Measurement and modeling of the flow behavior of aqueous foams using a recirculating pipe rheometer

A recirculating pipe rheometer associated with a foam generation system is described. In addition to the measurement of the volumetric flow rate and the pressure drop through straight pipes, the system allows simultaneous online measurement of the foam texture, foam density, temperature and inline static pressure. With this equipment, we measured steady-state flow curves of foams, stabilized by addition of a surfactant, over a shear rate range of ∼10 to 103 s−1. The data have been corrected for the apparent slip of the foam at the pipe wall. The flow behavior of foams is examined as a function of the gas volume fraction ϕ (or foam quality) ranging from 20 to 85%, at different static pressures and for various concentrations of the added surfactant. Foams at volume fractions up to ϕ = 50% contain isolated spherical bubbles. Their viscosity is Newtonian and governed by the volume fraction and not by the bubble size distribution, as shown by the good agreement with the predictions of the Taylor-Mooney viscosity model for moderately concentrated emulsions. For high volume fraction foams (ϕ ≥ 60%), the bubbles are separated by a thin liquid film. The viscosity/shear stress curves of these foams show a severe shear-thinning behavior beyond an apparent dynamic yield stress and a tendency to a high shear stress asymptote. Their shear stress/shear rate equivalent curves are adequately fitted by the Herschel-Bulkley model. The predictions of empirical foam and emulsion models, which incorporate physical parameters, are also analyzed. The volume equalization method, proposed by Valko and Economides, which assumes that a suitable parameter is the expansion ratio related to the foam compressibility, fails to reduce the steady-state flow curves to a master curve, whatever the type of flow curve. On the other hand, the model of Princen and Kiss, which describes the shear viscosity as a function of the capillary number, is found adequate to describe the behavior of foams having a yield stress, but only for volume fractions up to 75%. Finally, the scaling analysis proposed by Prud'homme and Otsubo for highly concentrated emulsions is considered. We demonstrate that, at a fixed high volume fraction, the shear viscosities obtained for various concentrations of added surfactant scale with the ratio of the interfacial tension to the Sauter diameter, reflecting the importance of the total interfacial area.