Two-dimensional flow of foam around an obstacle: force measurements.

A Stokes experiment for foams is proposed. It consists of a two-dimensional flow of a foam, confined between a water subphase and a top plate, around a fixed circular obstacle. We present systematic measurements of the drag exerted by the flowing foam on the obstacle versus various separately controlled parameters: flow rate, bubble volume, bulk viscosity, obstacle size, shape, and boundary conditions. We separate the drag into two contributions: an elastic one (yield drag) at vanishing flow rate and a fluid one (viscous coefficient) increasing with flow rate. We quantify the influence of each control parameter on the drag. The results exhibit in particular a power-law dependence of the drag as a function of the bulk viscosity and the flow rate with two different exponents. Moreover, we show that the drag decreases with bubble size and increases proportionally to the obstacle size. We quantify the effect of shape through a dimensional drag coefficient, and we show that the effect of boundary conditions is small.