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Fluid mechanics

Jets from a singular surface

Nature volume 403, pages 377–378 (2000)Cite this article

All theories of continuous systems begin with the assumption that there is a separation of scales between the macroscopic variables needed by the theory and the microscopic motions that are ignored. So, the bulk motion of fluid in a teacup stirred by a spoon occurs on a scale that is orders of magnitude larger than the distance between the molecules. When this basic assumption is violated for an instant in time, the consequences can be important and dramatic. On page 401 of this issue, Zeff et al.1 describe such a violation that occurs when a tub of viscous liquid is shaken up and down. When done just right, a relatively modest shaking can produce extremely thin and violent jets, which spout upwards at velocities of more than 50 metres per second.

Now, Zeff et al.1 demonstrate experimentally that the violent eruption of a jet does indeed arise out of a singular distortion of the free surface: the shape of the liquid–air interface develops an extremely high curvature an instant before the jet is produced. The release of this curvature produces the jet. Zeff et al. show that this singular event is driven by the inertia and surface tension of the fluid, and ultimately is stopped by the retarding influence of viscosity. When the inertia of the fluid is above a critical threshold, the high surface curvature produces both a jet and an air bubble, which reduces the velocity of the jet.

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Figure 1: Formation of a singularity.

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  1. Department of Mathematics Massachusetts Institute of Technology, 77 Massachusetts Avenue , Cambridge, 02139, Massachusetts, USA

    Michael P. Brenner

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  1. Michael P. Brenner
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Correspondence to Michael P. Brenner.

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Brenner, M. Jets from a singular surface. Nature 403, 377–378 (2000). https://doi.org/10.1038/35000330

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