Related papers: Dynamics and stability of surface waves with bulk-…
This work focuses on the dynamics of a train of unconfined bubbles flowing in microchan- nels. We investigate the transverse position of a train of bubbles, its velocity and the associated pressure drop when flowing in a microchannel…
We consider a free-boundary problem for the incompressible elastodynamics describing the motion of an elastic medium in a periodic domain with a moving boundary and a fixed bottom under the influence of surface tension. The local…
Parametric oscillations of an interface separating two fluid phases create nonlinear surface waves, called Faraday waves, which organise into simple patterns, like squares and hexagons, as well as complex structures, such as double…
In this paper we study a finite-depth layer of viscous incompressible fluid in dimension $n \ge 2$, modeled by the Navier-Stokes equations. The fluid is assumed to be bounded below by a flat rigid surface and above by a free, moving…
Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a great variety of excitable systems. In the limit of a large separation in timescale between fast excitation and slow recovery, one can reduce the spiral problem to…
The behavior of thin liquid films is known to be strongly affected by the presence of surfactants at the interfaces. The detailed mechanism by which the latter enhance film stability is still a matter of debate, in particular concerning the…
An unconstrained, non-linearly elastic, semi-infinite solid is maintained in a state of large static plane strain. A power-law relation between the pre-stretches is assumed and it is shown that this assumption is well-motivated physically…
We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken.…
In this work, we investigate flow topology modifications produced by a swarm of large surfactant-laden droplets released in a turbulent channel flow. Droplets have same density and viscosity of the carrier fluid, so that only surface…
We investigate the interaction of waves with surface flows by considering the full set of conserved quantities, subtle but important surface elevation changes induced by wave packets and by directly considering the necessary forces to…
When an ensemble of particles interact hydrodynamically, they generically display large-scale transient structures such as swirls in sedimenting particles [1], or colloidal strings in sheared suspensions [2]. Understanding these…
The coupled dynamics of two conjugated liquid layers of disparate thicknesses, which coat a solid substrate and are subjected to a transverse temperature gradient, is investigated. The upper liquid layer evolves under the short-wavelength…
The three-phase contact line of a droplet on a smooth surface can be characterized by the Young-Dupr\'e equation. It relates the interfacial energies with the macroscopic contact angle $\theta_e$. On the mesoscale, wettability is modeled by…
Consider the flow of a thin layer of non-Newtonian fluid over a solid surface. I model the case of a viscosity that depends nonlinearly on the shear-rate; power law fluids are an important example, but the analysis here is for general…
We prove that traveling waves in viscous compressible liquids are a generic phenomenon. The setting for our result is a horizontally infinite, finite depth layer of compressible, barotropic, viscous fluid, modeled by the free boundary…
For a natural number $m \ge 2$, we study $m$ layers of finite depth, horizontally infinite, viscous, and incompressible fluid bounded below by a flat rigid bottom. Adjacent layers meet at free interface regions, and the top layer is bounded…
The evolution of the interface separating a conduit of light, viscous fluid rising buoyantly through a heavy, more viscous, exterior fluid at small Reynolds numbers is governed by the interplay between nonlinearity and dispersion. Previous…
In this paper, we consider a free boundary problem of the incompressible elatodynamics, a coupling system of the Euler equations for the fluid motion with a transport equation for the deformation tensor. Under a natural force balance law on…
This paper studies the dynamics of an incompressible fluid driven by gravity and capillarity forces in a porous medium. The main interest is the stabilization of the fluid in Rayleigh-Taylor unstable situations where the fluid lays on top…
The duality between deformations of elastic bodies and non-inertial flows in viscous liquids has been a guiding principle in decades of research. However, this duality is broken when a spheroidal or other doubly-curved liquid film is…