The relative viscosity (μrel = suspension viscosity/suspending fluid viscosity) of low Reynolds number, dilute and surfactant-free bubble suspensions in simple shear is studied with a rotating cylinder, Couette rheometer. The conditions of the experiments correspond to capillary numbers (Ca) of order 1 and bridge previous experimental, theoritical and numerical results that focused on either Ca ≪ 1 or Ca ≫ 1. The suspensions are shear thinning with μrel > 1 for small Ca. At large Ca, μrel approaches a constant that is less than 1. These results are explained by a scaling analysis that considers how regions of viscous dissipation in and around bubbles change as bubbles are deformed by the flow. © 2002 Elsevier science B.V. All rights reserved.
Rust, A. C., & Manga, M. (2002). Effects of bubble deformation on the viscosity of dilute suspensions. Journal of Non-Newtonian Fluid Mechanics, 104(1), 53–63. https://doi.org/10.1016/S0377-0257(02)00013-7