Pinch-off in the presence of surface-active polymers

International audienceThe rupture of fluid necks in a surrounding liquid in the presence of surface-active polymers shows a variety of changes with respect to the pure-fluid case. The role of the surface rheology due solely to the presence of such agents at the surface is uncovered by studying how the fluid neck radius approaches zero at pinch-off. The thinning dynamics of the neck turn out to be exponential in time. The thinning rate extracted from this dynamics is related to the surface viscosity of the polymer layer coating the interface and estimates of this quantity are presented

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

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

Anomalous near-equilibrium capillary rise

We report and rationalize the observation of a crossover from the classical Lucas-Washburn dynamics to a long-lived anomalously slow regime for capillary rise in simple glass tubes. We propose an analytical model considering the role of thermal motion and the nanoscale surface topography to account for the experimental observations. The proposed model indicates that the contact line perimeter and the surface topography dimensions determine the crossover condition and anomalous imbibition rate. Our findings have important implications for the scientific understanding and technical application of capillary imbibition and suggest strategies to control the adsorption of specific liquids in porous materials

The Marangoni flow of soluble amphiphiles

Surfactant distribution heterogeneities at a fluid/fluid interface trigger the Marangoni effect, i.e. a bulk flow due to a surface tension gradient. The influence of surfactant solubility in the bulk on these flows remains incompletely characterized. Here we study Marangoni flows sustained by injection of hydrosoluble surfactants at the air/water interface. We show that the flow extent increases with a decrease of the critical micelle concentration, i.e. the concentration at which these surfactants self-assemble in water. We document the universality of the surface velocity field and predict scaling laws based on hydrodynamics and surfactant physicochemistry that capture the flow features.Comment: 5 pages, 4 figures, submitte

Reply to Karpitschka et al.: The Neumann force balance does not hold in dynamical elastowetting

International audienceIn their letter [1], Karpitschka et al. discuss our claim that the predictions of our theoretical description for the spreading of a droplet on a soft solid layer based on a global-dissipation approach [2] differ from the outcomes of Karpitschka et al.'s model based on a local-force-balance analysis [3]. In particular, Karpitschka et al. claim that our conclusion results from a misstep in our calculation. We explain here the motivations behind our approach and why we think that their model is different from ours, the latter being the only one able to reproduce our extensive set of experimental data. Let us state first that we agree with Karpitschka et al. that "models based on energy dissipation or on force balance" should be "equivalent". However, contrary to their claim, the dissipation power P visc due to viscoelastic stresses cannot be transformed into a contour integral in general. In particular, care must be taken when fields such as strains or stresses present jumps in their value. Such a jump occurs in the elastowetting problem, as the sign of the first derivative of the strain field jumps from negative to positive in the vicinity of the contact line. The solid must be divided in two regions A and B separated by a surface Γ that encompasses the contact line and that is normal to the flat elastomer surface. The dissipation P visc in this system reads: P visc = A B σ ij˙ ij d 2 s = ∂A ∂B/Γ σ ij n jui d + Γ [σ ijui ]n j d (1) where the symbol [f ] denotes the jump of f across Γ. The last term in the equation above does not vanish for arbitrary thickness and rheology. Thus, we conclude that the simple form of the divergence theorem on which Eq. 1 in ref. [1] is based cannot be used here. As a final note, we would like to indicate that current work in our group shows that configurational forces contribute to global dissipation besides Newtonian forces. In our paper [2], instead of calculating the full dissipation, we choose a simpler, approximated route. Indeed, we do not enforce Neumann's force balance at the contact line and we hypothesize that dissipation can be represented by a single term (∼ A B σ zx˙ zx d 2 s). Thus, our model is not equivalent to Karpitschka et al.'s. The remaining dissipative term is then calculated under some approximations, as an effective representation of the full dissipation. The resulting formula provides an excellent fit to the experimental data for the dependence of the dynamic contact angle on the thickness of the elastomer layer, indicating that the approximations underlying our description are reasonable. In contrast, Karpitschka et al.'s model does not capture our data. In other words, our results do not support the hypothesis that the Neumann force balance holds at the tip of a moving contact line, as stated in our paper. We note that our model is only one step among many others that remain to build a thorough and sound description of the dynamics of elastowetting. We agree with Karpitschka et al. that work remains to be done to explain the vast amount of observations that has been reported in the literature on the topic of elastowetting

Viscoelastic liquid curtains: Experimental results on the flow of a falling sheet of polymer solution

