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

流体在多孔介质中的流动是一个重要的问题，涉及到各种过程，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，这是流动突然转变为一种性质不同的流动类型。例如，当一种密度较大的流体覆盖在密度较小的流体上时，流体的“手指”会向上和向下延伸到两种流体中。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率。这个项目探索了占据两个垂直玻璃板之间狭窄间隙的流体层的不稳定性。该项目将调查流体中含有颗粒和溶质（如盐）的情况。实验将用于在一层咸水之上的一层淡水中成像。实验将跟踪不稳定性对流动的影响，并与数值模拟进行比较。将得到颗粒沉降的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颗粒沉降在引发不稳定性方面的作用，并有助于更好地预测何时可能发生不稳定性。项目成果将有助于制定高效能源生产战略，同时尽量减少对环境的影响。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的增加机会。将开展一项拓展计划，让堪萨斯城市中心的弱势儿童了解科学和工程的乐趣。该项目研究了沉积物沉降如何引发或改变Hele-Shaw池狭窄间隙中分层流体的流动不稳定性。将研究咸水之上的含沙淡水及其相关构型。在计算方面，达西定律与盐的平流-扩散方程和包含沉降速度的颗粒浓度平流-扩散方程相结合，将求解存在颗粒负载的二维分层流体。流动将根据稳定比、将重力与粘性力联系起来的重力参数和无量纲沉降速度进行参数化。结果将根据沉积物和盐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之上的沉积物淡水和相关结构。将介绍利用已知大小和密度的微球控制沉积物密度。粘度将使用不同浓度的甘油水溶液来控制，它直接影响重力参数。将测量无量纲波长、指尖速度和颗粒浓度剖面。瑞利-泰勒，双扩散和泄漏不稳定性是预期的。将计算与流动成像相结合，将有助于揭示沉积作用对这些不稳定性的影响，并有助于确定达西定律在预测哪些不稳定性发生以及何时发生方面的适用性。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.