SGER: The Slip Boundary Condition

SGER：滑移边界条件

• 批准号: 0200762
• 负责人: Seth Lichter
• 金额: $ 5.73万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-04-01 至 2003-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0200762&HistoricalAwards=false
• 关键词: SGER; Slip; Boundary; Condition

NSF Award Abstract - DMS-0200762Mathematical Sciences: The Slip Boundary ConditionAbstract0200762 LichterAlthough the no-slip boundary condition, which requires fluid adjacent to a solid substrate to move with the same velocity as the substrate, serves reliably to model fluid behavior in most circumstances, recent experiments and numerical simulations have shown that, in fact, there is a relative velocity between the fluid and the substrate. While the effects of this slip may remain negligible in some flows, accounting for slip is a prerequisite for predicting the correct behavior in many other types of flows, such as those in small geometries, flows in which an interface (between two fluids) moves along a solid, and flows in which particles must pass through an interface. This project seeks to develop models of the slip boundary condition. The formulation will incorporate results of recent experiments and numerical simulations to construct the equations of flow in the neighborhood of a solid substrate. Preliminary work indicates that such a model, as well as related useful simpler approximations, can be developed. The simplicity of the equations and consequent efficient numerical procedures for evaluating the dynamics near the wall should provide insight into how slip occurs and how the characteristics of the fluid and the substrate determine the amount and nature of slip. The recent availability of high quality experimental data and simulation results, as well as the advent of technologies demanding flow in small geometries, make this a timely undertaking. This project concerns mathematical modeling of the behavior of fluids where they adjoin solids. The results will allow highly accurate computation of fluid flow, which is essential for the design of small hydrodynamical instruments, including "lab-on-a-chip" devices.

美国国家科学基金会奖摘要- DMS-0200762数学科学：虽然无滑移边界条件要求邻近固体基底的流体以与基底相同的速度移动，在大多数情况下可靠地用于模拟流体行为，但最近的实验和数值模拟表明，事实上，在流体和衬底之间存在相对速度。 虽然这种滑移的影响在某些流动中可能仍然可以忽略不计，但考虑滑移是预测许多其他类型流动中正确行为的先决条件，例如小几何形状的流动、界面（两种流体之间）沿固体沿着移动的流动以及颗粒必须穿过界面的流动。 该项目旨在开发滑动边界条件的模型。该配方将结合最近的实验和数值模拟的结果，以构建在固体基板附近的流动方程。 初步工作表明，这样一个模型，以及相关的有用的更简单的近似，可以开发。简单的方程和随之而来的有效的数值程序，用于评估附近的动态壁应该提供洞察如何滑移发生和如何的特性的流体和基板确定的量和性质的滑移。最近获得的高质量实验数据和模拟结果，以及要求在小几何形状中流动的技术的出现，使这项工作成为一项及时的任务。这个项目关注的是流体在与固体相邻处的行为的数学模型。 这些结果将允许高度精确地计算流体流量，这对于设计小型流体动力学仪器，包括“芯片实验室”设备至关重要。