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Exposure of nanoparticles in a porous medium, such as a hydrogel, to low-intensity ultrasound has been observed to dramatically enhance particle penetration rate. Enhancement of nanoparticle penetration is a key issue affecting applications such as biofilm mitigation and targeted drug delivery in human tissue. The current study used fluorescent imaging to obtain detailed experimental measurements of the effect of ultrasound amplitude and frequency on diffusion of nanoparticles of different diameters in an agarose hydrogel, which is often used as a simulant for biofilms and biological tissues. We demonstrate that the acoustic enhancement occurs via the phenomenon of oscillatory diffusion, in which a combination of an oscillatory flow together with random hindering of the particles by interaction with hydrogel proteins induces a stochastic random walk of the particles. The measured variation of acoustic diffusion coefficients with amplitude and frequency were used to validate a previous statistical theory of oscillatory diffusion based on the continuous time random walk approach. 

A computational study was performed both of a single agglomerate and of the collision of two agglomerates in a shear flow. The agglomerates were extracted from a direct numerical simulation of a turbulent agglomeration process, and had the loosely packed fractal structure typical of agglomerate structures formed in turbulent agglomeration processes. The computation was performed using a discrete-element method for adhesive particles with four-way coupling, accounting both for forces between the fluid and the particles (and vice versa ) as well as force transmission directly between particles via particle collisions. In addition to understanding and characterizing the particle dynamics, the study focused on illuminating the fluid flow field induced by the agglomerate in the presence of a background shear and the effect of collisions on this particle-induced flow. Perhaps the most interesting result of the current work was the observation that the flow field induced by a particle agglomerate rotating in a shear flow has the form of two tilted vortex rings with opposite-sign circulation. These rings are surrounded by a sea of stretched vorticity from the background shear flow. The agglomerate rotates in the shear flow, but at a slower rate than the ambient fluid elements. In the computations with two colliding agglomerates, we observed cases resulting in agglomerate merger, bouncing and fragmentation. However, the bouncing cases were all observed to also result in an exchange of particles between the two colliding agglomerates, so that they were influenced both by elastic rebound of the agglomerate structures as well as by tearing away of particulate matter between the agglomerates. Overall, the problems of agglomerate–flow interaction and of the collision of two agglomerates in a shear flow are considerably richer in physical phenomena and more complex than can be described by the common approximation that represents each agglomerate by an ‘equivalent sphere’.