TY - JOUR

T1 - Cyclic deformation of bidisperse two-dimensional foams

AU - Vaz, M. Fátima

AU - Cox, S. J.

AU - Teixeira, P. I. C.

N1 - M. Fátima Vaz, S.J. Cox & P.I.C. Teixeira (2011): Cyclic deformation of
bidisperse two-dimensional foams, Philosophical Magazine, 91:34, 4345-4356

PY - 2011/11/1

Y1 - 2011/11/1

N2 - 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 \mu_2(N).
Foams that were initially mixed were found to remain mixed after the deformation. The response of sorted foams, however, depended on the initial geometry, including the area fraction of small bubbles and the total
number of bubbles. For a given experiment we found that (i) the perimeter
of a sorted foam varied little; (ii) each foam tended towards a mixed state,
measured through the saturation of Nsl; and (iii) the topological disorder
\mu_2(N) increased up to an ‘‘equilibrium’’ value. The results of different
experiments showed that (i) the change in disorder, Delta \mu_2 (N); decreased with
the area fraction of small bubbles under iso-strain, but was independent of it under iso-stress; and (ii) Delta \mu_2(N) increased with Delta Nsl under iso-strain, but
was again independent of it under iso-stress. We offer explanations for
these effects in terms of elementary topological processes induced by the
deformations that occur at the bubble scale.

AB - 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 \mu_2(N).
Foams that were initially mixed were found to remain mixed after the deformation. The response of sorted foams, however, depended on the initial geometry, including the area fraction of small bubbles and the total
number of bubbles. For a given experiment we found that (i) the perimeter
of a sorted foam varied little; (ii) each foam tended towards a mixed state,
measured through the saturation of Nsl; and (iii) the topological disorder
\mu_2(N) increased up to an ‘‘equilibrium’’ value. The results of different
experiments showed that (i) the change in disorder, Delta \mu_2 (N); decreased with
the area fraction of small bubbles under iso-strain, but was independent of it under iso-stress; and (ii) Delta \mu_2(N) increased with Delta Nsl under iso-strain, but
was again independent of it under iso-stress. We offer explanations for
these effects in terms of elementary topological processes induced by the
deformations that occur at the bubble scale.

U2 - 10.1080/14786435.2011.620995

DO - 10.1080/14786435.2011.620995

M3 - Article

SN - 1478-6435

VL - 91

SP - 4345

EP - 4356

JO - Philosophical Magazine

JF - Philosophical Magazine

IS - 34

ER -