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

流体在多孔介质中的流动是一个与各种过程相关的重要问题，如污染物的地下输送、某些过滤过程和水力压裂。这些流动有时会受到流动不稳定性的影响，这是流动到性质不同类型的流动的突然转变。例如，当一种稠密的流体覆盖在另一种密度较低的流体上时，就会形成向上和向下伸展到这两种流体中的流体的“指状物”。这种不稳定性被称为瑞利-泰勒不稳定性，可以增加流体混合和物质传输的速度。这个项目探索占据两个垂直玻璃板之间狭窄间隙的流体层中的不稳定性。该项目将调查流体中含有盐等颗粒和溶质的情况。实验将被用来成像咸水层之上的淡水层中的流动。实验中将跟踪不稳定性对流动的影响，并与数值模拟进行比较。将获得颗粒的沉降速率以及颗粒和盐在液体中的扩散速率。这些结果将有助于揭示粒子沉积在触发不稳定中的作用，并导致更好地预测何时可能发生不稳定。项目成果将有助于制定高效能源生产的战略，同时将对环境的影响降至最低。该项目将由一所小型文理学院的本科生进行，他们将受益于科学和工程教育机会的增加。将开展一项外展计划，让堪萨斯城市中心未被充分代表和处于不利地位的孩子们对科学和工程感到兴奋。本项目研究沉积如何引发或改变Hele-Shaw槽狭窄缝隙中分层流体的流动不稳定性。含沉积物的淡水高于咸水将与相关的配置一起研究。在计算方面，对于考虑颗粒载荷的二维层状流体，将求解达西定律、盐类的对流扩散方程和包括沉降速度的颗粒浓度的对流扩散方程。流动将根据稳定性比、将重力与粘性力联系起来的重力参数和无量纲沉降速度来参数化。结果将根据泥沙和盐分浓度剖面的相对维度进行分析。在实验方面，纹影成像将用于成像咸水上方的沉淀物淡水及其相关配置。将使用已知大小和密度的微球引入可控的沉淀物密度。粘度将使用不同浓度的甘油水进行控制，这将直接影响重力参数。将测量无量纲波长、指尖速度和颗粒浓度分布。预计会出现Rayleigh-Taylor、双扩散和泄漏不稳定性。将计算与流动成像相结合，将有助于揭示沉积对这些不稳定的作用，并有助于确定达西定律在预测哪些不稳定发生以及何时发生不稳定方面的适用性。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.