Deformation and Flow of a Two-Dimensional Foam under Continuous Shear

Abstract

We investigate the flow properties of a 2D foam (a confined monolayer of jammed bubbles) submitted to a continuous shear in a Couette geometry. A strong localization of the flow at the moving inner wall is evidenced. Moreover, velocity fluctuations measurements reveal self-similar dynamical structures consisting of clusters of bubbles moving coherently. A stochastic model is proposed where bubbles rearrangements are activated by local stress fluctuations produced by the shearing wheel. This model gives a complete description of our observations and is also consistent with available data on granular shear bands.

Stable small bubble clusters in two-dimensional foams

“…A key result of this work is the identification of the important role of both the range and strength of the potential in determining the structure of the mechanically stable clusters. First, we found that for N ≥ 6, as the range of the bubble interaction potential decreases from that for the (12,6) potential to that for the short-range "sticky" (30, 50) potential, the clusters tend to possess more gaps between bubble pairs on the periphery of the clusters. In this case, the distinct clusters obtained from simulations using the long-range potential are a better match to those from experiments.…”

“…6). We find that the distance in configuration space between each cluster obtained in simulations with long-range attractions (12,6) and the corresponding cluster obtained in experiments satisfies ∆R/σ LL < 0.2, as shown in Fig. 10.…”

“…For N = 6, we found that the simulations using the (12, 6) and (30,50) potentials generated N c = 22 mechanically stable clusters that were the same. Two clusters had similar topologies for the (12,6) and ( for the (30, 50) potential had more gaps between bubbles on the periphery of the clusters. In addition, the (30, 50) potential generated four clusters that were not found for the (12, 6) potential.…”

“…The bubble configurations suggest defining four clusters of three small bubbles each. We label the bubbles in the four clusters with indexes, (5, 9, 10), (1,2,3), (3,5,6), and (7,8,12). During the cyclic shear, the three-bubble clusters transition between linear and triangular structures.…”

“…In contrast, it is much more difficult to identify the relevant defects that control the mechanical response in amorphous materials 1 . Disordered materials span a wide range of length scales from atomic systems, such as metallic glasses 2 and ceramics 3 , to colloidal suspensions 4,5 , and macroscopic particulate materials, such as foams [6][7][8][9] , emulsions 10 , and granular matter [11][12][13][14] .…”