Two-Dimensional cusped interfaces
TL;DR: In this paper, the authors present an asymptotic analysis near the cusp tip for the case of zero surface tension, and make some remarks about the effects of a small surface tension.
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Abstract: Two-dimensional cusped interfaces are line singularities of curvature. We create such cusps by rotating a cylinder half immersed in liquid. A liquid film is dragged out of the reservoir on one side and is plunged in at the other, where it forms a cusp at finite speeds, if the conditions are right. Both Newtonian and non-Newtonian fluids form cusps, but the transition from a rounded interface to a cusp is gradual in Newtonian liquids and sudden in non-Newtonian liquids. We present an asymptotic analysis near the cusp tip for the case of zero surface tension, and we make some remarks about the effects of a small surface tension. We also present the results of numerical simulations showing the development of a cusp. In those simulations, the fluid is filling an initially rectangular domain with a free surface on top. The fluid enters from both sides and is sucked out through a hole in the bottom.
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Citations
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