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A suspended fluid film with two free surfaces convects when a sufficiently large voltage is applied across it. We present a linear stability analysis for this system. The forces driving convection are due to the interaction of the applied…
We report on the thinning of supported liquid films driven by thermocapillarity. The liquids are oil films, of initial thicknesses of a few tens of microns. A local and moderate heating of the glass substrate on which they are spread on…
We study the finite-temperature dynamics of thin elastic sheets in a single-clamped cantilever configuration. This system is known to exhibit a tilt transition at which the preferred mean plane of the sheet shifts from horizontal to a plane…
We study theoretically the evaporation-driven phase separation of a binary fluid mixture in a thin film deposited on a moving substrate, as occurs in meniscus-guided deposition for solution-processed materials. Our focus is on rapid…
Starting from a nonlinear 2D/1D fluid-structure interaction problem between a thin layer of a viscous fluid and a thin elastic structure, on the vanishing limit of the relative fluid thickness, we rigorously derive a sixth-order thin-film…
We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show that its asymptotic behavior, when the distance between the two surfaces tends to zero, is the same as that of the the Navier-Stokes…
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…
Glasses have a wide range of technological applications. The recent discovery of ultrastable glasses that are obtained by depositing the vapor of a glass-forming liquid onto the surface of a cold substrate has sparked renewed interest in…
Surface bubbles are an abundant source of aerosols, with important implications for climate processes. In this context, we investigate the stability and thinning dynamics of soap films under effective gravity fields. Experiments are…
In this paper, we have used the QUICK scheme of the finite volume method to investigate the problem of steady 2-D free convective incompressible flow with heat and mass transfer in an inclined rectangular domain at different Rayleigh…
Following the previous part of our study on unsteady non-New\-to\-nian fluid flows with boundary conditions of friction type we consider in this paper the case of pseudo-plastic (shear thinning) fluids. The problem is described by a…
Flow in thin films is highly dependent on the boundary conditions. Here, we study the capillary levelling of thin bilayer films composed of two immiscible liquids. Specifically, a stepped polymer layer is placed atop another, flat polymer…
We present a mathematical and numerical framework for thin-film fluid flows over planar surfaces including dynamic contact angles. In particular, we provide algorithmic details and an implementation of higher-order spatial and temporal…
In this Letter we investigate the rupture instability of thin liquid films by means of a bifurcation analysis in the vicinity of the short-scale instability threshold. The rupture time estimate obtained in closed form as a function of the…
We are concerned with a model describing the motion of two compressible, immiscible fluids with density-dependent viscosity in the whole $\mathbb R^3$. The phases of the flow may have different pressure and viscosity laws and are separated…
We consider the parabolic $p$-Laplace equation with $p>2$ in a moving thin domain under a Neumann type boundary condition corresponding to the total mass conservation. When the moving thin domain shrinks to a given closed moving…
Rupture is a nonlinear instability resulting in a finite-time singularity as a fluid layer approaches zero thickness at a point. We study the dynamics of rupture in a generalized mathematical model of thin films of viscous fluids with…
Pendant drops suspended on the underside of a wet substrate are known to accumulate fluid from the surrounding thin liquid film, a process that often results in dripping. The growth of such drops is hastened by their ability to translate…
A flexible sheet in uniform parallel flow is studied in order to quantify its fluid dynamic drag and fluid-elastic stability characteristics. An experimental campaign is undertaken that involves a cantilevered sheet in air flow…
In this paper, we derive an extension of the Reynolds law for quasi-Newtonian fluid flows through a thin domain with thickness $0<\varepsilon\ll 1$ with viscosity obeying the Carreau law without high-rate viscosity, by applying asymptotic…