The effect of gravitational settling on concentration profiles and dispersion within and above fractured media

The transport of heavy particles in a medium that consists of fluid and solid phases such as stream gravel beds, cracked soils and wetlands is affected by processes such as attachment-detachment, gravity and drag, and by mixing processes that are induced by Taylor dispersion and mechanical dispersion. This paper addresses an additional dispersion mechanism which is induced by gravitational settling and is a result of the coupling between the particle concentration and the fluid velocity profiles at the sub-scale. Heavy particles that move in areas of low horizontal velocity (e.g., near solid surfaces and wake regions) settle closer to the release source as compared to particles in high velocity regions. The macroscopic concentration field of such suspensions is influenced by the ratio between the settling velocity and the sub-scale distribution of the horizontal velocities. The objective of the study is to isolate and quantify this type of dispersion using controlled flow scenarios. We used a Taylor brush geometry (an array of vertical grooves) to numerically solve the flow. Particles were released from a vertical plane, generating a constant flux. The sub-scale Eulerian concentration was compiled from simulated trajectories and then spatially averaged to generate macroscopic concentration fields. The results show that this settling-induced dispersion is significant in regions near the source and that it cannot be modeled using Fick's law type of formulations. A parametric investigation shows that the location of the highest dispersion flux is linearly proportional to both the groove spacing and depth. A proposed model that estimates this location is used to evaluate where settling-induced dispersion should not be ignored.