Related papers: A Geometric Diffuse-Interface Method for Droplet S…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…
We investigate the wave-optical light scattering properties of deformed thin circular films of constant thickness using the discrete-dipole approximation. Effects on the intensity distribution of the scattered light due to different…
A microscopic, driven lattice gas model is proposed for the dynamics and spatio-temporal fluctuations of the precursor film observed in spreading experiments. Matter is transported both by holes and particles, and the distribution of each…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
We study the effects of nozzle geometry on the dynamics of thin fluid films flowing down a vertical cylindrical fibre. Recent experiments show that varying the nozzle diameter can lead to different flow regimes and droplet characteristics…
Controlling the spatial distribution of liquid droplets on surfaces via surface energy patterning can be used to control material delivery to specified regions via selective liquid/solid wetting. While studies of the equilibrium shape of…
We consider a thin droplet that spreads over a flat, horizontal and chemically heterogeneous surface. The droplet is subjected to changes in its volume though a prescribed, arbitrary spatiotemporal function, which varies slowly and vanishes…
The spontaneous spreading of non-volatile liquid droplets on solid substrates poses a classic problem in the context of wetting phenomena. It is well known that the spreading of a macroscopic droplet is in many cases accompanied by a thin…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
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 and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffusion processes in the context of the vapor deposition of thin…
In this work we address a novel feature of spreading dynamics of tiny liquid droplets on solid surfaces, namely the case where the ends of the molecules feel different interactions to the surface. We consider a simple model of dimers and…
We propose a numerical approach to study the mechanics of a flowing bubble in a constraint micro channel. Using an open source two phase flow solver (Gerris, gfs.sourceforge.net) we compute solutions of the bubble dynamics (i.e. shape and…
Models that involve coupled dynamics in a mixed-dimensional geometry are of increasing interest in several applications. Here, we describe the development of a simulation model for flow in fractured porous media, where the fractures and…
This paper is concerned with diffuse-interface approximations of the Willmore flow. We first present numerical results of standard diffuse-interface models for colliding one dimensional interfaces. In such a scenario evolutions towards…
Many multiphase fluid systems, such as those involving immiscible polymers or liquid-liquid systems with surfactants, have shown a breakdown of the no-slip condition at the material interface. This results in systems where the tangential…
The dynamics of a thin layer of liquid, between a flat solid substrate and an infinitely-thick layer of saturated vapor, is examined. The liquid and vapor are two phases of the same fluid, governed by the diffuse-interface model. The…
The motion of a contact line is examined, and comparisons drawn, for a variety of models proposed in the literature. Pressure and stress behaviours at the contact line are examined in the prototype system of quasistatic spreading of a thin…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…
The dynamics of thin, non-circular droplets evaporating in the diffusion-limited regime are examined. The challenging non-rectilinear mixed-boundary problem this poses is solved using a novel asymptotic approach and an asymptotic expansion…