Instabilities in Particle-laden Stratified Fluids in Hele-Shaw Cells

University Of North Georgia, Dahlonega GA

Investigators

Abstract

The flow of fluids through porous media is an important problem relevant to a variety of processes such as underground transport of contaminants, certain filtration processes, and hydraulic fracturing. These flows are sometimes subject to flow instabilities, which are sudden transitions of the flow to a qualitatively different type of flow. For example, when a dense fluid overlies a less dense fluid, "fingers" of fluid develop extending up and down into the two fluids. This instability, known as the Rayleigh-Taylor instability, can increase rates fluid mixing and material transport. This project explores instabilities in layers of fluids that occupy a narrow gap between two vertical glass plates. The project will investigate cases in which the fluids contain particles and solutes such as salt. Experiments will be used to image the flow in a layer of fresh water above a layer of salt water. The effects of instabilities on the flow will be tracked in the experiment and compared with numerical simulations. Rates at which the particles settle as well as rates of particle and salt diffusion through the liquids will be obtained. The results will help reveal the role of particle sedimentation in triggering instabilities and lead to better predictions when instabilities are likely to occur. Project outcomes will help devise strategies for efficient energy production while minimizing environmental impact. The project will be conducted by undergraduate students at a small liberal arts college who will benefit from increased opportunities in science and engineering education. An outreach program will be conducted to acquaint under-represented and disadvantaged kids in inner-city Kansas City to the excitement of science and engineering. This project addresses how sediment settling initiates or modifies flow instabilities for stratified fluids in the narrow gap of a Hele-Shaw cell. Sediment-laden fresh water above salt water will be studied along with related configurations. On the computational side, Darcy's Law coupled with an advection-diffusion equation for salt and an advection-diffusion equation for particle concentration that includes a settling velocity will be solved for two-dimensional stratified fluids in the presence of particle-loading. The flows will be parametrized in terms of a stability ratio, a gravity parameter that relates gravitational force to viscous forces, and a dimensionless settling velocity. Results will be analyzed in terms of relative dimensions of concentration profiles of sediment and salt. On the experimental side, Schlieren imaging will be used to image sediment-laden fresh water layered above salt water and related configurations. Controlled densities of sediment will be introduced using microspheres of known size and density. Viscosity will be controlled using various concentrations of aqueous glycerol, which directly effects the gravity parameter. Dimensionless wavelength, fingertip velocity, and particle concentration profiles will be measured. Rayleigh-Taylor, double-diffusive, and leaking instabilities are expected. Combining computation with flow imaging will help expose the role of sedimentation on these instabilities and help determine the applicability of Darcy's law in predicting which instabilities occur and when they occur. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.