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Updated: Aug 25, 2025

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Published on: August 18, 2018
Three-Dimensional Self-Similarity of Coalescing Viscous Drops in the Thin-Film Regime
Paul R Kaneelil1, Amir A Pahlavan2, Nan Xue1,3
1Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA.
Abstract:
Coalescence and breakup of drops are classic problems in fluid physics that often involve self-similarity and singularity formation. While the coalescence of suspended drops is axisymmetric, the coalescence of drops on a substrate is inherently three-dimensional. Yet, studies so far have only considered this problem in two dimensions. In this Letter, we use interferometry to reveal the three-dimensional shape of the interface as two drops coalescence on a substrate. We unify the known scaling laws in this problem within the thin-film approximation and find a three-dimensional self-similarity that enables us to describe the anisotropic shape of the dynamic interface with a universal curve.
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