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A numerical study of the relaxation and breakup of an elongated drop in a viscous liquid

Published online by Cambridge University Press:  29 October 2009

SHAOPING QUAN ,
DAVID P. SCHMIDT ,
JINSONG HUA  and
JING LOU
SHAOPING QUAN*
Affiliation:
Institute of High Performance Computing, 1 Fusionopolis Way, #16-16 Connexis, Singapore138632
DAVID P. SCHMIDT
Affiliation:
Department of Mechanical and Industrial Engineering, The University of Massachusetts at Amherst, 160 Governors Drive, Amherst, MA 01003-2210, USA
JINSONG HUA
Affiliation:
Department of Process and Fluid Flow Technology, Institute for Energy Technology, Kjeller NO-2027, Norway
JING LOU
Affiliation:
Institute of High Performance Computing, 1 Fusionopolis Way, #16-16 Connexis, Singapore138632
*
†Email address for correspondence: [email protected]
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Abstract

The relaxation and breakup of an elongated droplet in a viscous and initially quiescent fluid is studied by solving the full Navier–Stokes equations using a three-dimensional finite volume method coupled with a moving mesh interface tracking (MMIT) scheme to locate the interface. The two fluids are assumed incompressible and immiscible. The interface is represented as a surface triangle mesh with zero thickness that moves with the fluid. Therefore, the jump and continuity conditions across the interface are implemented directly, without any smoothing of the fluid properties. Mesh adaptations on a tetrahedral mesh are employed to permit large deformation and to capture the changing curvature. Mesh separation is implemented to allow pinch-off. The detailed investigations of the relaxation and breakup process are presented in a more general flow regime compared to the previous works by Stone & Leal (J. Fluid Mech., vol. 198, 1989, p. 399) and Tong & Wang (Phys. Fluids, vol. 19, 2007, 092101), including the flow field of the both phases. The simulation results reveal that the vortex rings due to the interface motion and the conservation of mass play an important role in the relaxation and pinch-off process. The vortex rings are created and collapsed during the process. The effects of viscosity ratio, density ratio and length ratio on the relaxation and breakup are studied. The simulations indicate that the fluid velocity field and the neck shape are distinctly different for viscosity ratios larger and smaller than O(1), and thus a different end-pinching mechanism is observed for each regime. The length ratio also significantly affects the relaxation process and the velocity distributions, but not the neck shape. The influence of the density ratio on the relaxation and breakup process is minimal. However, the droplet evolution is retarded due to the large density of the suspending flow. The formation of a satellite droplet is observed, and the volume of the satellite droplet depends strongly on the length ratio and the viscosity ratio.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 640 , 10 December 2009 , pp. 235 - 264
Copyright
Copyright © Cambridge University Press 2009

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