On the linear viscoelastic behavior of semidilute polydisperse bubble suspensions in Newtonian media

In this work, we investigated the linear viscoelasticity of semidilute polydisperse bubble suspensions via small amplitude oscillatory shear (SAOS) tests performed in a rheo-optical setup. For all tested suspensions, the measured viscoelastic moduli ( G ', G '') aligned with the theoretical predictions of the Jeffreys model for average dynamic capillary numbers ( < Cd >) greater than unity. But at lower < Cd > values, experimental G ' values exceeded theoretical predictions. To investigate this, we considered the effects of suspension polydispersity and various SAOS measurement artifacts, including bubble rise, coalescence, and changes in suspension microstructure over time. Polydispersity could not cause the observed deviation, because the viscoelastic trends deviate from those of classic single-mode relaxation only for bimodal bubble size distributions with equal volume fractions of very small and very large bubbles; in any other case, the polydisperse suspension behaves as monodisperse with a bubble radius equal to the volume-weighted mean radius. Furthermore, bubble rise proved to play a minor role, while SAOS rheo-optical experiments revealed that bubble size and organization varied negligibly during our measurements. The G ' deviation at low < Cd > values was linked to bubble fluid dynamic interactions induced by the bubble spatial distribution. Image analysis showed that at low bubble volume fractions, stronger and prolonged preshearing reduces these interactions by increasing the average interbubble distance. But this effect is negligible in denser suspensions, which show similar G ' trends for any applied preshearing. Finally, a multimode Jeffreys model fitted to the experimental data showed that bubble interactions complicate the relaxation process, introducing multiple relaxation modes.