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We have proposed a novel methodology using ultrasonic velocity profiling to estimate the effective viscosity of bubble suspensions that are accompanied by non-equilibrium bubble deformations in periodic shear flows. The methodology was termed "ultrasonic spinning rheometry" and validated on measurement of the effective viscosity of particle suspensions that has a semi-empirical formula giving good estimation of the actual viscosity. The results indicated that the proposed technique is valid for particle volume fractions below 3.0 %. Applying this to bubble suspensions suggested that the effective value of temporal variations in the capillary number, Carms, is an important indicator to distinguish regimes in estimating the effective viscosity: Unsteady flows having larger Carms number than the critical capillary number for the deformation of bubbles are categorized into Regime 2 that includes both highly unsteady conditions and large steady deformation of bubbles

Estimating the effective viscosity of bubble suspensions in oscillatory shear flows by means of ultrasonic spinning rheometry