Temporal evolution of microstructure and rheology of sheared two-dimensional foams

We measure the shear rheology of two-dimensional liquid foams in a Couette device, and correlate the variation of the shear stress with the evolution of the foam microstructure. For a monodisperse foam, inception of shearing results in a rapid rise of the shear stress, which then saturates into a quasi-steady state of fluctuations about a time-independent mean value. The dominant frequency of the oscillation correlates closely with the time scale of one row of bubbles sliding past the next row. The mean stress decreases with increasing bubble size. In bidisperse foams, the shear stress exhibits two regimes of transient behavior. If the shear rate and the large-to-small bubble size ratio are both below certain thresholds, the stress behaves similarly to that in a monodisperse foam. Above these thresholds, however, the instantaneous shear stress oscillates around a mean value that declines gradually over several minutes. The foam eventually approaches a quasi-steady state similar to that of a monodisperse foam. This gradual decrease in shear stress can be attributed to the size-based segregation of bubbles. Finally, we propose a mixing rule that relates the effective viscosity of a bidisperse foam in the quasi-steady state to those of monodisperse foams made of the two constituent bubble sizes.