The absorption of ultrasound in emulsions: computational modelling of thermal effects

Around liquid particles in a fluid of contrasting properties (for example, oil in water) in ultrasonic fields there are small regions where thermal waves can propagate with relatively high amplitudes. Herein, we demonstrate the existence and character of these waveforms using three-dimensional finite element modelling based on linearised Navier-Stokes equations. We investigate single particles and small clusters of particles, validating the expected thermal wavelength and the power dissipation due to viscous and thermal effects around the particle. The energy lost due to thermal and viscous dissipation is explored as a function of the average separation distance between the particles (linking to concentration) as well as the applied frequency. The determination of energy loss provides a new method for calculating the attenuation in particle systems. We demonstrate that the effective attenuation of an emulsion in which particles exist in clusters is influenced by the interparticle separation within the cluster, even at the same total particle concentration. Thus, the finite element modelling provides evidence for thermal interactions and their effect in correlated particle systems.