Abstract
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.
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