Interaction of bubbles in an inviscid and low-viscosity shear flow

The pressure loads on two identical spherical bubbles impulsively introduced in an inviscid simple shear flow are calculated. The interaction force due to these pressure loads is employed to model the dynamics of air bubbles injected to a low-viscosity 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 the interaction between the bubbles in the primary shear flow drives them away from each other. The performed simulations revealed that in an inviscid flow the separation distances between equal size bubbles undergo complex periodic motion. The presence of low-viscosity results in a qualitative change of the interaction pattern: The bubbles either eventually assume an ordered string with equal separation distances between all neighbors or some of them collide. The first regime is qualitatively similar to the behavior of bubbles at low Reynolds number [Prakash et al., Phys. Rev. E 87, 043002 (2013)]. Furthermore, if the Reynolds number exceeds some critical value the temporal behavior of the separations becomes nonmonotonic and exhibits over- and undershooting of the equilibrium separations. The latter effects were observed in the experiments, but are not predicted by the low Reynolds number model of the process [Prakash et al., Phys. Rev. E 87, 043002 (2013)].