arXiv subjects

Bruno Andreotti

Publications and source records attributed to Bruno Andreotti.

At least 37 records · Page 2Linked to original sources

arXiv2017

A one dimensional modal approach for flows controlled by contact line motion

The hydrodynamics of a liquid-vapour interface in contact with an heterogeneous surface is largely impacted by the presence of defects at the smaller scales. Such defects introduce morphological disturbances on the contact line and ultimately determine the force exerted on the wedge of liquid in contact with the surface. From the mathematical point of view, defects introduce perturbation modes, whose space-time evolution is governed by the interfacial hydrodynamic equations of the contact line. In this paper we derive the response function of the contact line to such generic perturbations. The contact line response may be used to design simplified 1+1 dimensional models accounting for the complexity of interfacial flows coupled to nanoscale defects, yet offering a more tractable mathematical framework to include thermal fluctuations and explore thermally activated contact line motion through a disordered energy landscape.

physics.flu-dyn↗

arXiv2017

Dynamical Theory of the Inverted Cheerios Effect

Recent experiments have shown that liquid drops on highly deformable substrates exhibit mutual interactions. This is similar to the Cheerios effect, the capillary interaction of solid particles at a liquid interface, but now the roles of solid and liquid are reversed. Here we present a dynamical theory for this inverted Cheerios effect, taking into account elasticity, capillarity and the viscoelastic rheology of the substrate. We compute the velocity at which droplets attract, or repel, as a function of their separation. The theory is compared to a simplified model in which the viscoelastic dissipation is treated as a localized force at the contact line. It is found that the two models differ only at small separation between the droplets, and both of them accurately describe experimental observations.

cond-mat.soft↗

arXiv2016

Active dry granular flows: rheology and rigidity transitions

The constitutive relations of a dense granular flow composed of self-propelling frictional hard particles are investigated by means of DEM numerical simulations. We show that the rheology, which relates the dynamical friction $μ$ and the volume fraction $ϕ$ to the inertial number $I$, depends on a dimensionless number $\mathcal{A}$, which compares the active force to the confining pressure. Two liquid/solid transitions -- in the Maxwell rigidity sense -- are observed. As soon as the activity is turned on, the packing becomes an `active solid' with a mean number of particle contacts larger than the isostatic value. The quasi-static values of $μ$ and $ϕ$ decrease with $\mathcal{A}$. At a finite value of the activity $\mathcal{A}_t$, corresponding to the isostatic condition, a second `active rigidity transition' is observed beyond which the quasi-static values of the friction vanishes and the rheology becomes Newtonian. For $\mathcal{A}>\mathcal{A}_t$, we provide evidence for a highly intermittent dynamics of this 'active fluid'.

cond-mat.soft↗

arXiv2015

Solid Capillarity: When and How does Surface Tension Deform Soft Solids?

Soft solids differ from stiff solids in an important way: their surface stresses can drive large deformations. Based on a topical workshop held in the Lorentz Center in Leiden, this Opinion highlights some recent advances in the growing field of solid capillarity and poses key questions for its advancement.

cond-mat.soft↗

arXiv2015

Paper waves in the wind

A flexible sheet clamped at both ends and submitted to a permanent wind is unstable and propagates waves. Here, we experimentally study the selection of frequency and wavenumber as a function of the wind velocity. These quantities obey simple scaling laws, which are analytically derived from a linear stability analysis of the problem, and which also involve a gravity-induced velocity scale. This approach allows us to collapse data obtained with sheets whose flexible rigidity is varied by two orders of magnitude. This principle may be applied in the future for energy harvesting.

physics.flu-dyn↗

arXiv2015

Non-local rheology in dense granular flows -- Revisiting the concept of fluidity

The aim of this article is to discuss the concepts of non-local rheology and fluidity, recently introduced to describe dense granular flows. We review and compare various approaches based on different constitutive relations and choices for the fluidity parameter, focusing on the kinetic elasto-plastic model introduced by Bocquet et al. [Phys. Rev. Lett 103, 036001 (2009)] for soft matter, and adapted for granular matter by Kamrin et al. [Phys. Rev. Lett. 108, 178301 (2012)], and the gradient expansion of the local rheology $μ(I)$ that we have proposed [Phys. Rev. Lett. 111, 238301 (2013)]. We emphasise that, to discriminate between these approaches, one has to go beyond the predictions derived from linearisation around a uniform stress profile, such as that obtained in a simple shear cell. We argue that future tests can be based on the nature of the chosen fluidity parameter, and the related boundary conditions, as well as the hypothesis made to derive the models and the dynamical mechanisms underlying their dynamics.

