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We investigate a one-dimensional model describing the motion of liquid drops sliding down an inclined plane (the so-called quasi-static approximation model). We prove existence and uniqueness of a solution and investigate its long time…

Analysis of PDEs · Mathematics 2012-03-15 Inwon Kim , Antoine Mellet

Evaporating suspensions of colloidal particles lead to the formation of a variety of patterns, ranging from a left-over ring of a dried coffee drop to uniformly distributed solid pigments left behind wet paint. To characterize the…

Soft Condensed Matter · Physics 2014-11-19 C. Nadir Kaplan , L. Mahadevan

We study chemically driven running droplets on a partially wetting solid substrate by means of coupled evolution equations for the thickness profile of the droplets and the density profile of an adsorbate layer. Two models are introduced…

Soft Condensed Matter · Physics 2007-05-23 K. John , M. Baer , U. Thiele

We present a comprehensive experimental and theoretical investigation of the evaporation dynamics of freely levitated water droplets in an upward airstream under varying temperature and relative humidity conditions, using a custom-designed…

The theory of solute transfer and deposit growth in evaporating sessile drops on a plane substrate is presented. The main ideas and the principal equations are formulated. The problem is solved analytically for two important geometries:…

Soft Condensed Matter · Physics 2007-05-23 Yuri Popov

Volatile viscous fluids on partially-wetting solid substrates can exhibit interesting interfacial instabilities and pattern formation. We study the dynamics of vapor condensation and fluid evaporation governed by a one-sided model in a low…

Fluid Dynamics · Physics 2018-02-07 Hangjie Ji , Thomas P. Witelski

Drainage and evaporation can occur simultaneously during the drying of porous media, but the interactions between these processes and their effects on drying are rarely studied. In this work, we develop a pore network model that considers…

Soft Condensed Matter · Physics 2020-03-23 Haiyi Wu , Chao Fang , Rui Wu , Rui Qiao

Evaporation of water droplets on a superhydrophobic substrate, on which the contact line is pinned, is investigated. While previous studies mainly focused on droplets with contact angles smaller than 90^\circ, here we analyze almost the…

A free-falling absorbing liquid drop hit by a nanosecond laser-pulse experiences a strong recoil-pressure kick. As a consequence, the drop propels forward and deforms into a thin sheet which eventually fragments. We study how the drop…

The distribution of liquid water in ice-free clouds determines their radiative properties, a significant source of uncertainty in weather and climate models. Evaporation and turbulent mixing cause a cloud to display large variations in…

Fluid Dynamics · Physics 2021-06-02 J. Fries , G. Sardina , G. Svensson , B. Mehlig

Gravitational settling of a droplet in air onto a soft substrate is a ubiquitous event relevant to many natural processes and engineering applications. We study this phenomenon by developing a three-phase lubrication model of droplet…

Fluid Dynamics · Physics 2022-02-02 Stéphane Poulain , Andreas Carlson

A classical model of fluid dynamics is considered which describes the shape evolution of a viscous liquid droplet on a homogeneous substrate. All equilibria are characterized and their stability is analyzed by a geometric reduction…

Analysis of PDEs · Mathematics 2018-08-14 Patrick Guidotti

We present a framework for calculating the surface density profile of a stain deposited by a drop with a receding contact line. Unlike a pinned drop, a receding drop pushes fluid towards its interior, continuously deposits mass across its…

Soft Condensed Matter · Physics 2014-10-10 Julian Freed-Brown

The evolution of a single raindrop falling below a cloud is governed by fluid dynamics and thermodynamics fundamentally transferable to planetary atmospheres beyond modern Earth's. Here, we show how three properties that characterize…

Earth and Planetary Astrophysics · Physics 2021-05-05 Kaitlyn Loftus , Robin Wordsworth

Escaping of the liquid molecules from their liquid bulk into the vapour phase at the vapour-liquid interface is controlled by the vapour diffusion process, which nevertheless hardly senses the macroscopic shape of this interface. Here,…

Soft Condensed Matter · Physics 2021-08-18 Pan Jia , Mo Zhou , Haiping Yu , Cunjing Lv , Guangyin Jing

Droplet evaporation in turbulent sprays involves unsteady, multiscale and multiphase processes which make its comprehension and model capabilities still limited. The present work aims to investigate droplet vaporization dynamics within a…

Fluid Dynamics · Physics 2017-03-20 Federico Dalla Barba , Francesco Picano

We experimentally investigate the evaporation dynamics of sessile water droplets on a micro-nano textured superhydrophobic aluminum substrate at various temperatures using shadowgraphy imaging. By comparing the evaporation behavior of two…

The wetting of soft elastic substrates exhibits many features that have no counterpart on rigid surfaces. Modelling the detailed elastocapillary interactions is challenging, and has so far been limited to single contact lines or single…

Fluid Dynamics · Physics 2023-08-11 Christopher Henkel , Jacco H. Snoeijer , Uwe Thiele

Drying complex fluids is a common phenomenon where a liquid phase transforms into a dense or porous solid. This transformation involves several physical processes, such as the diffusion of liquid molecules into the surrounding atmosphere…

Fluid Dynamics · Physics 2023-06-21 Ranajit Mondal , Hisay Lama , Kirti Chandra Sahu

We address the dynamics of a drop with viscosity $\lambda \eta$ breaking up inside another fluid of viscosity $\eta$. For $\lambda=1$, a scaling theory predicts the time evolution of the drop shape near the point of snap-off which is in…

Fluid Dynamics · Physics 2009-10-31 Itai Cohen , Michael P. Brenner , Jens Eggers , Sidney R. Nagel