Contact lines on soft solids with uniform surface tension: analytical solutions and double transition for increasing deformability

International audienceUsing an exact Green function method, we calculate analytically the substrate deformations near straight contact lines on a soft, linearly elastic incompressible solid, having a uniform surface tension γs. This generalized Flamant-Cerruti problem of a single contact line is regularized by introducing a finite width 2a for the contact line. We then explore the dependance of the substrate deformations upon the softness ratio ls/a, where ls = γs/(2µ) is the elastocapillary length built upon γs and on the elastic shear modulus µ. We discuss the force transmission problem from the liquid surface tension to the bulk and surface of the solid, and show that Neuman condition of surface tension balance at the contact line is only satisfied in the asymptotic limit a/ls → 0, Young condition holding in the opposite limit. We then address the problem of two parallel contact lines separated from a distance 2R, and we recover analytically the "double transition" upon the ratios ls/a and R/ls identified recently by Lubbers et al, when one increases the substrate deformability. We also establish a simple analytic law ruling the contact angle selection upon R/ls in the limit a/ls ≪ 1, that is the most common situation encountered in problems of wetting on soft materials

Elastic growth in thin geometries

International audienceGeneration of shapes in biological tissues is a complex multiscale phenomenon. Biochemical details of cell proliferation, death and mobility can be incorporated within a continuum mechanical framework by specifying locally the amplitude and direction of growth. For tissues exhibiting an elastic behavior, equilibrium shapes of growing bodies can be evaluated through the minimization of an appropriate energy. This model is applied to thin shells and plates, a geometry relevant to nuts and pollen grains but also leaves, petals and algae

Diffusiophoretic manipulation of particles in a drop deposited on a hydrogel

We report an experimental study on the manipulation of colloidal particles in a drop sitting on a hydrogel. The manipulation is achieved by diffusiophoresis, which describes a directed motion of particles induced by solute gradients. By letting the solute concentrations for the drop and the hydrogel be different, we control the motion of particles in a stable suspension, which is otherwise difficult to achieve. We show that diffusiophoresis can cause the particles to move either toward or away from the liquid-air interface depending on the direction of the solute gradient and the surface charge of the particles. We measure the particle adsorption experimentally and rationalize the results with a one-dimensional numerical model. We show that diffusiophoretic motion is significant at the lengthscale of a drop deposited on a hydrogel, which suggests a simple method for the deposition of particles on hydrogels

Homogeneous deposition of particles by absorption on hydrogels

When a drop containing colloidal particles evaporates on a surface, a circular stain made of these particles is often observed due to an internal flow toward the contact line. To hinder this effect, several approaches have been proposed such as flow modification by addition of surfactants or control of the interactions between the particles. All of these strategies involve the liquid phase while maintaining the drying process. However, substitution of evaporation by absorption into the substrate of the solvent has been investigated less. Here, we show that a droplet containing colloidal particles deposited on swelling hydrogels can lead to a nearly uniform coating. We report experiments and theory to explore the relation between the gel swelling, uniformity of deposition and the adsorption dynamics of the particles at the substrate. Our findings suggest that draining the solvent by absorption provides a robust route to homogeneous coatings

Irreversible Collective Migration of Cyanobacteria in Eutrophic Conditions

In response to natural or anthropocentric pollutions coupled to global climate changes, microorganisms from aquatic environments can suddenly accumulate on water surface. These dense suspensions, known as blooms, are harmful to ecosystems and significantly degrade the quality of water resources. In order to determine the physico-chemical parameters involved in their formation and quantitatively predict their appearance, we successfully reproduced irreversible cyanobacterial blooms in vitro. By combining chemical, biochemical and hydrodynamic evidences, we identify a mechanism, unrelated to the presence of internal gas vesicles, allowing the sudden collective upward migration in test tubes of several cyanobacterial strains (Microcystis aeruginosa PCC 7005, Microcystis aeruginosa PCC 7806 and Synechocystis sp. PCC 6803). The final state consists in a foamy layer of biomass at the air-liquid interface, in which micro-organisms remain alive for weeks, the medium lying below being almost completely depleted of cyanobacteria. These "laboratory blooms" start with the aggregation of cells at high ionic force in cyanobacterial strains that produce anionic extracellular polymeric substances (EPS). Under appropriate conditions of nutrients and light intensity, the high photosynthetic activity within cell clusters leads the dissolved oxygen (DO) to supersaturate and to nucleate into bubbles. Trapped within the EPS, these bubbles grow until their buoyancy pulls the biomass towards the free surface. By investigating a wide range of spatially homogeneous environmental conditions (illumination, salinity, cell and nutrient concentration) we identify species-dependent thresholds and timescales for bloom formation. We conclude on the relevance of such results for cyanobacterial bloom formation in the environment and we propose an efficient method for biomass harvesting in bioreactors.Comment: 16 Pages, 4 figure

