Fracture dynamics in foam: Finite-size effects

The injection of gas under a defined pressure difference and high enough rate into a layer of quasi-two-dimensional foam bubbles induces ruptures of successive films that travel steadily at well-defined speed. While this process analogous to type-I fracture propagation can be described successfully in its salient features by simple one-dimensional models, quantitative discrepancies to experiment remain. Within a two-dimensional network model incorporating fluid dynamical processes of film instabilities, shear dissipation, and deformation of free interfaces, we find that the dimensions of the foam sample significantly affect the speed of the cracks as well as the pressure necessary to sustain them: cracks in wider samples travel faster at a given driving stress, but are able to avoid arrest and maintain propagation at a lower pressure (the velocity gap becomes smaller). The system thus becomes a study case for stress concentration and the transition between discrete and continuum systems in dynamical fracture; taking into account the finite dimensions of the system improves agreement with experiment.