On a vertical chain of small bubbles ascending in a viscoelastic fluid

Recently, our direct numerical simulations [Yuan et al., Hydrodynamic interaction and coalescence of two inline bubbles rising in a viscoelastic liquid, Phys. Fluids 33, 083102 (2021)] indicated that a stable chain can be formed for a pair of bubbles rising in a viscoelastic liquid, consistent with experimental observations. Motivated by the fact that the flow in bubble chains is still poorly understood, this Letter extends the investigations to multiple small bubbles ascending in a vertical file in a viscoelastic medium with different configurations. With an increasing bubble number, it is found that the rising velocity of the bubble group increases and the vertical chain of bubbles becomes unstable due to the distinct oscillation of the uppermost bubble. The terminal separation distance between two adjacent bubbles decreases in the upward direction, diminished by the neighborhood rising bubbles due to increasing loading. By probing the polymeric stresses and deformation, our results demonstrated that the accumulation of viscoelastic normal stresses promotes the aggregation of rising bubbles, while the successive chain of bubbles is stable because of the near-field repulsion induced by the non-monotonic polymer stretching among the bubble chain. In addition, the large bubble deformation appears to enhance the accumulative polymeric normal stress effect, and the bubbles can form more stable vertical chains at increasing initial spacing. Our findings provide insights into the mechanism of bubbles clustering in viscoelastic fluids, as chaining of bubbles is believed to be more prevailing in highly elastic flows.

Automated summary

Our direct numerical simulations revealed that a stable chain can be formed for rising bubbles in viscoelastic liquid, but multiple small bubbles in a vertical file may become unstable as the bubble group ascends due to the distinct oscillation of the uppermost bubble. The accumulation of viscoelastic normal stresses promotes the aggregation of rising bubbles, while the non-monotonic polymer stretching induces near-field repulsion, stabilizing the successive chain of bubbles. Additionally, large bubble deformation enhances the accumulative polymeric normal stress effect, allowing for the formation of more stable vertical chains with increasing initial spacing.