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Propagation of a topological transition: The Rayleigh instability
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9.See also the seminal work of G. I. Taylor, “The formation of emulsions in definable fields of flow,” Proc. R. Soc. London, Ser. A 146, 501 (1934).
10.This result is reminiscent of the fact that the appearance of the von Kármán vortex street in the wake of a cylinder is related to the transition of the wake instability from absolute to convective. This transition can be understood using linear analysis;
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11.See also A. Z. Zinchenko, M. A. Rother, and R. H. Davis, “A novel boundary-integral algorithm for viscous interactions of deformable drops,” Phys. Fluids 9, 1493 (1997).
12.The kernels in (3) are
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17.The front parameters were determined through a nonlinear least-squares fitting algorithm [W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University Press, New York, 1988)].
18.Many of the breakup events involved smaller, satellite droplets, the analysis of which we have not pursued.
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24.It is well known that numerical boundary integral methods become less accurate at small λ (Ref. 11). We found that for the volume of the drop changed by about 10% during the continuous evolution.
25.There is another possible source of error. In the MSC picture, the front accelerates to the MSC velocity with a relaxation time that scales as (Refs. 8, 20). Thus, when retraction is unimportant, we would expect our numerical results to lie below the MSC curve. This discrepancy should be greatest for the smallest values of λ we considered, since it is precisely those values for which is getting small (Ref. 5). However, we saw no evidence of acceleration of the front in the numerical calculations.
26.S. Sankaran and D. A. Saville, “Experiments on the stability of a liquid bridge in an axial electric field,” Phys. Fluids A 5, 1081 (1993).
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