相关论文: On the geometry of rate independent droplet evolut…
We consider a toy model of rate independent droplet motion on a surface with contact angle hysteresis based on the one-phase Bernoulli free boundary problem. We introduce a notion of solutions based on an obstacle problem. These solutions…
In part 1, we proposed a model of dynamics of wetting for slow movements near a contact line formed at the interface of two immiscible fluids and a solid when viscous dissipation remains bounded. The contact line is not a material line and…
We consider the thin-film equation for a class of free boundary conditions modelling friction at the contact line, as introduced by E and Ren. Our analysis focuses on formal long-time asymptotics of solutions in the perfect wetting regime.…
In this paper, we investigate the dynamics of an incompressible viscous Navier-Stokes fluid evolving above a one-dimensional flat surface. The fluid is subject to a uniform gravitational field and capillary forces acting along the free…
We introduce a mathematical model with a mesh-free numerical method to describe contact-line motion in lubrication theory. We show how the model resolves the singularity at the contact line, and generates smooth profiles for an evolving,…
We study a rate independent energetic model of the Wilhelmy plate experiment in capillarity. The evolution is driven by vertical motions of the plate. We show stability of energy solutions to the evolution, in the sense used in the…
A dynamic wetting problem is studied for a moving thin fiber inserted in fluid and with a chemically inhomogeneous surface. A reduced model is derived for contact angle hysteresis by using the Onsager principle as an approximation tool. The…
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…
Controlling the shape and position of moving and pinned droplets on a solid surface is an important feature often found in microfluidic applications. In this work, we consider a well investigated phase field model including contact line…
We investigate the moving contact line problem for two-phase incompressible flows with a kinematic approach. The key idea is to derive an evolution equation for the contact angle in terms of the transporting velocity field. It turns out…
We consider a one-phase Bernoulli free boundary problem in a container $D$ - a smooth open subset of $\mathbb{R}^d$ - under the condition that on the fixed boundary $\partial D$ the normal derivative of the solutions is prescribed. We study…
We consider the problem of a rigid surface moving over a flat plane. The surfaces are separated by a small gap filled by a lubricant fluid. The relative position of the surfaces is unknown except for the initial time $t=0$. The total load…
The mechanical process of progressively debonding an adhesive membrane from a substrate is described as a quasistatic variational evolution of sets and herein investigated. Existence of energetic solutions, based on global minimisers of a…
Contact angle hysteresis of a macroscopic droplet on a heterogeneous but flat substrate is studied using the interface displacement model. First, the apparent contact angle of a droplet on a heterogeneous surface under the condition of…
We study the stability and breakup of liquid bridges with a free contact line on a surface with contact-angle hysteresis under zero-gravity conditions. Theoretical predictions of the stability limits are validated by experimental…
The idea of contact angle was generalized by using the principle of minimum total energy. The problems of the shape of the two-dimensional sessile drop and the drop on an inclined surface are considered. The differential equations…
Recent experiments (Guan et al. 2016a,b) showed many interesting phenomena on dynamic contact angle hysteresis while there is still a lack of complete theoretical interpretation. In this work, we study the time averaging of the apparent…
In an effort to study the stability of contact lines in fluids, we consider the dynamics of a drop of incompressible viscous Stokes fluid evolving above a one-dimensional flat surface under the influence of gravity. This is a free boundary…
We construct a mathematical model for a diffusiophoretic motion of a deformable droplet, which is floating on a liquid surface and is driven by the surface tension gradient originating from the surface concentration field of the chemicals…
We study the motion of phase interfaces in a diffusive lattice equation with bistable nonlinearity and derive a free boundary problem with hysteresis to describe the macroscopic evolution in the parabolic scaling limit. The first part of…