Shape of pendent droplets under a tilted surface

PHYSICA D-NONLINEAR PHENOMENA

卷:415

Article

De Coninck, Joel¹  Fernandez-Toledano, Juan Carlos¹  Dunlop, Francois²  Huillet, Thierry²  Sodji, Alvin² 

[1] Univ Mons, Lab Phys Surfaces & Interfaces, 20 Pl Parc, B-7000 Mons, Belgium

[2] CY Cergy Paris Univ, Lab Phys Theor & Modelisat, CNRS, UMR 8089, F-95302 Cergy Pontoise, France

关键词: Pendent droplets;    Young-Laplace equation;    Small Bond number perturbation;    Furmidge relation;    Contact angles;   

DOI  :  10.1016/j.physd.2020.132765

来源: Elsevier

【 摘 要 】

For a pendent drop whose contact line is a circle of radius r(0), we derive the Furmidge-like relation mg sin alpha = pi/2 gamma r(0) (cos theta(min) - cos theta(max)) at first order in the Bond number, where theta(min) and theta(max) are the contact angles at the back (uphill) and at the front (downhill), m is the mass of the drop and gamma the surface tension of the liquid. The Bond (or Eotvos) number is taken as Bo = mg/(2r(0)gamma). The tilt angle alpha may increase from alpha = 0 (sessile drop) to alpha = pi/2 (drop pinned on vertical wall) to alpha = n (drop pendent from ceiling). The focus will be on pendent drops with alpha = pi/2 and alpha = 3 pi/4, while alpha = pi/4 is also included for comparison. The drop profile is computed exactly, in the same approximation. Results are compared with Surface Evolver simulations, showing good agreement up to about Bo = 1.2, corresponding for example to hemispherical water droplets of volume up to about 50 mu L. An explicit formula for each contact angle theta(min) and theta(max) is also given and compared with the almost exact Surface Evolver values. (c) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

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