We present data for the rheology of suspensions of monodisperse particles of varying aspect ratio, from oblate to prolate, and covering particle volume fractions ϕ from dilute to highly concentrated. Rheology is characterized by fitting the experimental data to the model of Herschel & Bulkley (Herschel & Bulkley 1926 Kolloid Z. 39 , 291–300 ( doi:10.1007/BF01432034 )) yielding three rheometric parameters: consistency K (cognate with viscosity); flow index n (a measure of shear-thinning); yield stress τ ₀ . The consistency K of suspensions of particles of arbitrary aspect ratio can be accurately predicted by the model of Maron & Pierce (Maron & Pierce 1956 J. Colloid Sci. 11 , 80–95 ( doi:10.1016/0095-8522(56)90023-X )) with the maximum packing fraction ϕ _m as the only fitted parameter. We derive empirical relationships for ϕ _m and n as a function of average particle aspect ratio r _p and for τ ₀ as a function of ϕ _m and a fitting parameter τ *. These relationships can be used to predict the rheology of suspensions of prolate particles from measured ϕ and r _p . By recasting our data in terms of the Einstein coefficient, we relate our rheological observations to the underlying particle motions via Jeffery’s (Jeffery 1922 Proc. R. Soc. Lond. A 102 , 161–179 ( doi:10.1098/rspa.1922.0078 )) theory. We extend Jeffery’s work to calculate, numerically, the Einstein coefficient for a suspension of many, initially randomly oriented particles. This provides a physical, microstructural explanation of our observations, including transient oscillations seen during run start-up and changes of rheological regime as ϕ increases.

A semiempirical constitutive model for the visco-elastic rheology of bubble suspensions with gas volume fractions ϕ < 0.5 and small deformations (Ca ≪ 1) is developed. The model has its theoretical foundation in a physical analysis of dilute emulsions. The constitutive equation takes the form of a linear Jeffreys model involving observable material parameters: the viscosity of the continuous phase, gas volume fraction, the relaxation time, bubble size distribution and an empirically determined dimensionless constant. The model is validated against observations of the deformation of suspensions of nitrogen bubbles in a Newtonian liquid (golden syrup) subjected to forced oscillations. The effect of ϕ and frequency of oscillation f on the elastic and viscous components of the deformation are investigated. At low f, increasing ϕ leads to an increase in viscosity, whereas, at high f, viscosity decreases as ϕ increases. This behaviour can be understood in terms of bubble deformation rates and we propose a dimensionless quantity, the dynamic capillary number Cd, as the parameter which controls the behaviour of the system. Previously published constitutive equations and observations of the rheology of bubble suspensions are reviewed. Hitherto apparently contradictory findings can be explained as a result of Cd regime. A method for dealing with polydisperse bubble size distributions is also presented.