相关论文: Numerical solutions of thin film equations for pol…

Thin viscous liquid films driven by capillarity are well described in the lubrication theory through the thin film equation. In this article, we present an analytical solution of this equation for a particular initial profile: a stepped…

Surface tension-driven flow techniques have recently emerged as an efficient means of shedding light into the rheology of thin polymer films. Motivated by experimental and theoretical approaches in films bearing a varying surface…

The classical no-slip boundary condition of the Navier-Stokes equations fails to describe the spreading motion of a droplet on a substrate due to the missing small-scale physics near the contact line. In this thesis, we introduce a novel…

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…

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…

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…

Thin-film flows of viscoelastic fluids are encountered in various industrial and biological settings. The understanding of thin viscous film flows in Newtonian fluids is very well developed, which for a large part is due to the so-called…

This paper presents an analytical investigation of the solutions to a control volume model for liquid films flowing down a vertical fibre. The evolution of the free surface is governed by a coupled system of degenerate nonlinear partial…

The flow of thin liquid films on inclined or vertical surfaces is one of immense importance, with applications spanning many types of process industries, due to the increased mass and heat transfer brought about by the presence of waves on…

A homogeneous thin polymer film with a stepped height profile levels due to the presence of Laplace pressure gradients. Here we report on studies of polymeric samples with precisely controlled, spatially inhomogeneous molecular weight…

When a thin liquid film flows down on a vertical fiber, one can observe the complex and captivating interfacial dynamics of an unsteady flow. Such dynamics are applicable in various fluid experiments due to their high surface area-to-volume…

The effects of thermal fluctuations on nanoscale flows are captured by a numerical scheme that is underpinned by fluctuating hydrodynamics. A stochastic lubrication equation (SLE) is solved on non-uniform adaptive grids to study a series of…

We find solutions that describe the levelling of a thin fluid film, comprising a non-Newtonian power-law fluid, that coats a substrate and evolves under the influence of surface tension. We consider the evolution from both periodic and…

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…

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…

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…

This paper exploits the theory of geometric gradient flows to introduce an alternative regularization of the thin-film equation. The solution properties of this regularization are investigated via a sequence of numerical simulations whose…

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, we often use a thin film approximation, which…

We investigate stationary solutions of a thin-film model for liquid two-layer flows in an energetic formulation that is motivated by its gradient flow structure. The goal is to achieve a rigorous understanding of the contact-angle…

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…