J. Non-Newtonian Fluid Mech. 104 (2002) 53–63 Effects of bubble deformation on the viscosity of dilute suspensions A.C. Rust a , Michael Manga b,∗ a Department of Geological Sciences, 1272 University of Oregon, Eugene, OR 97403, USA b Department of Earth and Planetary Science, University of California, Berkeley, CA 94720, USA Received 15 May 2001; received in revised form 16 October 2001 Abstract The relative viscosity (µ rel = 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, theoretical and numerical results that focused on either Ca ≪ 1 or Ca ≫ 1. The suspensions are shear thinning with µ rel > 1 for small Ca. At large Ca, µ rel 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. Keywords: Rheology; Viscosity; Bubbles; Deformation; Dilute suspensions; Emulsions 1. Introduction In a low Reynolds number shear flow, the rheological properties of a two fluid phase suspension depend on the viscosity and volume fractions of the fluids, microstructures (shape, size, orientation and distribution of the dispersed phase) and interfacial properties (surface tension, concentration and behavior of surfactants). One useful rheological property of suspensions is the relative viscosity, µ rel , defined for simple shear flow as the ratio of the shear viscosity of the suspension (µ) to the shear viscosity of the suspending fluid (µ s ). In a dilute suspension: µ rel = 1 + fφ, (1) where φ is the volume fraction of the dispersed phase, and f a function that depends on the properties of the suspended particles. For example, Einstein [1] showed that f = 5/2 for rigid, spherical parti- cles. Taylor [2] generalized this result for spherical particles of arbitrary viscosity ratio, λ (the ratio of the ∗ Corresponding author. E-mail address: manga@seismo.berkeley.edu (M. Manga). 0377-0257/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII:S0377-0257(02)00013-7