Foam: a multiphase system with many facets

Abstract

Liquid foams are an extreme case of multiphase flow systems: capable of flow despite a very high dispersed phase volume fraction, yet exhibiting many characteristics of not only viscoelastic materials but also elastic solids. The non-trivial, well-defined geometry of foam bubbles is at the heart of a plethora of dynamical processes on widely varying length and time scales. We highlight recent developments in foam drainage (liquid dynamics) and foam rheology (flow of the entire gas-liquid system), emphasizing that many poorly understood features of other materials have precisely defined and quantifiable analogues in aqueous foams, where the only ingredients are well-known material parameters of Newtonian fluids and bubble geometry, together with subtle but important information on the surface mobility of the foam. Not only does this make foams an ideal model system for the theorist, but also an exciting object for experimental studies, in which dynamical processes span length scales from nanometres (thin films) to metres (foam continuum flows) and time scales from microseconds (film rupture) to minutes (foam rheology).

Cracks and fingers: Dynamics of ductile fracture in an aqueous foam

“…These brittle cracks proceed by successive breakage of the thin films between foams in almost perfect sequence along the pressure gradient [7,8]. In the latter case, observed for smaller rates of applied pressure, a much slower air/foam interface propagation is observed [9], morphologically resembling a fingering instability in homogeneous fluid systems described by Saffman and Taylor [10] and studied extensively as an example of nonlinear instability and shape selection [11][12][13]. While the system can also exhibit a brittle-to-ductile transition [8] between these modes, we will here focus on the ductile case only, see Fig.…”

“…Such fingers have been termed 'anomalous' [32], although they are probably more commonly encountered in experiments not carefully tuned to show ST selection. The morphology of anomalous fingers closely obeys (9), while the realized λ depends on C, decreasing as C → ∞.…”

“…According to our non-dimensionalisation (1), this total driving pressure difference should be set to 1 dimensionless unit. However, since our foams are much shorter relative to the bubble size than the experiments of [9], to achieve a comparable pressure drop per bubble we instead consider 0 ≤ ∆P d ≤ 1.…”

“…The dashed red lines in represent the fitted parabolae through the three most advanced points on the crack tip from which the radius of curvature is computed, while the shaded area represents the crack area and the dot-dashed line the crack length. The green line represents the corresponding prediction of the anomalous finger shape (9). Also shown are the temporal evolution of: (c) radius of curvature of the crack tip ρ(t) sampled every two time units and smoothed using a five point moving average; (d) relative crack width λ(t).…”

“…Reflecting a typical experimental geometry [7,9], we set b = 1/2, so that the aspect ratio of the channel cross-section is W/b = 44.…”