Deformation and breakup of a pendant drop with solidification

Abstract

This paper presents a numerical simulation of deformation and breakup of a solidifying liquid drop pendant from a cold solid surface by an axisymmetric front-tracking method combined with an interpolation technique for enforcing the no-slip velocity boundary at the solid–fluid interface. Many dimensionless parameters such as the Prandtl number Pr, the Stefan number St, the Rayleigh number Ra, the Ohnesorge number Oh and the Bond number Bo are varied to reveal their effects on the process. Numerical results show that depending on the flow conditions, the liquid drop can break up while solidifying. Starting from non-breakup, increasing Bo (from 1.0 to 3.5) or Pr (from 0.01 to 3.16) causes the solidifying drop to break up into liquid drops that fall away from the solid surface. The transition from non-breakup to breakup also appears when decreasing St from 1.0 to 0.01, Ra from 1000 to 50, or Oh from 0.316 to 0.01. In addition, the effects of these parameters on the solidification time and the height of the solidified products are investigated. Moreover, the effects of volume change (in terms of the solid-to-liquid density ratio) upon solidification and the tri-junction (in terms of the growth angle) are introduced. We also present a phase diagram of Bo versus St that shows the region of the non-breakup-to-breakup transition.