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arXiv · 1502.07846

Self-similar impulsive capillary waves on a ligament

Laurent Duchemin·Stéphane Le Dizès·Lionel Vincent·Emmanuel Villermaux
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Abstract

We study the short-time dynamics of a liquid ligament, held between two solid cylinders, when one is impulsively accelerated along its axis. A set of one-dimensional equations in the slender-slope approximation is used to describe the dynamics, including surface tension and viscous effects. An exact self-similar solution to the linearized equations is successfully compared to experiments made with millimetric ligaments. Another non-linear self-similar solution of the full set of equations is found numerically. Both the linear and non-linear solutions show that the axial depth at which the liquid is affected by the motion of the cylinder scales like $\sqrt{t}$. The non-linear solution presents the peculiar feature that there exists a maximum driving velocity $U^\star$ above which the solution disappears, a phenomenon probably related to the de-pinning of the contact line observed in experiments for large pulling velocities.

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Laurent Duchemin, Stéphane Le Dizès, Lionel Vincent, Emmanuel Villermaux. 2015-02-27. Self-similar impulsive capillary waves on a ligament. https://doi.org/10.1063/1.4921321

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