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The contact line of an evaporating droplet over a solid wedge and the pinned–unpinned transition
Hong, Seok Hyun,Fontelos, Marco A.,Hwang, Hyung Ju Cambridge University Press 2016 Journal of fluid mechanics Vol.791 No.-
<P>We compute the equilibrium contact angles for an evaporating droplet whose contact line lies over a solid wedge. The stability of the liquid interface is also considered and an integro-differential equation for small perturbations is deduced. The analysis of this equation yields criteria for stability and instability of the contact line, where the instability represents transition from the pinned to unpinned contact line representative of stick–slip motion.</P>
Capillary Oscillations of Drops on a Fan-Shaped Pillar
Kim, H. J.,Fontelos, M. A.,Hwang, H. J. Springer Science + Business Media 2017 Journal of mathematical fluid mechanics Vol.19 No.2
<P>We study the capillary oscillations of the surface of a 2D drop attached to a fan-shaped pillar. The fluid flow is modeled by means of a velocity potential and we assume a no-flux condition at the liquid-solid interface. The natural oscillation frequencies and oscillation modes are computed for two different physical situations depending on the contact line behavior: (1) free-end, when the contact line moves along the solid with a constant contact angle and (2) pinned-end when the contact line is pinned to the solid and does not move. We also study the linearized initial value problem and prove well-posedness results in both free-end and pinned-end cases. Hence, for capillary oscillations when the fluid is in partial contact with a solid, not only initial conditions must be prescribed but also the behavior of the contact line.</P>
Capillary oscillations at a circular orifice
Kim, H.J.,Fontelos, M.A.,Hwang, H.J. Pergamon Press ; Elsevier Science Ltd 2013 APPLIED MATHEMATICS LETTERS Vol.26 No.5
We compute the normal frequencies and normal modes for the oscillation of the free surface of a perfect incompressible fluid inside a semi-infinite container with a circular orifice. In doing that, a dual integral equation system involving the Bessel functions must be solved. We discuss the cases where the contact line between the free surface and the container is pinned as well as the case where it moves with a constant contact angle.