International audienceWe experimentally investigate the extensional flow of a sheet-or curtain-of viscoelastic liquid falling freely from a slot at constant flow rate under gravity. Extruded liquids are aqueous solutions of flexible polyethylene oxide (PEO) and of semi-rigid partially hydrolysed polyacrylamide (HPAM) with low shear viscosities. Velocimetry measurements reveal that the mean velocity field U(z), z being the distance from the slot exit, does not reduce to a free-fall. More precisely, we show that the liquid falls initially with sub-gravitational accelerations up to a distance from the slot which scales as gτ 2 f il , where g is gravity and τ f il is the extensional relaxation time of the liquid, beyond which the local acceleration reaches the asymptotic free-fall value g. The length of the sub-gravitational part of the curtain is shown to be much larger than the equivalent viscous length ((4η/ρ) 2 /g) 1/3 for Newtonian liquids of density ρ and dynamic viscosity η, which is usually small compared to the length of the curtain. The elastic length gτ 2 f il can indeed be surprisingly large when adding high molecular weight polymer molecules to a low-viscosity Newtonian solvent. By analogy with Newtonian curtains, we show that the velocity field U(z) rescales on a master curve. Besides, we show that the flow is only weakly affected by the history of polymer deformations in the die upstream of the curtain. Furthermore, investigations of the curtain stability reveal that polymer addition reduces the minimum flow rate required to maintain a continuous sheet of liquid

Interface breakup in presence of surface agents

Le détachement d'une goutte est un phénomène que nous observons quotidiennement. Il résulte de la rupture de l'interface entre le fluide dispersé en goutte et le fluide environnant. Cette rupture a fait l'objet de nombreuses études. Il est bien établi que sa dynamique est régie par une compétition entre la capillarité, l'inertie, et la viscosité du fluide. Ce manuscrit décrit l'influence sur la dynamique de rupture d'une modification des propriétés de l'interface entre deux fluides à l'aide d'agents de surface. Lorsque l'agent de surface est un surfactant (SDS), la dynamique d'amincissement peut se faire selon deux modes. Deux régimes linéaires en temps constituent le premier mode. Le second mode comporte trois régimes linéaires. Dans les deux cas, l'amincissement commence par un premier régime, suivi d'un deuxième régime de pente plus forte. Lorsque le troisième régime existe, sa pente est inférieure à celle du second régime. La variation des pentes des régimes linéaires témoigne du comportement dynamique du surfactant à l'interface. La valeur de la tension interfaciale extraite du premier régime linéaire correspond à la valeur à l'équilibre de la tension interfaciale du système, gamma_eq. La vitesse d'amincissement plus élevée au cours du second régime est reliée à une dépletion partielle en surfactant de la zone d'amincissement maximal. Le ralentissement constaté pendant le troisième régime est lié au déplacement de cette zone vers une région plus riche en surfactant, où la tension est plus faible. La dynamique d'amincissement du cou est très différente lorsque des polymères de poids moléculaire intermédiaire (env. 100 kDa) sont présents simultanément avec du SDS dans la phase continue. Lorsque [SDS] est supérieure à 0,15 fois la concentration micellaire critique (CMC), le comportement est identique à celui observé en présence de surfactant seul. En dessous de 0,15 CMC, l'amincissement ralentit exponentiellement à l'approche de la rupture, et un phénomène de beads-on-a-string apparaît. Ces constatations sont analogues à celles faites lorsqu'une solution de polymères est menée à la rupture. Dans notre cas, les polymères sont uniquement à la surface du jet et non dans son volume ! Une analyse des profils du cou au cours du temps démontre l'existence d'une auto-similarité à l'approche de la rupture. Bien que les systèmes étudiés soient plus complexes, ils présentent des caractéristiques qualitativement analogues à celles observées dans des systèmes de fluides simples. Toutefois, il existe une grande différence quantitative.Droplet detachment is ubiquitous in everyday life. It results from the rupture of an interface separating two fluids. This rupture has been widely studied. It is now well established that it relies on a competition between capillary, inertial and viscous phenomena. In this manuscript, we report on the influence on the breakup dynamics of the presence of surface agents at the interface. When SDS is used as a surface agent, thinning can proceed in two ways. In the first mode, the dynamics of thinning are characterized by two time-linear regimes. The second mode is made of three time-linear regimes. In both cases, thinning starts with a first regime, followed by a steeper second regime. When a third regime exists, its slope is smaller. Slope variation bears witness to a dynamical behaviour of the surfactants at the interface. The value for the interfacial tension gamma calculated from the slope of the first linear regime is in agreement with the equilibrium interfacial tension of the system, gamma_eq. The higher thinning speed during the second regime is linked to a partial depletion in surfactant of the maximal thinning zone. The slowdown in the tihrd regime is related to a displacement of the thinning zone in a region of higher surfactant concentration, where gamma is lower. The thinning dynamics is very different when polymers are added to the surfactant solution. If [SDS] is higher than 0.15 times the critical micellar concentration (CMC), a behaviour similar to the pure-surfactant case is observed. Below 0.15 CMC, an exponential slowdown is observed in the last instants, as well as a "'beads-on-a-string"' phenomenon. These observations are analogous to what is seen when a solution of polymers is led to breakup. In our case, polymers are not in the bulk ; they are at the interface of the two fluids ! Analysis of the profiles of the neck in both cases showed that profiles are self-similar. Qualitatively, they share features with profiles observed in the case of breakup of interfaces between simple fluids. Quantitatively, slopes and angles are different

