Sharp Interface Methods for Simulation and Analysis of Free Surface Flows with Singularities: Breakup and Coalescence

Abstract

A common feature of many free surface flows—drop/bubble breakup or coalescence and film/sheet rupture—is the occurrence of hydrodynamic singularities. Accurately computing such flows with continuum mechanical, multidimensional free surface flow algorithms is a challenging task given these problems’ multiscale nature, which necessitates capturing dynamics occurring over disparate length scales across 5–6 orders of magnitude. In drop breakup, the thinning of fluid threads that form and eventually pinch-off must be simulated until the thread's radius is about 10 nm. When two drops approach one another, the thickness of the fluid film separating them must fall below 10 nm before coalescence is said to have occurred. If the initial drop radii are 1 mm, simulations must remain faithful to the physics as thread radius or film thickness falls from 10−3 m to below 10−8 m. Here we review significant findings in interfacial flows with hydrodynamic singularities spearheaded by sharp interface algorithms. These multidimensional algorithms can achieve resolution that to date has only been possible with the use of simple 1D evolution equations. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 55 is January 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Coalescence of Two Equal-Sized Bubbles with Air Injection

“…8−10 The neck expansion resulting from the quasi-static bubble coalescence has been extensively studied. 3,11,12 In this case, the bubbles approach each other slowly, and no gas is introduced during the merging process. In contrast, the lateral coalescence of two growing bubbles is a common phenomenon near gas distributors in industrial applications.…”

“…Bubble coalescence plays a crucial role in the bubble size and void fraction distribution in gas–liquid two-phase flow systems and thus heat and mass transfer efficiency. , When two bubbles come into contact and merge, a kind of hydrodynamic singularity arises. , Subsequently, an air bridge (often called a “neck”) forms, connecting the two merging bubbles. Finite-approach velocities, arbitrary surface shapes, and fluid properties contribute to the variety. − The neck formation and temporal evolution are critical features in the study of bubble coalescence.…”

“…Finite-approach velocities, arbitrary surface shapes, and fluid properties contribute to the variety. − The neck formation and temporal evolution are critical features in the study of bubble coalescence. In addition to its theoretical significance, a precise understanding of bubble coalescence improves the predictive accuracy of system performance in engineering. − The neck expansion resulting from the quasi-static bubble coalescence has been extensively studied. ,, In this case, the bubbles approach each other slowly, and no gas is introduced during the merging process. In contrast, the lateral coalescence of two growing bubbles is a common phenomenon near gas distributors in industrial applications.…”

Flowrate effects on the lateral coalescence of two growing bubbles

“…And the capillary‐inertia model and scaling laws have been proposed to describe r n . [ 11–13 ] Paulsen et al [ 14 ] demonstrated that if the Ohnesorge number () is smaller than 0.3, the inertia dominates over the viscous stress after r n reaches . Here, μ l , ρ l , and σ are the viscosity, density, and surface tension of the liquid, respectively; R b is the bubble radius at contact; and μ g is the gas viscosity.…”

“…Without gas injection for static bubble coalescence, the neck evolution is solely driven by the unbalanced surface tension. [3,11] Nevertheless, the expansion characteristics of the neck with air injection and the flowrate effects remain unclear. Hereafter, we briefly review some studies on the static coalescence of two bubbles or drops without air or liquid injection.…”