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.

摘要

最近的理论和实验结果表明，对浓缩胶体悬浮液的超声波衰减进行建模需要包含剪切引起的贡献，这是大多数散射模型无法解释的元素。在这里，我们通过有效地将单粒子动态阻力与粒子浓度相关联，将流体动力学模型从低粒子体积分数扩展到高粒子体积分数，以解释流体动力学粒子间相互作用。我们计算了高浓度下复值有效动态质量密度的表达式，然后将其与粘度校正的有效体积模量相结合，以估计固体球形颗粒在粘性液体中的单分散悬浮液的超声速度和衰减。有效速度和衰减是粒子体积分数的函数，频率，以及粒子和液体的物理性质。我们将我们的结果与最近开发的两个散射模型的结果进行比较：多模态多重散射模型和核壳有效介质模型，每个模型都通过剪切波影响考虑了主体流体的粘度。最后，我们发现，与其他模型的结果相比，我们的扩展模型预测的实验衰减数据对于水悬浮二氧化硅来说是最好的。