Extremely small amounts of surface-active contaminants are known to drastically modify the hydrodynamic response of the water-air interface. Surfactant concentrations as low as a few thousand molecules per square micron are sufficient to eventually induce complete stiffening. In order to probe the shear response of a water-air interface, we design a radial flow experiment that consists in an upward water jet directed to the interface. We observe that the standard no-slip effect is often circumvented by an azimuthal instability with the occurence of a vortex pair. Supported by numerical simulations, we highlight that the instability occurs in the (inertia-less) Stokes regime and is driven by surfactant advection by the flow. The latter mechanism is suggested as a general feature in a wide variety of reported and yet unexplained observations.
We report an experimental investigation of spreading then shrinking of a surfactant droplet at the air-water interface with fingering instability appearing at the edge of the droplet stain. We find out that a droplet of a surfactant on the water shows three regimes of spreading, shrinking and resting at the appropriate parameters values. These regimes can be distinguished by measuring the mean square displacement of the droplet parts, fractal dimension of stain, or radius of fingerless part of the stain (to measure it, we define the angular box-counting dimension), versus time. The shrinking r…
We study the features of a radial Stokes flow due to a submerged jet directed toward a liquid-air interface. The presence of surface-active impurities confers to the interface an in-plane elasticity that resists the incident flow. Both analytical and numerical calculations show that a minute amount of surfactants is enough to profoundly alter the morphology of the flow. The hydrodynamic response of the interface is affected as well, shifting from slip to no-slip boundary condition as the surface compressibility decreases. We argue that the competition between the divergent outward flow and the…
The structure and stability of the convective flow generated by a source located at the water surface containing an insoluble surfactant layer are experimentally investigated. Application of a few types of source, which differ in the force driving the interface, and two surfactants with different rheological properties made it possible to generalize the results and to develop a unified approach to describing the flow patterns observed in this study. It is shown that, regardless of source type and surfactant used, the problem under consideration can be completely described in terms of two non-d…
A horizontal flow of two immiscible fluid layers with different densities, viscosities and thicknesses, subject to vertical gravitational forces and with an insoluble surfactant present at the interface, is investigated. The base Couette flow is driven by the horizontal motion of the channel walls. Linear and nonlinear stages of the (inertialess) surfactant and gravity dependent long-wave instability are studied using the lubrication approximation, which leads to a system of coupled nonlinear evolution equations for the interface and surfactant disturbances. The linear stability is determined …
Nonlinear stages of the recently uncovered instability due to insoluble surfactant at the interface between two fluids are investigated for the case of a creeping plane Couette flow with one of the fluids a thin film and the other one a much thicker layer. Numerical simulation of strongly nonlinear longwave evolution equations which couple the film thickness and the surfactant concentration reveals that in contrast to all similar instabilities of surfactant-free flows, no amount of the interfacial shear rate can lead to a small-amplitude saturation of the instability. Thus, the flow is stable …
A linear stability analysis of a two-layer plane Couette flow of two immiscible fluid layers with different densities, viscosities and thicknesses, bounded by two infinite parallel plates moving at a constant relative velocity to each other, with an insoluble surfactant along the interface and in the presence of gravity is carried out. The normal modes approach is applied to the equations governing flow disturbances. These equations, together with boundary conditions at the plates and the interface, yield a linear eigenvalue problem. When inertia is neglected velocity amplitudes are linear com…
The linear instability of a surfactant-laden two-layer falling film over an inclined slippery wall is analyzed under an influence of external shear which is imposed on the top surface of the flow. The free surface of the flow as well as the interface among the fluids are contaminated by insoluble surfactants. Dynamics of both the layers are governed by the Navier--Stokes equations, and the surfactant transport equation regulates the motion of the insoluble surfactants at the interface and free surface. Instability mechanisms are compared by imposing the external shear along and opposite to the…
In this work, we study the effect of insoluble surfactants on the three-dimensional rim-driven retraction dynamics of thin water sheets in air. We employ an interface-tracking/level-set method to ensure the full coupling between the surfactant-induced Marangoni-stresses, interfacial diffusion, and inertia. Our findings are contrasted with the (Newtonian) dynamics of a liquid sheet edge finding that the surfactant concentration can prevent, or delay, the breakup of the rim. Our simulations use the fastest growing Rayleigh-Plateau instability to drive droplet detachment from the fluid sheet (rim…
