Related papers: Finite-time self-similar rupture in a generalized …
Functionalized thin elastic films and membranes frequently feature internal sites of net forces or stresses. These are, for instance, active sites of actuation, or rigid inclusions in a strained membrane that induce counterstress upon…
Surfactant-laden thin liquid films overlaid on solid substrates are encountered in a variety of industrial and biological settings. As these films reach submicron thickness, they tend to become unstable owing to the influence of long-range…
In this study, we investigate the dynamics of particles overcoming the hydrodynamic barrier posed by a thin fluid film to achieve contact in finite time, a phenomenon critical in various natural and engineered processes such as enzyme…
The stability of nonvolatile thin liquid films and of sessile droplets is strongly affected by finite size effects. We analyze their stability within the framework of density functional theory using the sharp kink approximation, i.e., on…
In binary mixtures, the lifetimes of surface bubbles can be five orders of magnitude longer than those in pure liquids because of slightly different compositions of the bulk and the surfaces, leading to a thickness-dependent surface tension…
The effects of thermal coupling between two thin liquid layers, separated by a gas layer, are discussed. The liquid layers undergo long-wavelength instabilities driven by gravitational and thermocapillary stresses. To study the dynamics,…
A confined incompressible elastic film does not deform uniformly when subjected to adhesive interfacial stresses but with undulations which have a characteristic wavelength scaling linearly with the thickness of the film. In the classical…
Thin film dynamics and associated instability mechanisms have triggered a wide range of scientific innovations, as attributed to their abilities of creating fascinating patterns over small scales. Here, we demonstrate a new thin film…
Many physical systems give rise to dynamical behavior leading to cuspidal shapes which represent a singularity of the governing equation. The cusp tip often exhibits self-similarity as well, indicative of scaling symmetry invariant in time…
We construct a finite element approximation of a strain-limiting elastic model on a bounded open domain in $\mathbb{R}^d$, $d \in \{2,3\}$. The sequence of finite element approximations is shown to exhibit strong convergence to the unique…
We study the effects of stochastic thermal fluctuations on the instability of the free surface of a flat liquid film upon a solid substrate. These fluctuations are represented as a standard Brownian motion that can be added to the…
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…
Motivated by recent experimental observations [U. Delabre et al, Langmuir 24, 3998, 2008] we reconsider an instability of ultrathin nematic films, spread on liquid substrates. Within a continuum elastic theory of liquid crystals, in the…
Of concern is the study of a system of three equations describing the motion of a viscous complete wetting two-phase thin film endowed with a layer of insoluble surfactant on the surface of the upper fluid under the effects of capillary…
The rupture of a liquid film due to co-flowing turbulent shear flows in the gas phase is studied using a volume-of-fluid method. To simulate this multiphase problem, we use a simplified numerical setup where the liquid film is 'sandwiched'…
We report a theoretical and numerical investigation of the linear and nonlinear dynamics of a thin liquid film of viscosity $\mu$ sandwiched between a solid substrate and an unbounded liquid bath of viscosity $\lambda \mu$. In the limit of…
The Geometric Thin-Film equation is a mathematical model of droplet spreading in the long-wave limit, which includes a regularization of the contact-line singularity. We show that the weak formulation of the problem, given initial Radon…
We investigate perturbations of traveling wave solutions to a thin-film equation with quadratic mobility and a zero contact angle at the triple junction, where the three phases liquid, gas, and solid meet. This equation can be obtained in…
Self-similar large time behaviour of weak solutions of the fourth-order parabolic thin film equations with absorption is studued.
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…