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-dimensional parameters. The first is the elasticity number introduced earlier by Homsy and Meiburg (J. Fluid Mech., v.139, 1984). This parameter is the ratio of two shear stresses formed at the interface by surfactant and source, and it defines the formation of the convective zone at the center nearby the source and the size of the stagnant zone at the periphery. The second, called the surface Rayleigh number, is introduced for the first time in this paper. It is responsible for the appearance of the multi-vortex flow structure within the stagnant zone. We suppose that this structure occurs as a result of the mechanical equilibrium instability of the surfactant layer under the action of the momentum flux transported from the subphase by the viscous mechanism. Based on our results and those reported earlier by other researchers, we have determined the critical value of the surface Rayleigh number and analyzed the possibility and conditions for the occurrence of this instability, called by us the shear-driven surfactant layer (SDSL) instability, by addressing some problems of interfacial hydrodynamics.
We have developed a multi-phase SPH method to simulate arbitrary interfaces containing surface active agents (surfactants) that locally change the properties of the interface, such the surface tension coefficient. Our method incorporates the effects of surface diffusion, transport of surfactant from/to the bulk phase to/from the interface and diffusion in the bulk phase. Neglecting transport mechanisms, we use this method to study the impact of insoluble surfactants on drop deformation and breakup in simple shear flow and present the results in a fluid dynamics video.
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 the present study we analytically investigate the deformation and bulk rheology of a dilute emulsion of surfactant-laden droplets suspended in a linear flow. We use an asymptotic approach to predict the effect of surfactant distribution on the deformation of a single droplet as well as the effective shear and extensional viscosity for the dilute emulsion. The non-uniform distribution of surfactants due to the bulk flow results in the generation of a Marangoni stress which affects both the deformation as well as the bulk rheology of the suspension. The present analysis is done for the limiti…
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…
Superhydrophobic surfaces (SHSs) have the potential to reduce drag at solid boundaries. However, multiple independent studies have recently shown that small amounts of surfactant, naturally present in the environment, can induce Marangoni forces that increase drag, at least in the laminar regime. To obtain accurate drag predictions, one must solve the mass, momentum, bulk surfactant and interfacial surfactant conservation equations. This requires expensive simulations, thus preventing surfactant from being widely considered in SHS studies. To address this issue, we propose a theory for steady,…
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 simulat…
The effects of surfactant coating on a deformable viscous drop under the combined action of a shear flow and a uniform electric field, are investigated by solving the coupled equations of electrostatics, fluid flow and surfactant transport. Employing a comprehensive three-dimensional solution technique, the non-Newtonian shearing response of the bulk emulsion is analyzed in the dilute suspension regime. The present results reveal that the surfactant non-uniformity creates significant alterations in the flow disturbance around the drop, thereby influencing the viscous dissipation from the flowi…
The present study deals with the effect of interfacial slip on the deformation and emulsion rheology of a dilute suspension of droplets in a linear flow. The droplets are laden with surfactants that are bulk-insoluble and get transported only along the interface. An asymptotic approach is adopted for the present analysis in order to tackle the nonlinearity present due to deformation of droplets. The analysis is carried out under two different limiting scenarios namely: surface diffusion-dominated-surfactant transport and surface convection-dominated surfactant transport. For either of the limi…
We present three-dimensional numerical simulations, employing the well-established lattice Boltzmann method, and investigate similarities and differences between surfactants and nanoparticles as additives at a fluid-fluid interface. We report on their respective effects on the surface tension of such an interface. Next, we subject a fluid droplet to shear and explore the deformation properties of the droplet, its inclination angle relative to the shear flow, the dynamics of the particles at the interface, and the possibility of breakup. Particles are seen not to affect the surface tension of t…
We study shear-driven liquid flow over a planar surface with an embedded gas-filled groove, with the gas-liquid interface protruding slightly above or below the planar surface. The flow direction is along the groove, taken to be much longer than wide, and the gas-liquid interface is assumed to be covered by an incompressible surface fluid, representing a surfactant phase. Using the incompressiblity condition for the surface fluid, the equations of motion and corresponding boundary conditions for the liquid phase are obtained by minimizing the dissipation rate. Assuming a moderate deformation o…
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 …
