Propagation of a Topological Transition: the Rayleigh Instability

Thomas R. Powers; Dengfu Zhang; Raymond E. Goldstein; Howard A. Stone

doi:10.1063/1.869650

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Propagation of a Topological Transition: the Rayleigh Instability

Thomas R. Powers·Dengfu Zhang·Raymond E. Goldstein·Howard A. Stone

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Abstract

The Rayleigh capillary instability of a cylindrical interface between two immiscible fluids is one of the most fundamental in fluid dynamics. As Plateau observed from energetic considerations and Rayleigh clarified through hydrodynamics, such an interface is linearly unstable to fission due to surface tension. In traditional descriptions of this instability it occurs everywhere along the cylinder at once, triggered by infinitesimal perturbations. Here we explore in detail a recently conjectured alternate scenario for this instability: front propagation. Using boundary integral techniques for Stokes flow, we provide numerical evidence that the viscous Rayleigh instability can indeed spread behind a front moving at constant velocity, in some cases leading to a periodic sequence of pinching events. These basic results are in quantitative agreement with the marginal stability criterion, yet there are important qualitative differences associated with the discontinuous nature of droplet fission. A number of experiments immediately suggest themselves in light of these results.

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Thomas R. Powers, Dengfu Zhang, Raymond E. Goldstein, Howard A. Stone. 1997-08-21. Propagation of a Topological Transition: the Rayleigh Instability. https://doi.org/10.1063/1.869650

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