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Scaling laws and dynamics of bubble coalescence

Christopher R. Anthony1,*, Pritish M. Kamat1, Sumeet S. Thete1, James P. Munro2, John R. Lister2, Michael T. Harris1, and Osman A. Basaran1,†

  • 1School of Chemical Engineering, Purdue University, 480 Stadium Mall Drive, West Lafayette, Indiana 47907, USA
  • 2Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, CMS, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

  • *anthonc@purdue.edu
  • †obasaran@purdue.edu
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Phys. Rev. Fluids 2, 083601 – Published 11 August, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.083601

Abstract

The coalescence of bubbles and drops plays a central role in nature and industry. During coalescence, two bubbles or drops touch and merge into one as the neck connecting them grows from microscopic to macroscopic scales. The hydrodynamic singularity that arises when two bubbles or drops have just touched and the flows that ensue have been studied thoroughly when two drops coalesce in a dynamically passive outer fluid. In this paper, the coalescence of two identical and initially spherical bubbles, which are idealized as voids that are surrounded by an incompressible Newtonian liquid, is analyzed by numerical simulation. This problem has recently been studied (a) experimentally using high-speed imaging and (b) by asymptotic analysis in which the dynamics is analyzed by determining the growth of a hole in the thin liquid sheet separating the two bubbles. In the latter, advantage is taken of the fact that the flow in the thin sheet of nonconstant thickness is governed by a set of one-dimensional, radial extensional flow equations. While these studies agree on the power law scaling of the variation of the minimum neck radius with time, they disagree with respect to the numerical value of the prefactors in the scaling laws. In order to reconcile these differences and also provide insights into the dynamics that are difficult to probe by either of the aforementioned approaches, simulations are used to access both earlier times than has been possible in the experiments and also later times when asymptotic analysis is no longer applicable. Early times and extremely small length scales are attained in the new simulations through the use of a truncated domain approach. Furthermore, it is shown by direct numerical simulations in which the flow within the bubbles is also determined along with the flow exterior to them that idealizing the bubbles as passive voids has virtually no effect on the scaling laws relating minimum neck radius and time.

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Phys. Rev. Fluids 2, 083601– Published 11 August, 2017
  • Received 9 November 2016

©2017 American Physical Society

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