Using numerical simulations, we investigate the effects of Marangoni stresses induced by surfactants on the effective slip length of liquid-infused surfaces (LIS) with transverse grooves. The surfactants are assumed soluble in the external liquid shearing the surface and can adsorb onto the interfaces. Two different adsorption models are used: a classical Frumkin model and a more advanced model that better describes the decrease of surface tension for minuscule concentrations. The simulations show that LIS may face even more severe effects of surfactants than previously investigated superhydro…
We model the advective Marangoni spreading of insoluble surfactant at the free surface of a viscous fluid that is confined within a two-dimensional rectangular cavity. Interfacial deflections are assumed small, with contact lines pinned to the walls of the cavity, and inertia is neglected. Linearizing the surfactant transport equation about the equilibrium state allows a modal decomposition of the dynamics, with eigenvalues corresponding to decay rates of perturbations. Computation of the family of mutually orthogonal two-dimensional eigenfunctions reveals singular flow structures near each co…
Surfactant solutions exhibit multilamellar surfactant vesicles (MLVs) under flow conditions and in concentration ranges which are found in a large number of industrial applications. MLVs are typically formed from a lamellar phase and play an important role in determining the rheological properties of surfactant solutions. Despite the wide literature on the collective dynamics of flowing MLVs, investigations on the flow behavior of single MLVs are scarce. In this work, we investigate a concentrated aqueous solution of linear alkylbenzene sulfonic acid (HLAS), characterized by MLVs dispersed in …
Long-chained surfactant solutions have found widespread use in the oil and gas industry due to a host of attractive properties. In this paper, we characterize one such commercially used viscoelastic surfactant that forms a wormlike micellar gel at room temperature and a viscoelastic solution at higher temperatures. We probe both states by conducting linear and nonlinear rheological tests and analyze their behaviour under the framework of micellar rheology. Our study outlines departure from behaviour exhibited by more conventional micellar systems and uncovers interesting dynamics like shear-in…
The physico-chemistry of surfactants (amphiphilic surface active agents) is often used to control the dynamics of viscous drops and bubbles. Surfactant sorption kinetics has been shown to play a critical role in the deformation of drops in extensional and shear flows, yet to the best of our knowledge these kinetics effects on a viscous drop in an electric fieldhave not been accounted for. In this paper we numerically investigate the effects of sorption kinetics on a surfactant-covered viscous drop in an electric field. Over a range of electric conductivity and permittivity ratios between the i…
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…
In this paper, we study the flow physics underlying the recently developed remote sensing capability of detecting oceanic microplastics, which is based on the measurable surface roughness reduction induced by the presence of microplastics on the ocean surface. In particular, we are interested in whether this roughness reduction is caused by the microplastics as floating particles, or by the surfactants which follow similar transport paths as microplastics. For this purpose, we experimentally test the effects of floating particles and surfactants on surface roughness, quantified by the mean squ…
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 …
This letter investigates the effect of shear on Rayleigh-Taylor instability (RTI). Even simple uniform shear strongly influences the instability; longer waves are completely stabilized when density stratification is large (higher Atwood numbers). This apparently counter-intuitive result is due to the presence of Atwood number in the shear term. When the unstable density interface is embedded in a shear layer, shear is again found to stabilize the RTI. However, this configuration introduces additional unstable shear instability modes in the lower wavenumber regime. A new type of shear instabili…
Understanding and modulating the cross-stream motion of a surfactant-coated droplet in pressure driven flow has great implications in many practical applications. A combination of interfacial viscosity and Marangoni stress acting over a surfactant-coated droplet in pressure driven flow offers greater flexibility to modulate the cross-stream motion of it. Despite the intense theoretical and numerical research towards manipulating the surfactant-laden Newtonian droplets in Poiseuille flow, the experimental investigations are seldom explored. Herein, we report our study on understanding the influ…
Wave interaction theory can be used as a tool to understand and predict instability in a variety of homogeneous and stratified shear flows. It is however, most often limited to piecewise-linear profiles of the shear layer background velocity, in which stable vorticity wave modes can be easily identified, and their interaction quantified. This approach to understanding shear flow instability is extended herein to smooth shear layer profiles. We describe a method, by which the stable vorticity wave modes can be identified, and show that their interaction results in an excellent description of th…
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 surface shear viscosity of an insoluble surfactant monolayer often depends strongly on its surface pressure. Here, we show that a particle moving within a bounded monolayer breaks the kinematic reversibility of low-Reynolds-number flows. The Lorentz reciprocal theorem allows such irreversibilities to be computed without solving the full nonlinear equations, giving the leading-order contribution of surface-pressure-dependent surface viscosity. In particular, we show that a disk translating or rotating near an interfacial boundary experiences a force in the direction perpendicular to that bo…
