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Initial regime of drop coalescence

Christopher R. Anthony*, Michael T. Harris, and Osman A. Basaran†

  • Davidson School of Chemical Engineering, Purdue University, 480 Stadium Mall Drive, West Lafayette, Indiana 47907, USA

  • *anthonc@purdue.edu
  • †obasaran@purdue.edu
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Phys. Rev. Fluids 5, 033608 – Published 13 March, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.033608

Abstract

When two drops are slowly brought together and first touch, a microscopic liquid neck or a bridge forms between them. The expansion of the neck is controlled by the capillary (Laplace) pressure which diverges when the curvature of the interface is infinite at the point where the drops first touch. The change in topology and the flows that ensue as time advances and the bridge grows from microscopic to macroscopic scales, and the two drops merge into one, are intimately coupled to this singularity in the dynamics. Despite the large volume of work dedicated to this problem, currently experiment, theory, and computation are not in complete agreement with respect to the earliest times following the initial contact of the two drops. Experiments, supported by simulations, report an initial regime where the radius of the connecting bridge grows linearly in time before a transition to either a Stokes regime or an inertial regime where either viscous or inertial force balances capillary (surface tension) force. In the initial linear regime, referred to as the inertially limited viscous (ILV) regime, all three forces are thought to be important. This is in contrast to theory which predicts that all coalescence events begin in the Stokes regime where inertia is negligible. Here we use high-accuracy numerical simulations to show that the ILV regime is only realized when the two coalescing drops are initially separated by a finite distance. Moreover, for two drops that initially just touch at a point, coalescence always begins in the Stokes regime. It is demonstrated that the linear ILV regime is more akin to a Taylor-Culick-type regime whose existence and duration are purely consequences of the use of an initial bridge of finite size that poorly approximates the point contact condition that is a cardinal feature of the coalescence singularity.

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Phys. Rev. Fluids 5, 033608– Published 13 March, 2020
  • Received 15 September 2019
  • Accepted 20 February 2020
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