When two liquid spheres approach at low speed, their curvature (and therefore pressure) is infinite at they point where they first touch. A liquid neck then rapidly expands, due to the divergent Laplace pressure. Using high-speed imaging and an ultrafast electrical method, we have shown that water drops coalescing in air have an unexpectedly late viscous-to-inertial crossover. This is due to a small length-scale in the flows that was previously unappreciated. Moreover, with collaborators at Purdue University, we found a theoretically unanticipated “inertially limited viscous” regime that controls the asymptotic dynamics of coalescence for any finite viscosity.

Initial moments of coalescence for two millimeter-size water drops. Frames are 120 μs apart. The central white spot is due to the light source located behind the drops.
Initial moments of coalescence for two millimeter-size water drops. Frames are 120 μs apart. The central white spot is due to the light source located behind the drops.

Whereas these studies were for drops coalescing in vacuum or air, coalescence often occurs in an ambient fluid that can have significant density or viscosity. Surprisingly, we found that the velocity of the neck is independent of the outer fluid at early times, even in experiments where the outer fluid is 50 times more viscous than the drops! By studying gas bubbles coalescing in oil, we found that the flows in the outer fluid occur on a much larger length-scale than those in the drops, so they put negligible stresses on the drops at early times.

Publications:

Coalescence of bubbles and drops in an outer fluid. J. D. Paulsen, R. Carmigniani, A. Kannan, J. C. Burton, and S. R. Nagel, Nature Communications 5:3182 doi: 10.1038/ncomms4182 (2014).  pdf  link  bibtex

Approach and coalescence of liquid drops in air. J. D. Paulsen, Physical Review E 88, 063010 (2013).  pdf  link  bibtex

The inexorable resistance of inertia determines the initial regime of drop coalescence. J. D. Paulsen, J. C. Burton, S. R. Nagel, S. Appathurai, M. T. Harris, and O. A. Basaran, Proceedings of the National Academy of Sciences U.S.A. 109, 6857 (2012).  pdf  link  bibtex

Viscous to inertial crossover in liquid drop coalescence. J. D. Paulsen, J. C. Burton, and S. R. Nagel, Physical Review Letters 106, 114501 (2011).  pdf  link  bibtex

YouTube:

Video abstract to Approach and coalescence of liquid drops in air.  link