Problems in Fluid Dynamics and Elasticity

流体动力学和弹性问题

• 批准号: 0103813
• 负责人: Michael Renardy
• 金额: $ 10.49万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-15 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0103813&HistoricalAwards=false
• 关键词: Problems; Fluid; Dynamics; Elasticity

Research is proposed on the following topics:1. Breakup of liquid jets: This research will mathematically analyze the capillary breakup of jets of Newtonian and viscoelastic liquids. The effect of polymer additives in suppressing breakup is well known and exploited both in nature (spider webs) and in technology (control of drops sizes in spraying of liquids). The research will concentrate on the asymptotics of breakup and compare various constitutive theories.2. Stability of viscoelastic flows: Elastic instabilities have been investigated extensively over the past ten years. Such instabilities often pose limits for polymer processing conditions. In the numerical investigation of instabilities in complex flows, continuous spectra which are poorly resolved pose a significant challenge. The research is aimed at using analytical techniques to determine the location of these continuous spectra.3. Shape control in elasticity: An elastic medium is controlled by actuators which can supply a stress of a given type. The research will investigate the question whether such controls can achieve a given shape of the medium.4. Numerical simulation of two-fluid flows: The research will continue work on simulation of flows of two liquids using a volume of fluid code. The following three problems will be investigated: a) Formation of ``staircase" structures on impacting drops due to capillary waves. b) Tipstreaming in drop breakup under shear when surfactants are present. c) Effect of normal stresses on breakup of viscoelastic drops under shear.The proposed research addresses fundamental issues which arise in the processing anduse of polymeric liquids, the control of deformations of elastic solids and theformation of emulsions by shear mixing. The proposed topics include a comparison ofthe qualitative behavior various models of polymeric fluids in jet breakup, thestability of polymeric flows, the question which shapes of an elastic medium canbe achieved by a given type of control, and the development of numerical methods fortwo-fluid flows.

本文拟围绕以下主题进行研究：1.液体射流的破裂：这项研究将进行数学分析 牛顿流体和粘弹性流体射流的毛细管破裂。效果 聚合物添加剂在抑制破碎中的应用是众所周知的， 在自然界（蜘蛛网）和技术（控制喷雾中的液滴大小）中 液体）。研究将集中在分裂的渐近性， 比较各种本构理论.粘弹性流动的稳定性： 在过去的十年里进行了广泛的调查。这种不稳定性往往 对聚合物加工条件造成限制。在数值研究中 复杂流动中的不稳定性，连续光谱， 构成了一个重大挑战。该研究旨在利用分析 技术来确定这些连续光谱的位置。弹性中的形状控制：弹性介质由 可以提供给定类型的应力的致动器。这项研究将 调查这样的控制是否可以实现给定的形状的问题， 4.中间二流体流动的数值模拟：研究将继续 使用流体体积代码模拟两种液体的流动。的 将研究以下三个问题： （a）在撞击液滴上形成"楼梯”结构， 毛细血管波 B）当表面活性剂在剪切下的液滴破碎中的尖端流 礼物 c）法向应力对粘弹性液滴破裂的影响， 提出的研究解决了在聚合物液体的加工和使用中出现的基本问题，弹性固体变形的控制和通过剪切混合形成乳液。所提出的主题包括：聚合物流体在射流破碎中的各种模型的定性行为的比较，聚合物流动的稳定性，通过给定类型的控制可以实现弹性介质的形状的问题，以及双流体流动的数值方法的发展。