This study presents analytical and numerical investigations of Marangoni interfacial instability in a two-liquid-layer system with constant solute transfer across the interface. While previous research has established that both diffusivity and viscosity ratios affect hydrodynamic stability via the Marangoni effect, the specific nonlinear dynamics and the role of interfacial deformation remain fully unclear. To address this, we developed a phase-field-based numerical model, validated against linear stability analysis and existing theories. The validated parameter space includes Schmidt number, Marangoni number, Capillary number, and the diffusivity and viscosity ratio between the two layers. Our finding shows that solute transfer from a less diffusive layer triggers short-wave instability, governed by the critical Marangoni number, while solute transfer into a less viscous layer induces long-wave instability, controlled by the critical Capillary number. Nonlinear simulations reveal distinct field coupling behaviors: in the diffusivity-ratio-driven instability, the spatially averaged flow intensity remains symmetric about a flat interface, while solute gradient is uneven. In contrast, in viscosity-ratio-driven instability, a deforming interface separates the two layers, with a uniform solute gradient but asymmetric spatially averaged flow intensity. These results highlight the crucial role of diffusivity and viscosity in shaping Marangoni flows and enhance our understanding of interfacial instability dynamics.
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…
Surfactant-loaded capsules as Marangoni microswimmers at the air-water interface: Symmetry breaking and spontaneous propulsion by surfactant diffusion and advection
We have developed a microfluidic tool to measure the diffusion coefficient $D$ of solutes in an aqueous solution, by following the temporal relaxation of an initially steep concentration gradient in a microchannel. Our chip exploits multilayer soft lithography and the opening of a pneumatic microvalve to trigger the interdiffusion of pure water and the solution initially separated in the channel by the valve, the so-called free interface diffusion technique. Another microvalve at a distance from the diffusion zone closes the channel and thus suppresses convection. Using this chip, we have meas…
We study the effect of insoluble surfactants on the spatio-temporal evolution of turbulent jets. We use three-dimensional numerical simulations and employ an interface-tracking/level-set method that accounts for surfactant-induced Marangoni stresses. The present study builds on our previous work (Constante et al., 2021, J. Fluid Mech., 922, A6) in which we examined in detail the vortex-surface interaction in the absence of surfactants. Numerical solutions are obtained for a wide range of Weber and elasticity numbers in which vorticity production is generated by surface deformation and surfacta…
The evaporation from a micropillar evaporator is a problem governed by various interfacial phenomena such as the capillarity-induced liquid flow, thin-film evaporation intensifying near the contact lines, and thermocapillarity-induced Marangoni flow. However, past research has not been able to assess the effect of Marangoni flow due to the missing coupling between cell- and device-level modeling. In this work, we develop a comprehensive model for the evaporation from a micropillar evaporator by coupling the liquid flow with the energy transfer in both liquid and solid domains at both cell- and…
Central Moment Lattice Boltzmann Method using a Pressure-based Formulation for Multiphase Flows at High Density Ratios and including Effects of Surface Tension and Marangoni Stresses
A hybrid Volume of Fluid Phase-Field method for Direct Numerical Simulations of soluble surfactant-laden interfacial flows
Univ. Lille, CNRS, Centrale Lille, Univ. Polytechnique Hauts-de-France, UMR 8520, IEMN（里尔大学、法国国家科学研究中心、中央里尔学院、上法兰西高等工学院）；Institut Universitaire de France（法国国立高等教育学院）；Department of Chemical Engineering, Indian Institute of Technology Roorkee（印度鲁尔基理工学院化学工程系）
Living microorganisms in confined systems typically experience an affinity to populate boundaries. The reason for such affinity to interfaces can be a combination of their directed motion and hydrodynamic interactions at distances larger than their own size. Here we will show that self-propelled Janus particles (polystyrene particles partially coated with platinum) immersed in droplets of water and hydrogen peroxide tend to accumulate in the vicinity of the liquid/gas interface. Interestingly, the interfacial accumulation occurs despite the presence of an evaporation-driven flow caused by a so…
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）
A Sharp and Conservative VOF Method for Multicomponent Liquid--Gas Mass Transfer: Bubble Dissolution and Droplet Evaporation
School of Engineering Science, University of Chinese Academy of Sciences（中国科学院大学工程科学学院）；Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）；State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University（西安交通大学航空航天学院机械结构强度与振动国家重点实验室）
Active droplets can swim spontaneously in viscous flows as a result of the non-linear convective transport of a chemical solute produced at their surface by the Marangoni and/or phoretic flows generated by this solute's inhomogeneous distribution, provided the ratio of convective-to-diffusive solute transport, or Péclet number $\mbox{Pe}$ is large enough. As the result of their net buoyancy, active drops typically evolve at a small finite distance $d$ from rigid boundaries. Yet, existing models systematically focus on unbounded flows, ignoring the effect of the wall proximity on the intrisical…
A surfactant-laden droplet of one fluid dispersed in another immiscible fluid serves as an artificial model system capable of mimicking microbial swimmers. Either an interfacial chemical reaction or the process of solubilization generates gradients in interfacial tension resulting in a Marangoni flow. The resulting fluid flow propels the droplet toward a region of lower interfacial tension. The advective transport of surfactants sustains the active propulsion of these droplets. In these systems, the local interfacial tension is affected by the interfacial reaction kinetics as well as convectio…
Achieving control over the motion of dissolved particles in liquid metals is of importance for the meticulous realization of hierarchical particle assemblies in a variety of nanofabrication processes. Brownian forces can impede the motion of such particles, impacting the degree of perfection that can be realized in assembled structures. Here we show that light induced Marangoni flow in liquid metals (i.e., liquid-gallium) with Laguerre-gaussian (LG) lasers as heating sources, is an effective approach to overcome Brownian forces on particles, giving rise to predictable assemblies with high degr…
