Hydrodynamic interaction of coaxially rising bubbles in elasto-visco-plastic materials.*

We consider the buoyancy-driven rise and interaction between two initially stationary, tandem bubbles of constant volume inside an elastoviscoplastic material¹, extending our previous work on equal-size bubbles². We investigate the dynamics for three different initial separation distances in a wide range of bubble radii and we predict three distinct regimes: approach, separation, and formation of steady distance. The pair approaches exclusively when the leading bubble is smaller than the trailing one and when inertia is important for both bubbles. When the trailing bubble is not as large, hence the elastic effects play a key role, the leading one dictates the response. A significantly larger leading bubble results in separation of the pair, while a slightly larger leading bubble results in forming a steady distance of the pair. The steady distance configuration is observed only when the initial separation distance is larger than a critical value and elastic effects are intense. Below this critical value the pair approaches. Above this critical value the pair converges to a constant and common value regardless of the initial separation distance. We construct maps with regions of approach, separation, and constant distance in the plane of trailing bubble radius vs. bubble radii ratio for each initial separation distance we examined.

¹P. Saramito, J. NonNewton. Fluid Mech. 158, 154 (2009)

²A. Kordalis et al., Phys. Rev, Fluids, accepted