International Journal of Partial Differential Equations and Applications
ISSN (Print): 2376-9548 ISSN (Online): 2376-9556 Website: Editor-in-chief: Mahammad Nurmammadov
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International Journal of Partial Differential Equations and Applications. 2015, 3(1), 1-6
DOI: 10.12691/ijpdea-3-1-1
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Deformation and Breakup of an Axisymmetric Falling Drop under Constant Body Force

A. Bakhshi1, , D.D. Ganji1 and M. Gorji1

1Department of Mechanical Engineering, Babol University of science and technology, Babol, Iran

Pub. Date: January 11, 2015

Cite this paper:
A. Bakhshi, D.D. Ganji and M. Gorji. Deformation and Breakup of an Axisymmetric Falling Drop under Constant Body Force. International Journal of Partial Differential Equations and Applications. 2015; 3(1):1-6. doi: 10.12691/ijpdea-3-1-1


The secondary breakup of liquid drops, accelerated by a constant body force, is examined for small density differences between the drops and the surrounding fluid. a density ratio of ten has been studied. We used Volume of Fluid (VOF) method to simulate the breakup. The breakup is controlled by the Eötvös number (Eo), the Ohnesorge number (Oh), and the viscosity and density ratios. If viscous effects are small (small Oh), the Eotvos number is the main controlling parameter. At a density ratio of ten, as Eo increases the drops break up in a backward facing bag, transient breakup, and a shear breakup mode. Similar breakup modes have been seen experimentally for much larger density ratios. Although a backward facing bag is seen at low Oh, where viscous effects are small, comparisons with simulations of inviscid flows show that the bag breakup is a viscous phenomenon, due to boundary layer separation and the formation of a wake. At higher Oh, where viscous effects modify the evolution, the simulations show that the main effect of increasing Oh is to move the boundary between the different breakup modes to higher Eo. The results are summarized by “breakup maps” where the different breakup modes are shown in the Eo–Oh plane for different values of the viscosity and the density ratios.

VOF droplet secondary breakup free fall bag breakup

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