Publication Date:
2015-05-16
Description:
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 t , a consequence of the imposed radial uniformity of the axial velocity at the cylinder surface, and differs from t 2/3 known to prevail in surface-tension-driven flows. The non-linear solution presents the peculiar feature that there exists a maximum driving velocity U ⋆ above which the solution disappears, a phenomenon probably related to the de-pinning of the contact line observed in experiments for large pulling velocities.
Print ISSN:
1070-6631
Electronic ISSN:
1089-7666
Topics:
Physics
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