Two-dimensional simulation of drop deformation and breakup at around the critical Weber number

Abstract

The breakup of two-dimensional liquid drops is numerically investigated at around the critical Weber number. The Moving Particle Semi-implicit (MPS) method is used to solve the unsteady Navier–Stokes equations for both the drops and the ambient fluid. The two dominant forces affecting drop breakup, pressure drag and surface tension force, are verified using the two benchmarks: pressure distribution on the surface of a cylinder in a uniform flow and oscillation of a square drop under surface tension force. The results show that the breakup process occurs in two stages. During the first stage, the drops become stretched and thinned normal to the flow direction of the ambient fluid. During the second stage, detached points appear on the surface of the drops, which are ascribed to the unstable growth of surface waves. The post-breakup topology of the drops is dependent on the value of the Weber number: the larger the Weber number is, the more detached points on the surface of the drops emerge. Another feature commonly shared in the two stages is that some fine fragmentations are stripped from the equatorial edges of the drops. The critical Weber number is predicted to be 13 for uranium dioxide drops in water, at which breakup regime is consistent with the so-called vibration regime.