Interface breakup in presence of surface agents

Le détachement d'une goutte est un phénomène que nous observons quotidiennement. Il résulte de la rupture de l'interface entre le fluide dispersé en goutte et le fluide environnant. Cette rupture a fait l'objet de nombreuses études. Il est bien établi que sa dynamique est régie par une compétition entre la capillarité, l'inertie, et la viscosité du fluide. Ce manuscrit décrit l'influence sur la dynamique de rupture d'une modification des propriétés de l'interface entre deux fluides à l'aide d'agents de surface. Lorsque l'agent de surface est un surfactant (SDS), la dynamique d'amincissement peut se faire selon deux modes. Deux régimes linéaires en temps constituent le premier mode. Le second mode comporte trois régimes linéaires. Dans les deux cas, l'amincissement commence par un premier régime, suivi d'un deuxième régime de pente plus forte. Lorsque le troisième régime existe, sa pente est inférieure à celle du second régime. La variation des pentes des régimes linéaires témoigne du comportement dynamique du surfactant à l'interface. La valeur de la tension interfaciale extraite du premier régime linéaire correspond à la valeur à l'équilibre de la tension interfaciale du système, gamma_eq. La vitesse d'amincissement plus élevée au cours du second régime est reliée à une dépletion partielle en surfactant de la zone d'amincissement maximal. Le ralentissement constaté pendant le troisième régime est lié au déplacement de cette zone vers une région plus riche en surfactant, où la tension est plus faible. La dynamique d'amincissement du cou est très différente lorsque des polymères de poids moléculaire intermédiaire (env. 100 kDa) sont présents simultanément avec du SDS dans la phase continue. Lorsque [SDS] est supérieure à 0,15 fois la concentration micellaire critique (CMC), le comportement est identique à celui observé en présence de surfactant seul. En dessous de 0,15 CMC, l'amincissement ralentit exponentiellement à l'approche de la rupture, et un phénomène de beads-on-a-string apparaît. Ces constatations sont analogues à celles faites lorsqu'une solution de polymères est menée à la rupture. Dans notre cas, les polymères sont uniquement à la surface du jet et non dans son volume ! Une analyse des profils du cou au cours du temps démontre l'existence d'une auto-similarité à l'approche de la rupture. Bien que les systèmes étudiés soient plus complexes, ils présentent des caractéristiques qualitativement analogues à celles observées dans des systèmes de fluides simples. Toutefois, il existe une grande différence quantitative.Droplet detachment is ubiquitous in everyday life. It results from the rupture of an interface separating two fluids. This rupture has been widely studied. It is now well established that it relies on a competition between capillary, inertial and viscous phenomena. In this manuscript, we report on the influence on the breakup dynamics of the presence of surface agents at the interface. When SDS is used as a surface agent, thinning can proceed in two ways. In the first mode, the dynamics of thinning are characterized by two time-linear regimes. The second mode is made of three time-linear regimes. In both cases, thinning starts with a first regime, followed by a steeper second regime. When a third regime exists, its slope is smaller. Slope variation bears witness to a dynamical behaviour of the surfactants at the interface. The value for the interfacial tension gamma calculated from the slope of the first linear regime is in agreement with the equilibrium interfacial tension of the system, gamma_eq. The higher thinning speed during the second regime is linked to a partial depletion in surfactant of the maximal thinning zone. The slowdown in the tihrd regime is related to a displacement of the thinning zone in a region of higher surfactant concentration, where gamma is lower. The thinning dynamics is very different when polymers are added to the surfactant solution. If [SDS] is higher than 0.15 times the critical micellar concentration (CMC), a behaviour similar to the pure-surfactant case is observed. Below 0.15 CMC, an exponential slowdown is observed in the last instants, as well as a "'beads-on-a-string"' phenomenon. These observations are analogous to what is seen when a solution of polymers is led to breakup. In our case, polymers are not in the bulk ; they are at the interface of the two fluids ! Analysis of the profiles of the neck in both cases showed that profiles are self-similar. Qualitatively, they share features with profiles observed in the case of breakup of interfaces between simple fluids. Quantitatively, slopes and angles are different