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.
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