Interaction of equal-size bubbles in shear flow

The inertia-induced forces on two identical spherical bubbles in a simple shear flow at small but finite Reynolds number, for the case when the bubbles are within each other's inner viscous region, are calculated making use of the reciprocal theorem. This interaction force is further employed to model the dynamics of air bubbles injected to a viscous fluid sheared in a Couette device at the first shear flow instability where the bubbles are trapped inside the stable Taylor vortex. It was shown that, during a long time scale, the inertial interaction between the bubbles in the primary shear flow drives them away from each other and, as a result, equal-size bubbles eventually assume an ordered string with equal separation distances between all neighbors. We report on experiments showing the dynamic evolution of various numbers of bubbles. The results of the theory are in good agreement with the experimental observations.