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In recent years, slippery surfaces have attracted significant interest due to their excellent liquid-repellent properties and their potential in diverse commercial applications. Such surfaces are prepared by coating functionalized solid…
We introduce a system of shallow water-type equations to model laboratory experiments of particle-laden flows. We explore homogeneous liquid-solid suspensions of fine, non-cohesive, monodisperse glass beads which propagate as an equivalent…
Consider the 3D flow of a viscous Newtonian fluid upon a curved 2D substrate when the fluid film is thin as occurs in many draining, coating and biological flows. We derive a comprehensive model of the dynamics of the film, the model being…
We study the time evolution of a thin liquid film coating the outer surface of a sphere in the presence of gravity, surface tension and thermal gradients. We derive the fourth-order nonlinear partial differential equation that models the…
Phase field models for two-phase flow with a surfactant soluble in possibly both fluids are derived from balance equations and an energy inequality so that thermodynamic consistency is guaranteed. Via a formal asymptotic analysis, they are…
We propose the generalization of the thin film equation (TFE) to arbitrarily many immiscible liquid layers. Then, we provide different pathways for deriving the hydrodynamic pressure within the individual layers, showing how to understand…
We present a study of the spreading of liquid droplets on a solid substrate at very small scales. We focus on the regime where effective wetting energy (binding potential) and surface tension effects significantly influence steady and…
Droplet impact on surfactant-laden thin liquid films is investigated experimentally with emphasis on vortex ring dynamics. Bottom- and side-view imaging reveal that increasing surfactant concentration progressively stabilize vortex rings,…
Liquids in contact with solids are submitted to intermolecular forces making liquids heterogeneous and, in a mechanical model, the stress tensor is not any more spherical as in homogeneous bulks. The aim of this article is to show that a…
Consider the flow of a thin layer of non-Newtonian fluid over a solid surface. I model the case of a viscosity that depends nonlinearly on the shear-rate; power law fluids are an important example, but the analysis here is for general…
We consider the motion of a two-layer thin film that consists of two immiscible viscous fluids and is endowed with an anti-surfactant solute. The presence of such solute particles induces variations of the surface tension and interfacial…
The behavior of thin liquid films is known to be strongly affected by the presence of surfactants at the interfaces. The detailed mechanism by which the latter enhance film stability is still a matter of debate, in particular concerning the…
We show how dynamical equations for liquid films and drops on uneven surfaces, including contact line dynamics and evaporation/condensation effects, may be formulated as a variational dynamics, generated via Onsager's variational principle.…
A thermomechanical model of continuous fluid media based on second gradient theory is used to study motions in liquid-vapor interfaces. At equilibrium, the model is shown to be equivalent to mean-field molecular theories of capillarity. In…
We propose a generic model for thin films and shallow drops of a polar active liquid that have a free surface and are in contact with a solid substrate. The model couples evolution equations for the film height and the local polarization…
The spreading dynamics of surfactant molecules on a thin fluid layer is of both fundamental and practical interest. A mathematical model formulated by Gaver and Grotberg 1990 describing the spreading of a single layer of insoluble…
A variational model for epitaxially-strained thin films on rigid substrates is derived both by {\Gamma}-convergence from a transition-layer setting, and by relaxation from a sharp-interface description available in the literature for…
An arbitrary Lagrangian--Eulerian (ALE) finite element scheme for computations of soluble surfactant droplet impingement on a horizontal surface is presented. The numerical scheme solves the time-dependent Navier--Stokes equations for the…
Molecular dynamics study of a thin (one to five layers) lubricant film between two substrates in moving contact are performed using Langevin equations with an external damping coefficient depending on distance and velocity of atoms relative…
The sedimentation of a surfactant-laden deformable viscous drop acted upon by an electric field is considered theoretically. The convection of surfactants in conjunction with the the combined effect electrohydrodynamic flow and…