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

Abstract

The 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 320Mo 0.18 < We < 1500Mo 0.23 .

Critical density triplets for the arrestment of a sphere falling in a sharply stratified fluid

“…We plan to investigate the complicated dynamics of the momentary levitation discussed in this paper using a direct numerical simulation of the Navier-Stokes equation and understand the effect from the rigid boundaries. Second, we are interested in generalizing the theory to a dual problem, namely the rise of droplets in a sharply stratified fluid [20,22,14], which is important in the studying of the oil spill problem [2,7].…”

A flow map for core/shell microdroplet formation in the co-flow Microchannel using ternary phase-field numerical model

“…The diffusion coefficient , also known as mobility, defines the time scale of diffusion 61 : where . While it needs to be big enough to keep the interfacial thickness constant, it can't be too big or convective transport will be stifled.…”

“…The surface tension ( ) of the interface between phases i and j is denoted by . After that, the coefficient is defined as follows 61 : …”

“…In another study, a rising air bubble passes through a stratified horizontal interface between two Newtonian liquids. The interface between three immiscible fluids was modeled using a ternary phase-field model 61 .…”

Drag coefficient of a rising bubble in a shear-thinning fluid using the power-law scheme coupled with a Cahn-Hilliard equation with a variable mobility: A lattice Boltzmann study and comparison with experiment

“…Multiphase flow systems exist in many contexts such as water treatment processes, biomedical engineering, pharmaceutical and food industries, and so on [1,2]. Also, multiphase flow systems are found in the droplet-based microfluidic devices which is applicable in drug delivery and cell analysis [3,4,5]. Therefore, many research efforts are targeted on predicting interaction between liquid and gas not only in Newtonian liquids but also in non-Newtonian ones.…”