cond-mat.soft↗

arXiv2015

Microrheology to probe non-local effects in dense granular flows

A granular material is observed to flow under the Coulomb yield criterion as soon as this criterion is satisfied in a remote but contiguous region of space. We investigate this non-local effect using discrete element simulations, in a geometry similar, in spirit, to the experiment of Reddy et al. (Phys. Rev. Lett., 106 (2011) 108301): a micro-rheometer is introduced to determine the influence of a distant shear band on the local rheological behaviour. The numerical simulations recover the dominant features of this experiment: the local shear rate is proportional to that in the shear band and decreases (roughly) exponentially with the distance to the yield conditions. The numerical results are in quantitative agreement with the predictions of the non-local rheology proposed by (Phys. Rev. Lett., 111 (2013) 238301) and derived from a gradient expansion of the rheology $μ[I]$. The consequences of these findings for the dynamical mechanisms controlling non-locality are finally discussed.

cond-mat.soft↗

arXiv2014

Direct numerical simulations of aeolian sand ripples

Aeolian sand beds exhibit regular patterns of ripples resulting from the interaction between topography and sediment transport. Their characteristics have been so far related to reptation transport caused by the impacts on the ground of grains entrained by the wind into saltation. By means of direct numerical simulations of grains interacting with a wind flow, we show that the instability turns out to be driven by resonant grain trajectories, whose length is close to a ripple wavelength and whose splash leads to a mass displacement towards the ripple crests. The pattern selection results from a compromise between this destabilizing mechanism and a diffusive downslope transport which stabilizes small wavelengths. The initial wavelength is set by the ratio of the sediment flux and the erosion/deposition rate, a ratio which increases linearly with the wind velocity. We show that this scaling law, in agreement with experiments, originates from an interfacial layer separating the saltation zone from the static sand bed, where momentum transfers are dominated by mid-air collisions. Finally, we provide quantitative support for the use the propagation of these ripples as a proxy for remote measurements of sediment transport.

cond-mat.soft↗

arXiv2014

A two-phase flow model of sediment transport: transition from bedload to suspended load

The transport of dense particles by a turbulent flow depends on two dimensionless numbers. Depending on the ratio of the shear velocity of the flow to the settling velocity of the particles (or the Rouse number), sediment transport takes place in a thin layer localized at the surface of the sediment bed (bedload) or over the whole water depth (suspended load). Moreover, depending on the sedimentation Reynolds number, the bedload layer is embedded in the viscous sublayer or is larger. We propose here a two-phase flow model able to describe both viscous and turbulent shear flows. Particle migration is described as resulting from normal stresses, but is limited by turbulent mixing and shear-induced diffusion of particles. Using this framework, we theoretically investigate the transition between bedload and suspended load.

cond-mat.soft↗

arXiv2014

Drops on soft solids: Free energy and double transition of contact angles

The equilibrium shape of liquid drops on elastic substrates is determined by minimising elastic and capillary free energies, focusing on thick incompressible substrates. The problem is governed by three length scales: the size of the drop $R$, the molecular size $a$, and the ratio of surface tension to elastic modulus $γ/E$. We show that the contact angles undergo two transitions upon changing the substrates from rigid to soft. The microscopic wetting angles deviate from Young's law when $γ/Ea \gg 1$, while the apparent macroscopic angle only changes in the very soft limit $γ/ER \gg 1$. The elastic deformations are worked out in the simplifying case where the solid surface energy is assumed constant. The total free energy turns out lower on softer substrates, consistent with recent experiments.

physics.flu-dyn↗

arXiv2013

A non-local rheology for granular flows across yield conditions

The rheology of dense granular flows is studied numerically in a shear cell controlled at constant pressure and shear stress, confined between two granular shear flows. We show that a liquid state can be achieved even far below the yield stress, whose flow can be described with the same rheology as above the yield stress. A non-local constitutive relation is derived from dimensional analysis through a gradient expansion and calibrated using the spatial relaxation of velocity profiles observed under homogeneous stresses. Both for frictional and frictionless grains, the relaxation length is found to diverge as the inverse square-root of the distance to the yield point, on both sides of that point.

cond-mat.soft↗

arXiv2013

Capillarity of soft amorphous solids: a microscopic model for surface stress

The elastic deformation of a soft solid induced by capillary forces crucially relies on the excess stress inside the solid-liquid interface. While for a liquid-liquid interface this "surface stress" is strictly identical to the "surface free energy", the thermodynamic Shuttleworth equation implies that this is no longer the case when one of the phases is elastic. Here we develop a microscopic model that incorporates enthalpic interactions and entropic elasticity, based on which we explicitly compute the surface stress and surface free energy. It is found that the compressibility of the interfacial region, through the Poisson ratio near the interface, determines the difference between surface stress and surface energy. We highlight the consequence of this finding by comparing with recent experiments and simulations on partially wetted soft substrates.

cond-mat.soft↗

arXiv2013

Elasto-capillarity at the nanoscale: on the coupling between elasticity and surface energy in soft solids

