Scattering coefficients for a sphere in a visco-acoustic medium for arbitrary partial wave order

Alam, M. Mahbub; Pinfield, Valerie J.; Maréchal, Pierre

doi:10.1016/j.wavemoti.2020.102589

Cited by 3 publications

(6 citation statements)

References 19 publications

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“…where prime denotes the dispersed phase (inside the scatterers) and unprimed quantities the continuous phase (the embedding medium), except on Bessel and Hankel functions where prime represents the derivative. For n > 1 (presented in [39])…”

Section: Asymptotic Results For Multi-mode Scattering Coefficientsmentioning

confidence: 99%

Multi-mode multiple wave scattering in suspensions of solid particles in viscous liquids: part 1 asymptotic results

Pinfield,

Valier-Brasier

2024

Proc. R. Soc. A.

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The propagation of coherent longitudinal waves in a viscous liquid containing a random distribution of spherical elastic particles is analysed using a model based on multiple scattering theory. This model, initially developed to describe the propagation of coupled longitudinal and transverse elastic waves in isotropic solid materials, takes into account wave conversions at the particle surface as well as positional correlations between particles via the pair correlation function. By modelling a Newtonian viscous liquid through complex frequency-dependent elastic moduli (i.e. using an imaginary shear modulus), the model is adapted to the case of viscous fluids and we show that conversions of longitudinal waves into transverse waves are important to take into account. We present asymptotic results from the model for case of long wavelength for the longitudinal waves, without assumptions on the shear wavelength. For high concentrations, these wave conversions are reinforced by the contribution of position correlations between the particles. In a subsequent paper, we present numerical validation of the asymptotic approximations and compare them with experimental results for solid particles in water.

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Section: Asymptotic Results For Multi-mode Scattering Coefficientsmentioning

confidence: 99%

Multi-mode multiple wave scattering in suspensions of solid particles in viscous liquids: part 1 asymptotic results

Pinfield,

Valier-Brasier

2024

Proc. R. Soc. A.

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“…[41] . As each of the four models is studied for the long-compressional wavelength approximation, for the simplicity of the numerical calculation, we have used the closed-form analytical expressions for the multimodal scattering coefficients [21,39] (given in the Appendix) rather than obtaining them numerically from the matrix-inversion of boundary equations to evaluate the effective wavenumbers from the multiple scattering model and the core-shell model.…”

Section: Resultsmentioning

confidence: 99%

“…where q = 2* is assumed to avoid the overlapping among spheres, with * being the particle radius; = √−1 is the imaginary unit, r : and ℎ : are zero order Bessel and Hankel functions; P u vw (presented in the Appendix) is the xth order partial wave scattering coefficient of a scattered wave of mode y = m or o produced from an incident wave of mode | = m or o. [39] Δ QU and Δ 5 QU are additional terms in the model that include the mode-conversion (acoustic-shear) contributions; in the high frequency or long shear wavelength limit, these two terms vanish, and Eq. ( 14) reduces to the effective wavenumber for solid particles in inviscid liquid suspensions, as given by the Lloyd-Berry model.…”

Section: Multi-modal Multiple Scatteringmentioning

confidence: 99%

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

Alam

2020

Journal of Dispersion Science and Technology

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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 inter-particle 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.

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“…We have investigated the predictions of the effective attenuation of the coherent longitudinal wave with a wavenumber close to that of the longitudinal (compressional) wave in the embedding medium. The particles are assumed to be spherical and their scattering coefficients are calculated directly from the boundary equations using the Epstein-Carhart, Allegra-Hawley formulation reported elsewhere [3][4][5][6][7], omitting thermal effects since they are very small for solid-in-liquid scattering systems. The analytical asymptotic forms shown in [1] eqns (3.4)- (3.13) were not used for the calculations except for one illustration, but a validation of these analytical forms is shown in the companion paper.…”

Section: Introductionmentioning

confidence: 99%

Multimode multiple wave scattering in suspensions of solid particles in viscous liquids: part 2: numerical validation

Pinfield,

Valier-Brasier

2024

Proc. R. Soc. A.

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In the first paper in this series, we presented asymptotic results for the effective wavenumber of the coherent longitudinal waves propagating through a system of pseudo-randomly distributed spherical elastic scatterers in a viscous medium. The analysis was based on multi-modal multiple scattering theory to account for both longitudinal and shear waves in the viscous embedding medium, arising from wave conversions at the scatterers surface, and identified asymptotic results in the long wavelength limit of the longitudinal waves. In this second paper, we present numerical validation of the various asymptotic approximations presented previously, including truncation of the number of partial wave orders and the use of the low concentration expansion of the dispersion relation. We explore the important contributions of wave conversion and of correlations in particle positions to the effective attenuation and to the frequency of the dipolar resonance of the scatterers. A comparison of the experimental results obtained with water containing sub-micrometric silica beads shows the very good validity of the model, particularly in the vicinity of the dipolar resonance.

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Scattering coefficients for a sphere in a visco-acoustic medium for arbitrary partial wave order

Cited by 3 publications

References 19 publications

Multi-mode multiple wave scattering in suspensions of solid particles in viscous liquids: part 1 asymptotic results

Multi-mode multiple wave scattering in suspensions of solid particles in viscous liquids: part 1 asymptotic results

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

Multimode multiple wave scattering in suspensions of solid particles in viscous liquids: part 2: numerical validation

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