Abstract
As rodlike domains pinch off owing to Rayleigh instabilities, a finite-time singularity occurs as the interfacial curvature at the point of pinch-off becomes infinite. The dynamics controlling the interface become independent of initial conditions and, in some cases, the interface attains a universal shape1. Such behaviour occurs in the pinching of liquid jets and bridges2,3,4,5,6,7,8,9 and when pinching occurs by surface diffusion10,11,12. Here we examine an unexplored class of topological singularities where interface motion is controlled by the diffusion of mass through a bulk phase. We show theoretically that the dynamics are determined by a universal solution to the interface shape (which depends only on whether the high-diffusivity phase is the rod or the matrix) and materials parameters. We find good agreement between theory and experimental observations of pinching liquid rods in an Al–Cu alloy. The universal solution applies to any physical system in which interfacial motion is controlled by bulk diffusion, from the break-up of rodlike reinforcing phases in eutectic composites13,14,15,16 to topological singularities that occur during coarsening of interconnected bicontinuous structures17,18,19,20, thus enabling the rate of topological change to be determined in a broad variety of multiphase systems.
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Acknowledgements
This work was partially supported by NSF RTG grant DMS-0636574 (L.K.A.). M.J.M. acknowledges support from US National Science Foundation RTG grant DMS-0636574 and NSF grant DMS-0616468. A.E.J., J.L.F. and P.W.V. acknowledge the US Department of Energy, grant DE-FG02-99ER45782, for financial support. E.M.L. and S.O.P. acknowledge the Danish National Research Foundation for supporting the Center for Fundamental Research: Metal Structures in 4D, within which part of this work was carried out. The authors thank the Paul Scherrer Institut for beam time at the TOMCAT beamlines of the Swiss Light Source. We would also like to thank G. Mikuljan from the TOMCAT team for his support in setting up the experiment at the beamline.
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L.K.A. carried out the theoretical analysis and prepared the manuscript. M.J.M. and P.W.V. were involved with the theoretical calculations. P.W.V. and E.M.L. conceived the experiments. J.L.F., S.O.P. and E.M.L. conducted the experiments. A.E.J. and J.L.F. analysed the experimental data. F.M. and M.S. provided technical guidance for the experiments.
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Aagesen, L., Johnson, A., Fife, J. et al. Universality and self-similarity in pinch-off of rods by bulk diffusion. Nature Phys 6, 796–800 (2010). https://doi.org/10.1038/nphys1737
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DOI: https://doi.org/10.1038/nphys1737
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