相关论文: Universal Self-Similar Attractor in the Bending-Dr…

We compare the capillary levelling of a random surface perturbation on a thin polystyrene film with a theoretical study on the two-dimensional capillary-driven thin film equation. Using atomic force microscopy, we follow the time evolution…

We present an analytical and numerical study of the two-dimensional capillary-driven thin film equation. In particular, we focus on the intermediate asymptotics of its solutions. Linearising the equation enables us to derive the associated…

The surface of a thin liquid film with nonconstant curvature flattens as a result of capillary forces. While this leveling is driven by local curvature gradients, the global boundary conditions greatly influence the dynamics. Here, we study…

We develop a unified theoretical framework for thin-film hydrodynamics on inclined solid substrates, integrating capillarity, intermolecular forces, gravitational symmetry breaking, confined transport and stochastic wetting into a single…

We consider the thin-film equation with linear mobility and a stabilizing second-order porous-medium type term modeling gravity. The model admits self-similar solutions, and our goal is to analyze their stability. We reformulate the problem…

Thin film rupture is a type of nonlinear instability that causes the solution to touch down to zero at finite time. We investigate the finite-time rupture behavior of a generalized elastohydrodynamic lubrication model. This model features…

For homogeneous and isotropic linearly elastic solids and for incompressible fluids under low-Reynolds-number conditions the fundamental solutions of the associated continuum equations were derived a long time ago for bulk systems. That is,…

We study the free-surface deformation dynamics of an immersed glassy thin polymer film supported on a substrate, induced by an air nanobubble at the free surface.We combine analytical and numerical treatments of the glassy thin film…

We consider a two-dimensional motion of a thin film flowing down an inclined plane under the influence of the gravity and the surface tension. In order to investigate the stability of such flow, it is hard to treat the Navier--Stokes…

The surface of a thin liquid film with nonconstant curvature is unstable, as the Laplace pressure drives a flow mediated by viscosity. We present the results of experiments on one of the simplest variable curvature surfaces: a stepped…

A linear sixth-order partial differential equation (PDE) of ``parabolic'' type describes the dynamics of thin liquid films beneath surfaces with elastic bending resistance when deflections from the equilibrium film height are small. On a…

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 study existence and long-time behavior of weak solutions to a thin-film equation with a confinement potential and a second-order degenerate diffusion term. It is known that in absence of second order effects, solutions for general…

The surface structure of converging thin fluid films displays self-similar behavior, as was shown in the work by Diez et al [Q. Appl. Math 210, 155, 1990]. Extracting the related similarity scaling exponents from either numerical or…

The force-level Elastically Collective Nonlinear Langevin Equation theory of activated relaxation in glass-forming free-standing thin films is re-visited to improve its treatment of collective elasticity effects. The naive cut off of the…

We present experiments to study the relaxation of a nano-scale cylindrical perturbation at one of the two interfaces of a thin viscous free-standing polymeric film. Driven by capillarity, the film flows and evolves towards equilibrium by…

The study of viscous thin film flow has led to the development of highly nonlinear partial differential equations that model how the evolution of the film height is affected by different forces. We investigate a model of interaction between…

Lubricant viscoelasticity arises due to a finite polymer relaxation time ($\lambda$) and can provide beneficial effects. In applications, such as bearings, gears, biological joints, etc., where the height-to-length ratio is small ($H_0 /…

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…

Vertical soap films drain under the influence of gravity, as indicated by the downward motion of colorful horizontal interference fringes observed on their surfaces. In this study conducted with rectangular soap films, we experimentally…