The capillary forces exerted by liquid drops and bubbles on a soft solid are directly measured using molecular dynamics simulations. The force on the solid by the liquid near the contact line is not oriented along the liquid vapor interface nor perpendicular to the solid surface, as usually assumed, but points towards the liquid. It is shown that the elastic deformations induced by this force can only be explained if, contrary to an incompressible liquid, the surface stress is different from the surface energy. Using thermodynamic variations we show that the the surface stress and the surface energy can both be determined accurately by measuring the deformation of a slender body plunged in a liquid. The results obtained from molecular dynamics fully confirm those recently obtained experimentally [Marchand et al. Phys. Rev. Lett. 108, 094301 (2012)] for an elastomeric wire.

cond-mat.soft↗

arXiv2012

Dynamical compressibility of dense granular shear flows

It has been conjectured by Bagnold [1] that an assembly of hard non-deformable spheres could behave as a compressible medium when slowly sheared, as the average density of such a system effectively depends on the confining pressure. Here we use discrete element simulations to show the existence of transverse and sagittal waves associated to this dynamical compressibility. For this purpose, we study the resonance of these waves in a linear Couette cell and compare the results with those predicted from a continuum local constitutive relation.

cond-mat.stat-mech↗

arXiv2012

Why is surface tension a force parallel to the interface?

A paperclip can float on water. Drops of mercury refuse to spread on a surface. These capillary phenomena are macroscopic manifestations of molecular interactions, and can be explained in terms of surface tension. For students, the concept of surface tension is quite challenging since the microscopic intuition is often in conflict with the common macroscopic interpretations. In this paper we address a number of conceptual questions that are often encountered when teaching capillarity. By answering these questions we provide a perspective that reconciles the macroscopic viewpoints, from thermodynamics or fluid mechanics, and the microscopic perspective from statistical physics.

physics.flu-dyn↗

arXiv2012

The bar instability revisited

The river bar instability is revisited, using a hydrodynamical model based on Reynolds averaged Navier-Stokes equations. The results are contrasted with the standard analysis based on shallow water Saint-Venant equations. We first show that the stability of both transverse modes (ripples) and of small wavelength inclined modes (bars) predicted by the Saint-Venant approach are artefacts of this hydrodynamical approximation. When using a more reliable hydrodynamical model, the dispersion relation does not present any maximum of the growth rate when the sediment transport is assumed to be locally saturated. The analysis therefore reveals the fundamental importance of the relaxation of sediment transport towards equilibrium as it it is responsible for the stabilisation of small wavelength modes. This dynamical mechanism is characterised by the saturation number, defined as the ratio of the saturation length to the water depth Lsat/H. This dimensionless number controls the transition from ripples (transverse patterns) at small Lsat/H to bars (inclined patterns) at large Lsat/H. At a given value of the saturation number, the instability presents a threshold and a convective-absolute transition, both controlled by the channel aspect ratio β. We have investigated the characteristics of the most unstable mode as a function of the main parameters, Lsat/H, β and of a subdominant parameter controlling the relative influence of drag and gravity on sediment transport. As previously found, the transition from alternate bars to multiple bars is mostly controlled by the river aspect ratio β. By contrast, in the alternate bar regime (large Lsat/H), the selected wavelength does not depend much on β and approximately scales as H^(2/3)L^(1/3)/C, where C is the Chézy number.

physics.flu-dyn↗

arXiv2012

Transition from viscous to inertial regime in dense suspensions

Non-Brownian suspensions present a transition from Newtonian behavior in the zero-shear limit to a shear thickening behaviour at a large shear rate, none of which is clearly understood so far. Here, we carry out numerical simulations of such an athermal dense suspension under shear, at an imposed confining pressure. This set-up is conceptually identical to the recent experiments of Boyer and co-workers [Phys. Rev. Lett. 107,188301 (2011)]. Varying the interstitial fluid viscosities, we recover the Newtonian and Bagnoldian regimes and show that they correspond to a dissipation dominated by viscous and contact forces respectively. We show that the two rheological regimes can be unified as a function of a single dimensionless number, by adding the contributions to the dissipation at a given volume fraction.

cond-mat.soft↗

arXiv2012

Shear flow of non-Brownian suspensions close to jamming

The dynamical mechanisms controlling the rheology of dense suspensions close to jamming are investigated numerically, using simplified models for the relevant dissipative forces. We show that the velocity fluctuations control the dissipation rate and therefore the effective viscosity of the suspension. These fluctuations are similar in quasi-static simulations and for finite strain rate calculations with various damping schemes. We conclude that the statistical properties of grain trajectories -- in particular the critical exponent of velocity fluctuations with respect to volume fraction ϕ-- only weakly depend on the dissipation mechanism. Rather they are determined by steric effects, which are the main driving forces in the quasistatic simulations. The critical exponent of the suspension viscosity with respect to ϕcan then be deduced, and is consistent with experimental data.

cond-mat.soft↗