Shear break-up of reversible fractal clusters is investigated by ultrasound and multiple light scattering in the low shear regime. We consider a dense suspension of Rayleigh scatterers (particles or clusters) with acoustic properties close to those of the surrounding liquid so that the attenuation of the ultrasonic coherent field is weak and multiple scattering is negligible. The concept of variance in local particle volume fraction is used to derive an original expression of the ultrasound scattering cross-section per unit volume for Rayleigh fractal clusters. On the basis of a scaling law for the shear break-up of aggregates, then we derive the shear stress dependence of the ultrasound scattered intensity from a suspension of reversible fractal clusters. In a second part, we present rheo-acoustical experiments to study the shear breakup of hardened red cell aggregates in plane-plane flow geometry and we examine both the self consistent field approximation and the scaling laws used in microrheological models. We further compare the ability of acoustical backscattering and optical reflectometry techniques to estimate the critical disaggregation shear stress and the particle surface adhesive energy. Finally, the microrheological model from Snabre and Mills [5] based on a fractal approach is shown to describe the non Newtonian behavior of a dense distribution of hardened red cell aggregates.
PACS. 42.25.Fx Diffraction and scattering -43.35.+d Ultrasonics, quantum acoustics, and physical effects of sound -43.80.+p Bioacoustics Nomenclature ν frequency (Hz), λ wavelength (m), a particle radius (m), R cluster radius (m), R maximum size of filling space subclusters at rest (m), δz axial resolution of the transducer (m), h gap width between rotating plates (m), z distance between the transducer and the insonified region (m), V particle volume (m 3 ), V a cluster volume (m 3 ), Ω volume of an elemental voxel (m 3 ), n particle number per unit volume (m −3 ), n a cluster number per unit volume (m −3 ), k, s incident and scattered wave number (m −1 ), q scattering wave number (q = s − k) (m −1 ), B cross-sectional area of the ultrasound beam (m 2 ), A c contact area between two particles (m 2 ), A particle area (m 2 ), a e-mail: snabre@imp-odeillo.fr b UPR 8521 du CNRS c phase velocity of the ultrasound wave (m/s), δtpulsewidth (s), ω particle number in a voxel, N particle number in a cluster, N b number of subunits of size 1/q in a cluster, D fractal dimension of a cluster, φ particle volume fraction, φ a cluster volume fraction, φ * maximum packing volume fraction, φ g gelation or percolation threshold, m critical exponent for cluster breakup, γ shear rate (s −1 ), τ shear stress (N/m 2 ), τ c critical disaggregation shear stress (N/m 2 ), τ * critical shear stress for cluster breakup (N/m 2 ), τ o yield stress (N/m 2 ), µ, µ a shear viscosity of the suspension (Ns/m 2 ), µ o shear viscosity of the suspending fluid (Ns/m 2 ), µ r relative shear viscosity of the suspension (µ r = µ a /µ o ), σ, σ α differential scattering...