Light-controlled flows in active fluids

International audienceMany photosynthetic microorganisms are able to detect light and move toward optimal intensities. This ability, known as phototaxis, plays a major role in ecology by affecting natural phytoplankton mass transfers and has important applications in bioreactor and artificial microswimmers technologies. Here we show that this property can be exploited to generate macroscopic fluid flows using a localized light source directed toward shallow suspensions of phototactic microorganisms. Within the intensity range of positive phototaxis, algae accumulate beneath the excitation light where collective effects lead to the emergence of radially symmetric convective flows. These flows can thus be used as hydrodynamic tweezers to manipulate small floating objects. At high cell density and layer depth, we uncover a new kind of instability wherein the viscous torque exerted by self-generated fluid flows on the swimmers induces the formation of traveling waves. A model coupling fluid flow, cell concentration and orientation finely reproduces the experimental data

Nonlinear force balance at moving contact lines

The spreading of a liquid over a solid material is a key process in a wide range of applications. While this phenomenon is well understood when the solid is undeformable, its "soft" counterpart is still ill-understood and no consensus has been reached with regards to the physical mechanisms ruling the spreading of liquid drops over soft deformable materials. In this work we show that the motion of a triple line on a soft elastomer is opposed both by nonlinear localized capillary and visco-elastic forces. We give an explicit analytic formula relating the dynamic contact angle of a moving drop with its velocity for arbitrary rheology. We then specialize this formula to the experimentally relevant case of elastomers with Chasset-Thirion (power-law) type of rheologies. The theoretical prediction are in very good agreement with experimental data, without any adjustable parameters. Finally, we show that the nonlinear force balance presented in this work can also be used to recover the classical de Gennes model of wetting

On growth and form of Bacillus subtilis biofilms

International audienceA general feature of mature biofilms is their highly heterogeneous architecture that partitions the microbial city into sectors with specific micro-environments. To understand how this heterogeneity arises, we have investigated the for- mation of a microbial community of the model organism Bacillus subtilis. We first show that the growth of macroscopic colonies is inhibited by the accumulation of ammoniacal by-products. By constraining biofilms to grow approximately as two-dimensional layers, we then find that the bacteria which differentiate to produce extracellular polymeric substances form tightly packed bacterial chains. In addition to the process of cellular chaining, the bio- mass stickiness also strongly hinders the reorganization of cells within the biofilm. Based on these observations, we then write a biomechanical model for the growth of the biofilm where the cell density is constant and the physical mechanism responsible for the spreading of the biomass is the pressure gener- ated by the division of the bacteria. Besides reproducing the velocity field of the biomass across the biofilm, the model predicts that, although bacteria divide everywhere in the biofilm, fluctuations in the growth rates of the bacteria lead to a coarsening of the growing bacterial layer. This process of kin- etic roughening ultimately leads to the formation of a rough biofilm surface exhibiting self-similar properties. Experimental measurements of the biofilm texture confirm these predictions

Morphology and stability of droplets sliding on soft viscoelastic substrates

Soft solids such as gels and elastomers can be compliant enough to deform when a droplet lies on their surface, in particular at the line of contact between the solid, the liquid and the atmosphere. While axisymmetric contact line motion has received a lot of attention, much less is known about droplets moving on soft substrates, a configuration often encountered in applications in which symmetry may be lost. We investigate here the dynamic properties of droplets sliding on thick viscoelastic layers. We show that the partition of energy dissipation between the liquid and the solid sets the shape and velocity of droplets. When dissipation parts equally between the liquid and the solid, droplet dynamics are similar to that of droplets on rigid substrates. In the opposite case, we observe shapes that indicate the presence of contact angle hysteresis. We compare our observations to a non-linear model of the wetting of soft solids that we proposed recently. We find the model to be in excellent agreement with our data, in particular regarding the prediction of the hysteresis that we show to be only apparent. This work opens fondamental questions on the connection between the properties of the substrate and the dynamics, shapes and fragmentation of moving droplets that are relevant to all applications where soft gel coatings may be used.Comment: 19 pages, 7 figures, supplemental materials include