Related papers: Perturbation Theory for Traveling Droplets
The percolation of a liquid through a porous material is investigated with the help of equations of the Onsager type. An expression is derived for the molecular attraction, starting from Sutherland's potential approximation to the van der…
When a binary fluid demixes under a slow temperature ramp, nucleation, coarsening and sedimentation of droplets lead to an oscillatory evolution of the phase separating system. The advection of the sedimenting droplets is found to be…
A fluid droplet may exhibit self-propelled motion by modifying the wetting properties of the substrate. We propose a novel model for droplet propagation upon a terraced landscape of ordered layers formed as a result of surface freezing…
We identify two rather novel types of (compound) dynamical bifurcations generated primarily by interactions of an invariant attracting submanifold with stable and unstable manifolds of hyperbolic fixed points. These bifurcation types -…
Using Molecular Dynamics simulations of a coarse-grained polymer liquid we investigate the transport of droplets on asymmetrically structured (saw-tooth shaped), vibrating substrates. Due to a continuous supply of power by substrate…
Active fluids operate by constantly dissipating energy at the particle level to perform a directed motion, yielding dynamics and phases without any equilibrium equivalent. The emerging behaviors have been studied extensively, yet…
'A basic and basically unsolved problem in fluid dynamics is to determine the evolution of rising bubbles and falling drops of one miscible liquid in another' [1]. Here, we address this important literature gap and present the first theory…
The flow of deformable particles, such as droplets, dragged by a fluid, through a network of narrow pores inside rocks or other porous media is key in a range of applications, from enhanced oil recovery and water filtration to lab on a chip…
The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of…
Over the past decade the study of fluidic droplets bouncing and skipping (or ``walking'') on a vibrating fluid bath has gone from an interesting experiment to a vibrant research field. The field exhibits challenging fluids problems,…
Droplet solitons are a strongly nonlinear, inherently dynamic structure in the magnetization of ferromagnets, balancing dispersion (exchange energy) with focusing nonlinearity (strong perpendicular anisotropy). Large droplet solitons have…
These lecture notes describe a basic theory of chemically active droplets, which are droplets kept away from equilibrium by driven chemical reactions. The notes assume a basic familiarity with equilibrium thermodynamics of phase separation,…
We report a new type of fluid-based driven dissipative oscillator system consisting of a lattice of millimetric fluid droplets bouncing on a vertically vibrating liquid bath and bound within an annular ring. We characterize the system…
A vibrational model of transport properties of dense fluids assumes that solid-like oscillations of atoms around their temporary equilibrium positions dominate the dynamical picture. The temporary equilibrium positions of atoms do not form…
This paper considers the interaction between two droplets placed on a substrate in immediate vicinity. We show here that when the two droplets are of different fluids and especially when one of the droplet is highly volatile, a wealth of…
Using the advection-diffusion equation, we analytically study contaminant transport in a sharply contrasting medium with a diffusion barrier due to localization of a contaminant source in a low-permeability medium. Anomalous diffusion…
We consider a situation commonly encountered in microfluidics: two streams of miscible liquids are brought at a junction to flow side by side within a microchannel, allowing solutes to diffuse from one stream to the other and possibly…
The dynamics of steps on crystal surfaces is considered. In general, the meandering of the steps obeys a subdiffusive behaviour. The characteristic asymptotic time laws depend on the microscopic mechanism for detachment and attachment of…
We consider analytically and numerically head-on collision between two self-propelled drops. Each drop is driven by chemical reactions that produce or consume the concentration isotropically. The isotropic distribution of the concentration…
Travelling waves of densities of binary fluid mixtures are investigated near a critical point. The free energy is considered in a non-local form taking account of the density gradients. The equations of motions are applied to a universal…