Related papers: Free surface flows with large slopes: beyond lubri…
We investigate the consequences of fluid flowing on a continuous surface upon the geometric and statistical distribution of the flow. We find that the ability of a surface to collect water by its mere geometrical shape is proportional to…
Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the…
Centre manifold techniques are used to derive rationally a description of the dynamics of thin films of fluid. The derived model is based on the free-surface $\eta(x,t)$ and the vertically averaged horizontal velocity $\avu(x,t)$. The…
We consider some basic principles of fluid-induced lubrication at soft interfaces. In particular, we show how the presence of a soft substrate leads to an increase in the physical separation between surfaces sliding past each other. By…
The free elastic flow is the $L^2$-gradient flow for Euler's elastic energy, or equivalently the Willmore flow with translation invariant initial data. In contrast to elastic flows under length penalisation or preservation, it is more…
Granular flows down inclined channels with smooth boundaries are common in nature and in the industry. Nevertheless, the common setup of flat boundaries has comparatively been much less investigated than the bumpy boundaries one, which is…
This brief note addresses the free boundary problem arising from the steady two-dimensional seepage flow through a rectangular dam. The flow problem consists in finding the free boundary location, and the velocity and pressure fields. The…
Many fundamental problems in fluid dynamics are related to the effects of solid boundaries. In general, they install sharp gradients and contribute to the developement of small-scale structures, which are computationally expensive to…
Based on a microscopic density functional theory we calculate the internal structure of the three-phase contact line between liquid, vapor, and a confining wall as well as the morphology of liquid wetting films on a substrate exhibiting a…
Steady fluid flows have very special topology. In this paper we describe necessary and sufficient conditions on the vorticity function of a 2D ideal flow on a surface with or without boundary, for which there exists a steady flow among…
The dynamic behavior of the slip length in a fluid flow confined between atomically smooth surfaces is investigated using molecular dynamics simulations. At weak wall-fluid interactions, the slip length increases nonlinearly with the shear…
A moving contact line occurs at the intersection of an interface formed between two immiscible liquids and a solid. According to viscous theory, the flow is entirely governed by just two parameters, the viscosity ratio, $\lambda$, and the…
In this paper, we derive a lubrication model to describe the non-stationary free liquid film that is created when a vertical frame is pulled out of a liquid reservoir at a given velocity. We here focus on the case of a pure liquid,…
We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…
We derive several lubrication approximation models, using Shikhmurzaev's approach to the contact line problem, obtained in \cite{GNV}. The first two lubrication models describe thin film flow of incompressible fluids on solid substrates,…
Free boundaries of biofilms advancing on surfaces evolve according to conservation laws coupled with systems of partial differential equations for velocities, pressures and chemicals affecting cell behavior. Thin film approximations lead to…
A wide range of equations related to free surface motion in two dimensions exhibit the formation of cusp singularities either in time, or as function of a parameter. We review a number of specific examples, relating in particular to fluid…
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
The problem of two-phase flow in straight capillaries of polygonal cross section displays many of the dynamic characteristics of rapid interfacial motions associated with pore-scale displacements in porous media. Fluid inertia is known to…
A recently proposed schematic model for the non--linear rheology of dense colloidal dispersions is compared to flow curves measured in suspensions that consist of thermosensitive particles. The volume fraction of this purely repulsive model…