Related papers: Thin film dynamics on a vertically rotating disk p…
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…
Thin liquid films with floating active protein machines are considered. Cyclic mechanical motions within the machines, representing microscopic swimmers, lead to molecular propulsion forces applied to the air-liquid interface. We show that,…
An analytical method is proposed for computing the low-Reynolds-number hydrodynamic mobility function of a small colloidal particle asymmetrically moving inside a large spherical elastic cavity, the membrane of which is endowed with…
Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation…
We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show, using a formal asymptotic expansion of the solution, that its asymptotic behavior, when the distance between the two surfaces tends to…
We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We rigorously clarify how the elastic energy enters the evolution equation for…
This study investigates the nonlinear stability and dynamics of gravity-driven viscous films on a vertical rotating cylinder, considering both outer and inner surface flows with slip conditions at the cylinder wall. We develop an asymptotic…
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…
The aim of the paper is to construct and justify asymptotic approximations for solutions to quasilinear convection-diffusion problems with a predominance of nonlinear convective flow in a thin cylinder, where an inhomogeneous nonlinear…
The thin runback water films driven by the gas flow, the pressure gradient and the gravity on the iced aircraft surface are investigated in this paper. A three-dimensional film flow model based on Finite Volume Method (FVM) and the…
The kinetics of dissolution of an amorphous solid is studied using a simple model of a glass that captures with reasonable accuracy the dynamic heterogeneities associated with the relaxation of an amorphous material at low temperatures. The…
The retraction of thin films, as described by the Taylor-Culick (TC) theory, is subject to widespread debate, particularly for films at the nanoscale. We use non-equilibrium molecular dynamics simulations to explore the validity of the…
We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a Lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects…
We study the dynamic behaviour of solutions to a fourth-order quasilinear degenerate parabolic equation for large times arising in fluid dynamical applications. The degeneracy occurs both with respect to the unknown and with respect to the…
We consider the time evolution of a sessile drop of volatile partially wetting liquid on a rigid solid substrate. Thereby, the drop evaporates under strong confinement, namely, it sits on one of the two parallel plates that form a narrow…
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…
A solid withdrawn from a liquid bath entrains a film. In this review, after recalling the predictions and results for pure Newtonian liquids coated on simple solids, we analyze the deviations to this ideal case exploring successively three…
We provide an ab-initio scaling analysis for liquid film thickness and Nusselt number of a steady laminar jet impacting a rotating heated plate. The limiting scaling regimes incorporating the evaporative effects along the liquid-vapor…
A finite element model was developed to compute the fluid flow inside a sessile evaporating droplet on hydrophilic substrate in ambient conditions. The evaporation is assumed as quasi-steady and the flow is considered as axisymmetric with a…
We examine theoretically the spreading of a viscous liquid drop over a thin film of uniform thickness, assuming the liquid's viscosity is regulated by the concentration of a solute that is carried passively by the spreading flow. The solute…