Velocity profiles in slowly sheared bubble rafts

Measurements of average velocity profiles in a bubble raft subjected to slow, steady shear demonstrate the coexistence between a flowing state and a jammed state similar to that observed for three-dimensional foams and emulsions [P. Coussot et al., Phys. Rev. Lett. 88, 218301 (2002)]. For sufficiently slow shear, the flow is generated by nonlinear topological rearrangements. We report on the connection between this short-time motion of the bubbles and the long-time averages. We find that velocity profiles for individual rearrangement events fluctuate, but a smooth, average velocity is reached after averaging over only a relatively few events.