Gas-Liquid Foam Dynamics: From Structural Elements to Continuum Descriptions

Abstract

Gas-liquid foams are important in applications ranging from oil recovery and mineral flotation to food science and microfluidics. Beyond their practical use, they represent an intriguing prototype of a soft material with a complex, viscoelastic rheological response. Crucially, foams allow detailed access to fluid-dynamical processes on the mesoscale of bubbles underlying the large-scale material behavior. This review emphasizes the importance of the geometry and interaction of mesoscale structural elements for the description of the dynamics of entire foams. Using examples including bulk flow of foam under steady shear, interfacial instabilities, and foam fracture through bubble rupture, this article highlights the wide variety of available theoretical descriptions, ranging from network modeling approaches coupling structural element equations of motion to full continuum models with elastoviscoplastic constitutive relations. Foams offer the opportunity to develop rigorous links between such disparate descriptions, providing a blueprint for physical modeling of dynamical multiscale systems with complex structure. 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.

Air invasion into three-dimensional foam induces viscous fingering instabilities

“…Yanagisawa et al reported that a liquid film of foam bubble bursts with a velocity greater than 20 m/s 44 . In addition, finer, needle like fractures at the fingertips signal the onset of film ruptures in a radial Hele-Shaw cell 20 . In this study, the fingertip velocities are 0.5 m/s at 4.0 psi and 3.2 m/s at 10.0 psi.…”

“…There are a few studies on the displacement of liquid foam by gas in a Hele-Shaw cell. Injecting gas at a continuous flow rate or constant pressure into a body of liquid foam in a Hele-Shaw cell leads to finger-like gas/foam interfaces 20 . This behavior is the well-known Saffman-Taylor instability because viscous foam is pushed by a less viscous gas in a porous medium 2 , 21 .…”

A cluster of N -bubbles driven along a channel at high imposed driving pressure: film orientations and bubble pressures

“…As has been mentioned, various components can be included in models for foam structures (bubbles, films, vertices, Plateau borders and such like [50]). In the viscous froth model, however, the basic structural unit is an element of foam film [36].…”

“…The staircase structures studied here are comprised [50] of the bubbles themselves, films between bubbles and also vertices at which three films meet. The foam is considered to be dry, so films can be treated as one-dimensional lines (or more generally curves) and vertices can be treated as points.…”