Cyclic deformation of bidisperse two-dimensional foams

In-plane deformation of foams was studied experimentally by subjecting bidisperse foams to cycles of traction and compression at a prescribed rate. Each foam contained bubbles of two sizes with given area ratio and one of three initial arrangements: sorted perpendicular to the axis of deformation (iso-strain), sorted parallel to the axis of deformation (iso-stress), or randomly mixed. Image analysis was used to measure the characteristics of the foams, including the number of edges separating small from large bubbles Nsl, the perimeter (surface energy), the distribution of the number of sides of the bubbles, and the topological disorder μ2(N). Foams that were initially mixed were found to remain mixed after the deformation. The response of sorted foams, however, depends on the initial geometry, including the area fraction of small bubbles and the total number of bubbles. For a given experiment we find that (i) the perimeter of a sorted foam varies little; (ii) each foam tends towards a mixed state, measured through the saturation of Nsl; and (iii) the topological disorder μ2(N) increases up to an “equilibrium” value. The results of different experiments show that (i) the change in disorder, ∆μ2(N) decreases with the area fraction of small bubbles under iso-strain, but is independent of it under iso-stress; and (ii) ∆μ2(N) increases with ∆Nsl under iso-strain, but is again independent of it under iso-stress. We offer explanations for these effects in terms of elementary topological processes induced by the deformation that occur at the bubble scale.