We study the destabilization of a round liquid jet by a fast annular gas stream. We measure the frequency of the shear instability waves for several geometries and air/water velocities. We then carry out a linear stability analysis, and show that there are three competing mechanisms for the destabilization: a convective instability, an absolute instability driven by surface tension, and an absolute instability driven by confinement. We compare the predictions of this analysis with experimental results, and propose scaling laws for wave frequency in each regime. We finally introduce criteria to…
The present study theoretically predicts the effect of interfacial viscosity on the deformation of a compound drop as well as on the bulk rheology. The system at hand comprises of a dilute emulsion of concentric compound drops, laden with surfactants and suspended in a linear flow. Two types of linear flows are considered in this study, namely, a uniaxial extensional flow and a simple shear flow. Presence of surfactants along the drop surface leads to the generation of an interfacial viscosity, which is different from the bulk. This interfacial viscosity generates a viscous drag that along wit…
We analyze both theoretically and experimentally the breakup of a pendant water droplet loaded with Sodium Dodecyl Sulfate (SDS). The free surface minimum radius measured in the experiments is compared with that obtained from a numerical solution of the full Navier-Stokes equations for different values of the shear and dilatational surface viscosities. This comparison shows the small but measurable effect of the surface viscous stresses on the system dynamics for sufficiently small spatiotemporal distances from the breakup point, and allows to establish upper bounds for the values of the shear…
In this paper, the instability of shallow water shear flow with a sheared parallel magnetic field is studied. Waves propagating in such magnetic shear flows encounter critical levels where the phase velocity relative to the basic flow $c-U(y)$ matches the Alfvén wave velocities $\pm B(y)/\sqrt{μρ}$, based on the local magnetic field $B(y)$, the magnetic permeability $μ$ and the mass density of the fluid $ρ$. It is shown that when the two critical levels are close to each other, the critical layer can generate an instability. The instability problem is solved, combining asymptotic solutions at …
The merging of two soap bubbles is a fundamental fluid mechanical process in foam formation. In the present experimental study the liquid films from two soap bubbles are brought together. Once the liquid layers initially separated by a gas sheet are bridged on a single spot the rapid merging of the two liquid films proceed. Thereby the connecting rim is rapidly accelerated into the separating gas layer. We show that due to the dimple formation the velocity is not uniform and the high acceleration causes initially a Rayleigh-Taylor instability of the liquid rim. At later times, the rim takes he…
The Holmboe wave instability is one of the classic examples of a stratified shear instability, usually explained as the result of a resonance between a gravity wave and a vorticity wave. Historically, it has been studied by linear stability analyses at infinite Reynolds number, $Re$, and by direct numerical simulations at relatively low $Re$ in the regions known to be unstable from the inviscid linear stability results. In this paper, we perform linear stability analyses of the classical `Hazel model' of a stratified shear layer (where the background velocity and density distributions are assu…
The presence of even small amount of surfactant at the particle-laden fluid interface subjected to shear makes surface flow incompressible if the shear rate is small enough [T. M. Fischer et al, J. Fluid Mech. 558, 451 (2006)]. In the present paper the effective surface shear viscosity of a flat, low-concentration, particle-laden incompressible interface separating two immiscible fluids is calculated. The resulting value is found to be 7.6% larger than the value obtained without account for surface incompressibility.
Computational fluid dynamics (CFD) simulations, in-vitro setups, and experimental ex-vivo approaches have been applied to numerous alveolar geometries over the past years. They aimed to study and examine airflow patterns, particle transport, and particle-alveolar wall deposition fractions. These studies are imperative to both pharmaceutical and toxicological studies, especially nowadays with the escalation of the menacing COVID-19 virus. However, most of these studies ignored the surfactant layer that covers the alveoli and the effect of the air-surfactant surface tension on flow dynamics and …
Surfactants are often used to stabilise two-dimensional (2D) materials in environmentally friendly solvents such as water. Aqueous-surfactant solutions prevent agglomeration of nanosheets through steric and electrostatic repulsion, facilitating the production of high concentration nanomaterial dispersions. Turbulent, shear-assisted liquid exfoliation of layered precursor materials produces defect-free nanosheets by promoting mixing and generating sufficiently high shear rates to overcome out-of-plane van der Waals bonds. In the presence of a liquid-gas interface, a consequence of using surfact…
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）
