Modelling viscous boundary layer dissipation effects in liquid surrounding individual solid nano and micro-particles in an ultrasonic field

Upon application of ultrasonic waves to a suspension of solid particles in liquid, multiple scattering occurs at the particle/liquid interfaces leading to attenuation. It was recently shown through experimental verification that multiple scattering theory must include shear wave influences at the boundary between the liquid and solid particles in a nanofluid when the concentration of the scatterers is even as low as a few percent by volume. Herein, we consider silica spheres of 50–450 nm diameter in the long-wavelength regime to elucidate the form of the shear decay fields at the liquid/solid interface for individual particles. This is important because the overlap of these fields ultimately leads to the conversion of a compressional wave to shear waves and back into the compressional wave, the effect originating due to the density contrast between the particle and the liquid. Therefore, we examine in detail the velocity, vorticity and viscous dissipation in the shear wave field and around the silica spheres using finite element modelling, giving clarity to the viscous boundary effects. We also compare the numerical modelling to semi-analytical results.