相关论文: Making sessile drops easier
We study the equilibrium solutions of a sessile drop on top of a horizontal substrate when it is partially covered by another inmiscible liquid, so that part of the drop is in contact with a third fluid (typically, air). The shapes of the…
A new set of mathematical identities is presented for axi-symmetric sessile drops on flat and curved substrates. The geometrical parameters, including the apex curvature and height, and the contact radius, are related by the identities. The…
We introduce a solvable Lagrangian model for droplet bouncing. The model predicts that, for an axisymmetric drop, the contact time decreases to a constant value with increasing Weber number, in qualitative agreement with experiments,…
Contact angle is an important parameter in characterizing the wetting properties of fluids. The most common methods for measuring the contact angle is to measure it directly from the profile curve of a sessile drop, a method with certain…
The wetting behavior of drops on natural and industrial surfaces is determined by the advancing and receding contact angles. They are commonly measured by the sessile drop technique, also called goniometry, which doses liquid through a…
We present a fully analytical solution for the natural oscillation of an inviscid sessile drop of arbitrary contact angle on a horizontal plate for the case for the case of low Bond number, when surface tension dominates gravity. The…
In our fluid dynamics video, we demonstrate our method of visualizing and identifying various mode shapes of mechanically oscillated sessile drops. By placing metal mesh under an oscillating drop and projecting light from below, the drop's…
Exact mathematical identities are presented between the relevant parameters of droplets displaying circular contact boundary based on flat tilted surfaces. Two of the identities are derived from the force balance, and one from the torque…
We provide a numerical method for computing solutions to a free boundary problem arising from the equilibrium state of a floating drop. This numerical method is based on a Newton's method for the underlying nonlinear boundary value…
By solving the Young Laplace equation of capillary hydrostatics one can accurately determine equilibrium shapes of droplets on relatively smooth solid surfaces. The solution, however of the Young Laplace equation becomes tricky when a…
An analytical model is proposed for the Young-Laplace equation of two-dimensional (2D) drops under gravity. Inspired by the pioneering work of Landau & Lifshitz (1987), we derive analytical expressions of the profile of drops on flat…
The idea of contact angle was generalized by using the principle of minimum total energy. The problems of the shape of the two-dimensional sessile drop and the drop on an inclined surface are considered. The differential equations…
In this short note we review results on equilibrium shapes of minimizers to the sessile drop problem. More precisely, we study the Winterbottom problem and prove that the Winterbottom shape is indeed optimal. The arguments presented here…
In random sample consensus (RANSAC), the problem of ellipsoid fitting can be formulated as a problem of minimization of point-to-model distance, which is realized by maximizing model score. Hence, the performance of ellipsoid fitting is…
Multiple-shooting is a parameter estimation approach for ordinary differential equations. In this approach, the trajectory is broken into small intervals, each of which can be integrated independently. Equality constraints are then applied…
The equilibrium shape of liquid drops on elastic substrates is determined by minimising elastic and capillary free energies, focusing on thick incompressible substrates. The problem is governed by three length scales: the size of the drop…
This paper presents an adaptive multiple-shooting method to solve stochastic multi-point boundary value problems. The heuristic to choose the shooting points is based on separating the effects of drift and diffusion terms and comparing the…
Superhydrophobicity relies on the stability of drops's interfaces pinned on sharp edges to sustain non-wetting (Cassie-Baxter) equilibrium states. Gibbs already pointed out that equilibrium is possible as long as the pinning angle at the…
In this paper, a theoretical framework is presented for the use of a Kansa-like method to numerically solve elliptic partial differential equations on spheres and other manifolds. The theory addresses both the stability of the method and…
We perform a joint numerical and experimental study to sistematically characterize the motion of drops sliding over a periodic array of alternating hydrophobic and hydrophilic stripes with large wettability contrast, and typical width of…