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

流体通过多孔介质的流动是与各种过程相关的重要问题，例如污染物的地下运输、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，流动不稳定性是流动突然转变为性质不同的流动类型。 例如，当稠密的流体覆盖在较不稠密的流体上时，形成向上和向下延伸到两种流体中的流体“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材料输送的速率。 这个项目探讨了两个垂直玻璃板之间狭窄间隙中的流体层的不稳定性。 该项目将调查液体中含有颗粒和溶质（如作为盐）的情况。 实验将被用来对盐水层上的淡水层中的流动进行成像。 将在实验中跟踪不稳定性对流动的影响，并与数值模拟进行比较。 将获得颗粒沉降的速率以及颗粒和盐通过液体的扩散速率。 结果将有助于揭示粒子沉降在触发不稳定性中的作用，并在可能发生不稳定性时进行更好的预测。 项目成果将有助于制定有效能源生产战略，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机会增加。 将开展一项推广计划，让堪萨斯城市中心代表性不足和处境不利的孩子了解科学和工程的兴奋。这个项目解决了如何沉积物沉降开始或修改分层流体在狭窄的间隙的海勒-肖细胞的流动不稳定性。 将沿着相关配置研究盐水上方的含沉积物淡水。在计算方面，达西定律与盐的对流扩散方程和颗粒浓度的对流扩散方程（包括沉降速度）相结合，将在存在颗粒负载的情况下求解二维分层流体。流动将被参数化的稳定性比，重力参数，涉及重力的粘性力，和无量纲的沉降速度。将根据沉积物和盐的浓度分布的相对尺寸对结果进行分析。在实验方面，纹影成像将用于对盐水和相关结构上方分层的充满沉积物的淡水进行成像。将使用已知大小和密度的微球来控制沉积物的密度。将使用各种浓度的甘油水溶液控制粘度，这直接影响重力参数。将测量无反射波长、指尖速度和颗粒浓度分布。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对这些不稳定性的作用，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NSF的法定使命，并被认为值得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来支持。

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.