviors. We find that macroscopic hardening and plastic responses are characterized by avalanche distributions, which exhibit an algebraic decay with exponents between 5/2 and 2 different from those observed in mean-field fiber bundle models. We also derive analytically the phase diagram of a family of CDFBM which covers a large variety of potential avalanche size distributions. Our results provide a unified view of the statistics of breaking avalanches in fiber bundle models.