Effect of polydispersity and bubble interactions on the linear viscoelastic behaviour of semidilute bubble suspensions in Newtonian media

We examined the effect of polydispersity on the linear viscoelastic moduli (G΄,G΄΄) of semidilute bubble suspensions. Theoretical analysis showed that polydispersity affects G΄,G΄΄ only if the bubble size distribution is bimodal with equal volume fractions of small and large bubbles. Otherwise, the polydisperse suspension can be treated as monodisperse with a volume-weighted mean bubble radius. To confirm the theory, we conducted small amplitude oscillatory shear tests. The measured G΄ values exceeded the theoretical ones for average dynamic capillary numbers (〈Cd〉) lower than 1. Visualizing the bubbles under oscillatory shear showed minimal changes in the suspension microstructure, suggesting that the enhanced elasticity at low 〈Cd〉 arises from bubble fluid dynamic interactions, whose effect is revealed at longer characteristic flow times. At low bubble volume fraction, stronger and prolonged pre-shear can reduce the interactions among the bubbles, by increasing the mean inter-bubble distance. But in denser suspensions, pre-shear has little impact on the bubble spatial distribution. Fitting a multi-mode Jeffreys model to the experimental data revealed that bubble interactions induce multiple relaxation modes.