Simulations and Models for Sedimentation at Small Reynolds Numbers

该奖项支持对各种低雷诺数沉积流进行同步数学和数值研究。 这些系统是复杂的长范围的性质所产生的流体流动由个别固体颗粒，因为他们下降，需要efficientalgorithms的粒子模拟，引入可变的非线性系数的不同的依赖关系模型连续偏微分方程，并导致非平凡的分布在thestatistical力学的相互作用的粒子。 在这项工作中，高效的算法专门稀释壁有界沉积，以前开发的调查在单分散沉积的velocityfluctuations的缩放，将被用来providequantitative data与现有的和新开发的kinetic和流体模型进行比较。 模拟将被推广到包括由于倾斜通道，多分散性，非球形颗粒，和小的非零雷诺数的影响。在流体中沉积的固体颗粒之间的相互作用在许多自然和工业过程中是重要的，包括河流中的泥沙和空气中的灰尘的沉降运动，以及在使用离心或重力分离的应用中，如蛋白质，矿物质，废水，虽然描述单个颗粒和悬浮流体之间相互作用的数学是众所周知的，但基于这些规则的大规模流动的模拟是计算禁止的。 更可取的是使用宏观模型，因为它们忽略了单个粒子的详细运动，求解成本更低。 不幸的是，现有的沉积宏观模型的有效性范围非常有限。 这项工作将考虑限制类的沉降系统中的有效计算大量的粒子之间的相互作用仍然是可能的，因为简化的几何形状和限制的数学规则描述粒子运动。 研究结果将用于帮助确定改进的宏观模型，以描述这些限制类和更一般的沉积流。最终，这项工作将导致改进的方程，用于模拟自然界中的沉积流，并更好地设计基于沉积的分离过程。

This award supports simultaneous mathematical and numerical study ofvarious low Reynolds number sedimentation flows. These systems arecomplicated by the long range nature of the fluid flows generated byindividual solid particles as they fall, requiring efficientalgorithms for particle simulations, introducing variable nonlinearcoefficients of different dependencies into model continuum partialdifferential equations, and leading to nontrivial distributions in thestatistical mechanics of the interacting particles. In this work,efficient algorithms specialized to dilute wall-bounded sedimentation,previously developed to investigate the scaling of velocityfluctuations in monodisperse sedimentation, will be used to providequantitative data for comparison with existing and newly-developedkinetic and fluid models. The simulations will be generalized toinclude effects due to inclined channels, polydispersity,non-spherical particles, and small non-zero Reynolds numbers.Interactions between solid particles sedimenting in a fluid areimportant in many natural and industrial processes, including thesettling motions of silt in rivers and dust in the air, and inapplications which use centrifugal or gravitational separation such asthose for proteins, minerals, waste water, and recyclable plastics.While the mathematics describing the interactions between individualparticles and the suspending fluid are well known, simulations oflarge scale flows based on these rules are computationallyprohibitive. It would be far preferable to use macroscopic modelswhich are less costly to solve because they neglect the detailedmotion of individual particles. Unfortunately, existing macroscopicmodels for sedimentation have very limited ranges of validity. Thiswork will consider restricted classes of sedimentation systems inwhich efficient computation of the interactions between large numbersof particles remains possible because of simplified geometries andlimits for the mathematical rules describing particle motion. Resultswill be used to help identify improved macroscopic models to describeboth these restricted classes and more general sedimentation flows.Ultimately, this work will lead to improved equations for modelingsedimentation flows in nature and for better design of separationprocesses based on sedimentation.