Free radially expanding liquid sheet in air: time- and space-resolved measurement of the thickness field

The collision of a liquid drop against a small target results in the formation of a thin liquid sheet that extends radially until it reaches a maximum diameter. The subsequent retraction is due to the air-liquid surface tension. We have used a time- and space-resolved technique to measure the thickness field of this class of liquid sheet, based on the grey level measurement of the image of a dyed liquid sheet recorded using a fast camera. This method enables a precise measurement of the thickness in the range $(10-450) \, \mathrm{\mu m}$, with a temporal resolution equal to that of the camera. We have measured the evolution with time since impact, $t$, and radial position, $r$, of the thickness, $h(r,t)$, for various drop volumes and impact velocities. Two asymptotic regimes for the expansion of the sheet are evidenced. The scalings of the thickness with $t$ and $r$ measured in the two regimes are those that were predicted in \citet{Rozhkov2004} fort the short-time regime and \citet{Villermaux2011} for the long time regime, but never experimentally measured before. Interestingly, our experimental data also evidence the existence of a maximum of the film thickness $h_{\rm{max}}(r)$ at a radial position $r_{\rm{h_{max}}}(t)$ corresponding to the crossover of these two asymptotic regimes. The maximum moves with a constant velocity of the order of the drop impact velocity, as expected theoretically. Thanks to our visualization technique, we also evidence an azimuthal thickness modulation of the liquid sheets.Comment: accepted for publication in Journal of Fluid Mechanic

Inwardly curved polymer brushes : Concave is not like Convex

Inwardly curved polymer brushes are present in cylindrical and spherical micelles or in membranes tubes and vesicles decorated with anchored polymers, and influence their stability. We consider such polymer brushes in good solvent and show that previous works, based on a self-similar concentric structure of the brush, are physically inconsistent. We use scaling laws to derive very simply the leading term of the free energy in the high curvature limit, where the osmotic pressure is the relevant physical ingredient. We also derive the complete conformation at all curvatures using a self-consistent field approach. The free energy is computed therefrom using a local scaling description.Comment: Subm. to Eur. Phys. J. E., rev. version, 12 pages plus 9 figures, PACS : 36.20.Ey / 82.35.Gh / 82.70.-y. Figure 1 modified. In introduction, discussion added on concentration gradients near the edge of the brush. [email protected] [email protected] [email protected] [email protected]

Linear viscoelasticity of entangled wormlike micelles bridged by telechelic polymers : an experimental model for a double transient network

We survey the linear viscoelasticity of a new type of transient network: bridged wormlike micelles, whose structure has been characterized recently [Ramos and Ligoure, (2007)]. This composite material is obtained by adding telechelic copolymers (water-soluble chains with hydrophobic stickers at each extremity) to a solution of entangled wormlike micelles (WM). For comparison, naked WM and WM decorated by amphiphilic copolymers are also investigated. While these latter systems exhibit almost a same single ideal Maxwell behavior, solutions of bridged WM can be described as two Maxwell fluids components blends, characterized by two markedly different characteristic times, t_fast and t_slow, and two elastic moduli, G_fast and G_slow, with G_fast >> G_slow. We show that the slow mode is related to the viscoelasticity of the transient network of entangled WM, and the fast mode to the network of telechelic active chains (i.e. chains that do not form loops but bridge two micelles). The dependence of the viscoelasticity with the surfactant concentration, phi, and the sticker-to-surfactant molar ratio, beta, is discussed. In particular, we show that G_fast is proportional to the number of active chains in the material, phi beta. Simple theoretical expectations allow then to evaluate the bridges/loops ratio for the telechelic polymers

Brittle fracture of polymer transient networks

We study the fracture of reversible double transient networks, constituted of water suspensions of entangled surfactant wormlike micelles reversibly linked by various amounts of telechelic polymers. We provide a state diagram that delineates the regime of fracture without necking of the filament from the regime where no fracture or break-up has been observed. We show that filaments fracture when stretched at a rate larger than the inverse of the slowest relaxation time of the networks. We quantitatively demonstrate that dissipation processes are not relevant in our experimental conditions and that, depending on the density of nodes in the networks, fracture occurs in the linear viscoelastic regime or in a non-linear regime. In addition, analysis of the crack opening profiles indicates deviations from a parabolic shape close to the crack tip for weakly connected networks. We demonstrate a direct correlation between the amplitude of the deviation from the parabolic shape and the amount of non linear viscoelasticity

Instabilities in freely expanding sheets of associating viscoelastic fluids

We use the impact of drops on a small solid target as a tool to investigate the behavior of viscoelastic fluids under extreme deformation rates. We study two classes of transient networks: semidilute solutions of supramolecular polymers and suspensions of spherical oil droplets reversibly linked by polymers. The two types of samples display very similar linear viscoelastic properties, which can be described with a Maxwell fluid model, but contrasting nonlinear properties due to different network structure. Upon impact, weakly viscoelastic samples exhibit a behavior qualitatively similar to that of Newtonian fluids: A smooth and regular sheet forms, expands, and then retracts. By contrast, for highly viscoelastic fluids, the thickness of the sheet is found to be very irregular, leading to instabilities and eventually formation of holes. We find that material rheological properties rule the onset of instabilities. We first provide a simple image analysis of the expanding sheets to determine the onset of instabilities. We then demonstrate that a Deborah number related to the shortest relaxation time associated to the sample structure following a high shear is the relevant parameter that controls the heterogeneities in the thickness of the sheet, eventually leading to the formation of holes. When the sheet tears-up, data suggest by contrast that the opening dynamics depends also on the expansion rate of the sheet.Comment: accepted for publication in Soft Matte

A double rigidity transition rules the fate of drying colloidal drops

The evaporation of drops of colloidal suspensions plays an important role in numerous contexts, such as the production of powdered dairies, the synthesis of functional supraparticles, and virus and bacteria survival in aerosols or drops on surfaces. The presence of colloidal particles in the evaporating drop eventually leads to the formation of a dense shell that may undergo a shape instability. Previous works propose that, for drops evaporating very fast, the instability occurs when the particles form a rigid porous solid, constituted of permanently aggregated particles at random close packing. To date, however, no measurements could directly test this scenario and assess whether it also applies to drops drying at lower evaporation rates, severely limiting our understanding of this phenomenon and the possibility of harnessing it in applications. Here, we combine macroscopic imaging and space- and time-resolved measurements of the microscopic dynamics of colloidal nanoparticles in drying drops, measuring the evolution of the thickness of the shell and the spatial distribution and mobility of the nanoparticles. We find that, above a threshold evaporation rate, the drop undergoes successively two distinct shape instabilities. While the second instability is due to the permanent aggregation of nanoparticles, as hypothesized in previous works on fast-evaporating drops, we show that the first one results from a reversible glass transition of the shell, unreported so far. We rationalize our findings and discuss their implications in the framework of a unified state diagram for the drying of colloidal drops