Related papers: Dynamics and stability of surfactant-driven surfac…
This work focuses on the interfacial dynamics with interfacial mass flux in the presence of acceleration and surface tension. We employ the general matrix method to find the fundamental solutions for the linearized boundary value problem…
The nonlinear dynamics of the free surface of an ideal dielectric liquid in a strong electric field is studied. The equation for the evolution of surface electrohydrodynamic waves is derived in the approximation of small surface-slope…
We consider thin fluid films placed on thermally conductive substrates and exposed to time-dependent spatially uniform heat source. The evolution of the films is considered within the long-wave framework in the regime such that both…
In this paper, we consider a layer of a viscous incompressible electrically conducting fluid interacting with the magnetic filed in a horizontally periodic setting. The upper boundary bounded by a free boundary and below bounded by a flat…
Regularizing effects of surface tension are studied for interfacial waves between a two-dimensional, infinitely-deep and irrotational flow of water and vacuum. The water wave problem under the influence of surface tension is formulated as a…
Superhydrophobic surfaces (SHSs) have the potential to reduce drag at solid boundaries. However, multiple independent studies have recently shown that small amounts of surfactant, naturally present in the environment, can induce Marangoni…
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…
Governing equations of motion for a viscous incompressible material surface are derived from the balance laws of continuum mechanics. The surface is treated as a time-dependent smooth orientable manifold of codimension one in an ambient…
In this paper we consider two-dimensional, stratified, steady water waves propagating over an impermeable flat bed and with a free surface. The motion is assumed to be driven by capillarity (that is, surface tension) on the surface and a…
In this paper we prove short-time existence of a smooth solution in the plane to the surface diffusion equation with an elastic term and without an additional curvature regularization. We also prove the asymptotic stability of strictly…
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…
We study the Muskat problem for one fluid in arbitrary dimension, bounded below by a flat bed and above by a free boundary given as a graph. In addition to a fixed uniform gravitational field, the fluid is acted upon by a generic force…
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…
The presence of surfactants has a pronounced effect on the surface tension and, hence, on the stress balance at the phase separating interface of two-phase flows. The transport of momentum induced by the local variations of the capillary…
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 sedimentation of a surfactant-laden deformable viscous drop acted upon by an electric field is considered theoretically. The convection of surfactants in conjunction with the the combined effect electrohydrodynamic flow and…
We consider a colony of point-like self-propelled surfactant particles (swimmers) without direct interactions that cover a thin liquid layer on a solid support. Although the particles predominantly swim normal to the free film surface,…
In this work, we study the effect of insoluble surfactants on the three-dimensional rim-driven retraction dynamics of thin water sheets in air. We employ an interface-tracking/level-set method to ensure the full coupling between the…
We consider the spreading dynamics of some insoluble surface-active species along an aqueous interface. The model includes both diffusion, Marangoni convection and first-order reaction kinetics. An exact solution of the nonlinear transport…
In this paper, we revisit the global well-posedness of the classical viscous surface waves in the absence of surface tension effect with the reference domain being the horizontal infinite slab, for which the first complete proof was given…