Experimental observations indicate that chemically active droplets suspended in a surfactant-laden fluid can self-propel spontaneously. The onset of this motion is attributed to a symmetry-breaking Marangoni instability resulting from the nonlinear advective coupling of the distribution of surfactant to the hydrodynamic flow generated by Marangoni stresses at the droplet's surface. Here, we use weakly nonlinear analysis to characterize the self-propulsion near the instability threshold and the influence of the droplet's deformability. We report that in vicinity of the threshold, deformability …
In experiments, an individual chemically active liquid crystal (LC) droplet submerged in the bulk of a surfactant solution may self-propel along a straight, helical, or random trajectory. In this paper, we develop a minimal model capturing all three types of self-propulsion trajectories of a drop in the case of a nematic LC with homeotropic anchoring at LC-fluid interface. We emulate the director field within the drop by a single preferred polarization vector that is subject of two reorientation mechanisms, namely, the internal flow-induced displacement of the hedgehog defect and the droplet's…
Solutocapillary instability in slipping falling films
Centre for Applied Sciences (CAS), International Institute of Information Technology（国际信息技术学院应用科学中心）；Université Claude Bernard Lyon 1, LMFA, UMR 5509, CNRS, Ecole Centrale de Lyon, INSA Lyon（里昂第一大学）；Department of Mathematics, Vivekananda Mahavidyalaya（维韦卡南达学院数学系）
Flow structure stability of a steady radial thermocapillary flow from the local heat source in cylindrical geometry has been studied numerically. The up boundary of the liquid was partially covered by the stationary film of an insoluble surfactant, pushed to the wall of the cavity. The calculations are fulfilled on the base of interfacial hydrodynamics equations by using mathematical package Comsol Multiphysics. It is shown that the effect of a radial flow symmetry breakdown is appeared as a result of convective instability, so that the initial poloidal rotation of the liquid transforms into t…
The instability of ideal non-divergent zonal flows on the sphere is determined numerically by the instability criterion of Arnol'd (1966) for the sectional curvature. Zonal flows are unstable for all perturbations besides for a small set which are in approximate resonance. The sectional curvature scales with $m/\ell$ for large total and zonal wave numbers $\ell$ and $m$ of the perturbations. The planetary rotation is stable and the presence of rotation reduces the instability of perturbations.
Flexible rings and rectangle structures floating at the surface of water are prone to deflect under the action of surface pressure induced by the addition of surfactant molecules on the bath. While the frames of rectangles bend inward or outward for any surface pressure difference, circles are only deformed by compression beyond a critical buckling load. However, compressed frames also undergo a secondary buckling instability leading to a rhoboidal shape. Following the pioneering works of \cite{Hu} and \cite{Zell}, we describe both experimentally and theoretically the different elasto-capillar…
Natural icicles often exhibit ripples about their circumference which are due to a morphological instability. We present an experimental study that explores the origin of the instability, using laboratory-grown icicles. Contrary to theoretical expectations, icicles grown from pure water do not exhibit growing ripples. The addition of a non-ionic surfactant, which reduces the surface tension, does not produce ripples. Instead, ripples emerge on icicles grown from water with dissolved ionic impurities. We find that even very small levels of impurity are sufficient to trigger ripples, and that th…
Electrokinetic flow can be generated as a highly coupled phenomenon among velocity field, electric conductivity field and electric field. It can exhibit different responses to AC electric fields in different frequency regimes, according to different instability/receptivity mechanisms. In this investigation, by both flow visualization and single-point laser-induced fluorescence (LIF) method, the response of AC electrokinetic flow and the transition routes towards chaos and turbulence have been experimentally investigated. It is found, when the AC frequency $f_f<30$ Hz, the interface responds at…
In this paper, the instability of layered two-phase flows caused by the presence of a soluble surfactant (or a surface active solute) is studied. The fluids have different viscosities, but are density matched to focus on Marangoni effects. The fluids flow between two flat plates, which are maintained at different solute concentrations. This establishes a constant flux of solute from one fluid to the other in the base state. A linear stability analysis is performed, using a combination of asymptotic and numerical methods. In the creeping flow regime, Marangoni stresses destabilize the flow, pro…
Although the critical Reynolds number for linear instability of the laminar flow in a straight pipe is infinite, we show that it is finite for a divergent pipe, and approaches infinity as the inverse of the divergence angle. The velocity profile at the threshold of inviscid stability is obtained. A non-parallel analysis yields linear instability at surprisingly low Reynolds numbers, of about 150 for a divergence of 3 degrees, which would suggest a role for such instabilities in the transition to turbulence. A multigrid Poisson equation solver is employed for the basic flow, and an extended eig…
