Dissipation in foam flowing through narrow channels

We present measurements on simple foam structures flowing through a narrow channel. Driving pressure and bubble velocity are found to be related by a power law with exponent 2/3, thus extending this relationship from single bubble trains (see Bretherton F. P., J. Fluid Mech., 10 (1961) 166) to more complicated foam structures. This nonlinear behaviour is due to the dominant dissipation mechanism, related to the sliding of Plateau borders over the channel walls. For the first time, we show that the prefactor in the power law strongly depends on the foam structure, through the orientation of the Plateau borders with respect to the flow direction. Our evidence suggests that the normal motion largely dominates the dissipation. We discuss implications for quasi-planar rheological experiments on foams confined between glass plates.