Passage of a rising bubble through a liquid‐liquid interface: A flow map for different regimes

Abstract

AbstractThe passage of a rising air bubble through a stratified horizontal interface between two Newtonian liquids is studied numerically. A ternary phase‐field model has been utilized for capturing the interface between three immiscible fluids. According to the previous studies, the density, viscosity, and surface tension of the two liquids, in addition to the bubble diameter, are the effective parameters of bubble interaction with the interface. By changing these variables, three main flow patterns are identified in numerical simulations. Penetration flow regime is observed when the bubble enters the upper liquid alone and does not raise the lower liquid. Entrainment flow regime occurs when the bubble lifts some of the heavier liquid to the lighter liquid but still rises alone. If the bubble holds a film of the denser liquid when it rises in the upper liquid, envelopment flow regime takes place. A flow regime map is represented to distinguish the aforementioned flow patterns using Weber and Morton numbers and determine regime transition criteria based on these two dimensionless parameters. For Weber numbers lower than 30, or Morton numbers higher than 1.7 × 10−2, the penetration regime is observed. On the contrary, when the Weber number is higher than 65 and the Morton number is lower than 7 × 10−5, the envelopment regime occurs. The entrainment pattern happens between these ranges and two additional limiting relations of 320Mo0.18 < We < 1500Mo0.23.