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Rotationally symmetric bodies with longitudinal cross sections of parabolic shape are frequently used to model astrophysical objects, such as magnetospheres and other blunt objects, immersed in interplanetary or interstellar gas or plasma…
When a volatile droplet is deposited on a floating swellable sheet, it becomes asymmetric, lobed and mobile. We describe and quantify this phenomena that involves nonequilibrium swelling, evaporation and motion, working together to realize…
In this work, we numerically study the elastic contact between isotropic and anisotropic, rigid, randomly rough surfaces and linearly elastic counterfaces as well as the subsequent Reynolds flow through the gap between the two contacting…
A vanishing viscosity method is formulated for two-dimensional transonic steady irrotational compressible fluid flows with adiabatic constant $\gamma\in [1,3)$. This formulation allows a family of invariant regions in the phase plane for…
Several dynamical stages of the Marangoni convection of an evaporating sessile drop are obtained. We jointly take into account the hydrodynamics of an evaporating sessile drop, effects of the thermal conduction in the drop and the diffusion…
Evaporating colloidal droplets have long been used as model systems to understand capillarity, interfacial transport, and particle assembly, most prominently through the coffee ring effect. In classical descriptions, suspended particles are…
We study the asymptotic behavior of solutions of the two dimensional incompressible Euler equations in the exterior of a curve when the curve shrinks to a point. This work links two previous results: [Iftimie, Lopes Filho and Nussenzveig…
This brief note addresses the free boundary problem arising from the steady two-dimensional seepage flow through a rectangular dam. The flow problem consists in finding the free boundary location, and the velocity and pressure fields. The…
The effects of line tension on the morphology of a sessile droplet placed on top of a convex spherical substrate are studied. The morphology of the droplet is determined from the global minimum of the Helmholtz free energy. The contact…
We search exact analytical solutions of spherically symmetric dissipative fluid distributions satisfying the vanishing expansion condition (vanishing expansion scalar $\Theta$). To do so we shall impose additional restrictions allowing the…
Hypothesis: Evaporation of surfactant droplets on leaves is complicated due to the complex physical and chemical properties of the leaf surfaces. However, for certain leaf surfaces for which the evaporation process appears to follow the…
We present a continuum level analytical model of a droplet of active contractile fluid consisting of filaments and motors. We calculate the steady state flows that result from a splayed polarisation of the filaments. We account for the…
The dissolution process of small (initial (equivalent) radius $R_0 < 1$ mm) long-chain alcohol (of various types) sessile droplets in water is studied, disentangling diffusive and convective contributions. The latter can arise for high…
The present study deals with the numerical as well as asymptotic analysis of the electrohydrodynamic interaction between two deformable droplets in a confined shear flow. Considering both the phases as leaky dielectric, we have performed…
This paper studies Mullins' model of thermal grooving which consists of a surface diffusion flow equation with contact angle and no-flux boundary conditions. We consider this problem in a multi-dimensional half space and prove that if the…
We are interested in a complete characterization of the contact-line singularity of thin-film flows for zero and nonzero contact angles. By treating the model problem of source-type self-similar solutions, we demonstrate that this…
We introduce a mesoscopic hydrodynamic model for drops of binary mixtures of volatile partially wetting liquids on brush-covered substrates, i.e., we model the coupled dynamics of spreading, evaporation, imbibition, diffusion and partial…
We develop a model for the thermodynamics and evaporation dynamics of aerosol droplets of a liquid such as water, surrounded by the gas. When the temperature and the chemical potential (or equivalently the humidity) are such that the vapour…
Due to the potential application of regulating droplet shape by external fields in microfluidic technology and micro devices, it becomes increasingly important to understand the shape formation of a droplet in the presence of an electric…
We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the…