Droplet and bubble pinch-off computations using level sets

  • Authors:

  • Maria Garzon;L. J. Gray;James Sethian

  • Affiliations:

  • Department of Applied Mathematics, University of Oviedo, Spain;Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN, United States;Department of Mathematics, University of Berkeley, CA, United States

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2012

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Abstract

A two fluid potential flow model is employed to analyze the pinching characteristics of an inviscid fluid immersed in a second inviscid fluid of different density. The system behavior is controlled by the relative density of the two fluids, D=@r"E/@r"I, where D=0 corresponds to droplets in air, and D=100 to bubbles in water. The numerical method employed combines the level set method for advancing the free surface position and boundary condition, together with a 3D axisymmetric boundary integral formulation to obtain fluid velocities. This approach provides a numerical methodology to analyze the pinch-off behavior up to and beyond the initial break-up of the inner fluid. The combined algorithm is validated using the analytical solution for an oscillating sphere. A series of numerical experiments, up to and beyond the initial break-up of the inner fluid, have been carried out for the two extremes, D=0 and D=100. The calculated scaling exponents match the theoretical values, and the computed front profiles are in good agreement with recent experimental findings.