Rheology of concentrated mixtures of fluid with small particles, parameters of phase interaction

et al. 2007

An extension of the classical coupled phase theory is proposed to account for hydrodynamic interactions between neighboring rigid particles, which are essential to describe properly the sound propagation in concentrated suspensions. Rigorous ensemble-averaged equations are derived for each phase and simplified in the case of acoustical wave propagation. Then, closure is achieved by introducing a self-consistent scheme originally developed by Buyevich and Shchelchkova [Prog. Aerosp. Sci. 18, 121-151 (1978)] for incompressible flows, to model the transfer terms between the two phases. This provides an alternative to the effective medium self-consistent theory developed by Spelt et al. [J. Fluid Mech. 430, 51-86 (2001)] in which the suspension is considered as a whole. Here, a significantly simpler formulation is obtained in the long wavelength regime. Predictions of this self-consistent theory are compared with the classical coupled phase theory and with experimental data measuring the attenuation in concentrated suspensions of silica in water. Our calculation is shown to give a good description of the attenuation variation with volume fraction. This theory is also extended to the case of polydisperse suspensions. Finally, the link between the self-consistent theory and the different orders of the multiple scattering theory is clarified.

Section: ͑44͒mentioning

confidence: 98%

“…The first integrand ͑18͒ corresponds to the classical calculation of the force applied on a moving sphere embedded in an unsteady nonuniform velocity field, sometimes called the Basset-BoussinesqOseen force. 29 The calculation of the second integrand ͑19͒ is less usual and can be found in some papers by Buyevich: 29,23…”

Section: The Self-consistent Conditionmentioning

confidence: 99%

An extended coupled phase theory for the sound propagation in polydisperse concentrated suspensions of rigid particles

et al. 2007

“…42 The details of this calculation can be found in Appendixes A and B. In this section, we only give the final expressions of the coefficient n k which result from the identification of the expression of F and S calculated in the Appendix and formulas ͑27͒ and ͑28͒.…”

Section: Calculation Of the Closure Termsmentioning

confidence: 99%

“…Moreover, these functions must depend on the frequency to take into account the time derivatives in the Fourier space. For a moving sphere embedded in a pure ambient fluid, the expressions of f and s are well known: 41,42 …”

Section: B the Self-consistent Effective Medium Closure Schemementioning

confidence: 99%

On the influence of spatial correlations on sound propagation in concentrated solutions of rigid particles

2008

In a previous paper [J. Acoust. Soc. Am. 121, 3386-3387 (2007)], a self-consistent effective medium theory has been used to account for hydrodynamic interactions between neighboring rigid particles, which considerably affect the sound propagation in concentrated solutions. However, spatial correlations were completely left out in this model. They correspond to the fact that the presence of one particle at a given position locally affects the location of the other ones. In the present work, the importance of such correlations is demonstrated within a certain frequency range and particle concentration. For that purpose, spatial correlations are integrated in our two-phase formulation by using a closure scheme similar to the one introduced by Spelt et al. [''Attenuation of sound in concentrated suspensions theory and experiments," J. Fluid Mech. 430, 51-86 (2001)]. Then, the effect is shown through a careful comparison of the results obtained with this model, the ones obtained with different self-consistent approximations and the experiments performed by Hipp et al. ["Acoustical characterization of concentrated suspensions and emulsions. 2. Experimental validation," Langmuir, 18, 391-404 (2002)]. With the present formulation, an excellent agreement is reached for all frequencies (within the limit of the long wavelength regime) and for concentrations up to 30% without any adjustable parameter.

“…For an unsteady motion, this force is the sum of the Stokes, Basset, Added mass and Archimedes forces. 26 The first term is the classic Stokes drag applied on a sphere embedded in a steady viscous flow. The Basset hereditary force is an unsteady viscous term due to the time required by the viscous diffusion layer to adapt to new boundary conditions.…”

Section: B Outline Of the Modelmentioning

confidence: 99%

Sound, infrasound, and sonic boom absorption by atmospheric clouds

2011

This study quantifies the influence of atmospheric clouds on propagation of sound and infrasound, based on an existing model [Gubaidulin and Nigmatulin, Int. J. Multiphase Flow 26, 207-228 (2000)]. Clouds are considered as a dilute and polydisperse suspension of liquid water droplets within a mixture of dry air and water vapor, both considered as perfect gases. The model is limited to low and medium altitude clouds, with a small ice content. Four physical mechanisms are taken into account: viscoinertial effects, heat transfer, water phase changes (evaporation and condensation), and vapor diffusion. Physical properties of atmospheric clouds (altitude, thickness, water content and droplet size distribution) are collected, along with values of the thermodynamical coefficients. Different types of clouds have been selected. Quantitative evaluation shows that, for low audible and infrasound frequencies, absorption within clouds is several orders of magnitude larger than classical absorption. The importance of phase changes and vapor diffusion is outlined. Finally, numerical simulations for nonlinear propagation of sonic booms indicate that, for thick clouds, attenuation can lead to a very large decay of the boom at the ground level.