Ultrasonic propagation in concentrated colloidal dispersions: improvements in a hydrodynamic model

Abstract

Recent theoretical and experimental findings demonstrate that modeling ultrasonic attenuation of a concentrated colloidal suspension requires inclusion of shear-induced contributions, an element being unaccounted for by most scattering models. Herein, we extend a hydrodynamic model from low to high particle volume fraction by effectively relating the single particle dynamic drag to particle concentration to account for hydrodynamic interparticle interactions. We calculate an expression for the complex-valued effective dynamic mass density at high concentrations, which is then combined with a viscosity-corrected effective bulk modulus to estimate ultrasonic velocity and attenuation for a monodisperse suspension of solid spherical particles in a viscous liquid. The effective velocity and attenuation are functions of particle volume fraction, frequency, and physical properties of particles and liquid. We compare our results with those from two recently developed scattering models: a multi-modal multiple scattering model and a core-shell effective medium model, each taking into account the viscosity of the host fluid through shear wave influences. Finally, we find that our extended model predicts experimental attenuation data the best for a silica in water suspension compared to the results of other models.

Graphical Abstract

Keywords:

• Ultrasound
• concentrated colloid
• acoustic model
• viscous liquid
• hydrodynamics

Acknowledgments

I acknowledge Prof Francine Luppé’s earlier work with me that has helped develop ideas in this paper. I thank Prof Luc Mongeau (McGill University, Canada) and Dr. Oleg B. Gus’kov (Institute of Applied Mechanics, RAS, Russia) for supplying helpful comments on the dynamic drag.