Related papers: Stokes flow in a drop evaporating from a liquid su…
The two-phase horizontally periodic quasistationary Stokes flow in $\mathbb{R}^2$, describing the motion of two immiscible fluids with equal viscosities that are separated by a sharp interface, which is parameterized as the graph of a…
Understanding the physics of a three-phase contact line between gas, liquid, and solid is important for numerous applications. At the macroscale, the three-phase contact line response to an external force action is often characterized by a…
We derive a homogenized macroscopic model for fluid flows over ordered homogeneous porous surfaces. The unconfined free-flow is described by the Navier-Stokes equation, and the Darcy equation governs the seepage flow within the porous…
A double-layer integral equation for the surface tractions on a body moving in a viscous fluid is derived which allows for the incorporation of a background flow and/or the presence of a plane wall. The Lorentz reciprocal theorem is used to…
Individual chemically active drops suspended in a surfactant solution were observed to self-propel spontaneously with straight, helical, or chaotic trajectories. To elucidate how these drops can exhibit such strikingly different dynamics…
Inspired by the recent realization of a 2D chiral fluid as an active monolayer droplet moving atop a 3D Stokesian fluid, we formulate mathematically its free-boundary dynamics. The surface droplet is described as a general 2D linear,…
In the theory of the Navier-Stokes equations, the viscous fluid in incompressible flow is modelled as a homogeneous and dense assemblage of constituent "fluid particles" with viscous stress proportional to rate of strain. The crucial…
We address the fluid-structure interaction between a viscous incompressible fluid and an elastic plate forming its moving upper boundary in three dimensions. The fluid is described by the incompressible Navier-Stokes equations with a free…
In this paper, we present a novel approach to model the fluid/solid interaction forces in a direct solver of the Navier-Stokes equations based on the volume of fluid interface tracking method. The key ingredient of the model is the explicit…
The effects of surfactant coating on a deformable viscous drop under the combined action of a shear flow and a uniform electric field, are investigated by solving the coupled equations of electrostatics, fluid flow and surfactant transport.…
Motivated by the dynamics of microbubbles near catalytic surfaces in bubble-powered microrockets, we consider theoretically the growth of a free spherical bubble near a flat no-slip surface in a Stokes flow. The flow at the bubble surface…
Droplet impact in airflow environments is ubiquitous in nature and industry, making the understanding of this multiphase behavior crucial for technologies such as anti-icing and spray cooling. In this study, the dynamics of droplet impact…
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…
The deposition of particles on a surface by an evaporating sessile droplet is important for phenomena as diverse as printing, thin-film deposition and self-assembly. The shape of the final deposit depends on the flows within the droplet…
We show that an attempt to compute numerically a viscous flow in a domain with a piece-wise smooth boundary by straightforwardly applying well-tested numerical algorithms (and numerical codes based on their use, such as COMSOL Multiphysics)…
Contact angle hysteresis of droplets will be examined in light of static friction between liquid drop and solid surface. Unlike frictions in solid-solid interfaces, pinning forces at contact points or contact lines would be the cause of…
We report on the controlled transport of drops of magnetic liquid, which are swimming on top of a non-magnetic liquid layer. A magnetic field which is rotating in a vertical plane creates a torque on the drop. Due to surface stresses within…
In this work the evolution of a fluid droplet in vacuum is considered. This means that the surface tension and the fluid forces are in equilibrium at the free boundary. The fluid is governed by the incompressible quasi-steady Stokes…
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…
The present article reports the hitherto unreported phenomenon of arrested evaporation dynamics in pendent droplets in an electric field ambience. The evaporation kinetics of pendant droplets of electrically conducting saline solutions in…