Mathematical Analysis of the Orientation of Symmetric Particles Sedimenting in Newtonian and Viscoelastic Liquids

牛顿和粘弹性液体中对称粒子沉降方向的数学分析

基本信息

  • 批准号:
    0103970
  • 负责人:
  • 金额:
    $ 12万
  • 依托单位:
  • 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:
    2001-08-01 至 2005-07-31
  • 项目状态:
    已结题

项目摘要

Over the last 40 years the study of the motion of small particles in a viscous liquid has become one of the main focuses of applied research. The presence of the particles affects the flow of the liquid, and this, in turn, affects the motion of the particles, so that the problem of determining the flow characteristics is highly coupled. It is just this latter feature that makes any fundamental mathematical problem related to liquid-particle interaction a particularly challenging one. The goal of this project is to furnish a mathematical analysis of one of the several important and still not completely understood aspects of this fascinating subject, namely, the orientation of homogeneous, symmetric particles sedimenting in Newtonian and viscoelastic liquids. In particular, the PI intends to furnish a quantitative and rigorous explanation of the challenging "tilt-angle phenomenon" that is observed in certain viscoelastic liquids, where particles orient themselves at a preferred angle with the main flow. The angle depends on the shape of the particle, their mass and on the physical properties of the liquid. Liquid models such as Oldroyd-B with shear-dependent viscosity will be used, along with some suitable analytical tools (the "splitting method") that the PI with his collaborators has been developing over the last few years for the study of well-posedness of several viscoelastic liquid models.The orientation of homogeneous long bodies in liquids of different nature is a fundamental issue in many problems of practical interest. In composite materials, the addition of short fiber-like particles to a polymer matrix will to enhance the mechanical properties of the material; for instance, it could make the material softer or harder, and more durable. The degree of enhancement depends strongly on the orientation of the fibers and the fiber orientation is in turn caused by the flow occurring in the mold. Another important application occurs in separation of macromolecules by electrophoresis. Modern applications include weight determination of proteins, DNA sequencing, and diagnosis of genetic disease. Electrophoresis involves the motion of charged particles (macromolecules) in solution, under the influence of an electric field. The orientation of the molecules plays an important role, since it is responsible for the loss of separability during steady-field gel electrophoresis. A final, but not less important application of particle orientation, occurs in blood flow, where the blood cells under certain flow conditions tend to chain themselves along the axis of the artery at certain preferred angles (tilt angle).
在过去的40年里,粘性液体中小颗粒运动的研究已成为应用研究的主要焦点之一。颗粒的存在影响液体的流动,而这又影响颗粒的运动,因此确定流动特性的问题是高度耦合的。正是这后一个特征使得任何与液体-粒子相互作用有关的基本数学问题都成为一个特别具有挑战性的问题。这个项目的目标是提供一个数学分析的几个重要的,仍然没有完全理解的方面,这一迷人的主题,即均匀的,对称的粒子在牛顿和粘弹性液体中沉降的方向。特别是,PI旨在提供一个具有挑战性的“倾斜角现象”,在某些粘弹性液体中观察到的,其中颗粒定向在一个优选的角度与主流的定量和严格的解释。该角度取决于颗粒的形状、它们的质量和液体的物理性质。液体模型,如Oldrophil-B与剪切相关的粘度将被使用,随着沿着一些合适的分析工具(“分裂法”),PI与他的合作者已经开发了在过去几年的研究适定性的几个粘弹性液体models.The取向均匀的长机构在不同性质的液体是一个基本问题,在许多问题的实际利益。在复合材料中,向聚合物基体中添加短纤维状颗粒将增强材料的机械性能;例如,它可以使材料更软或更硬,并且更耐用。增强的程度强烈地依赖于纤维的取向,而纤维取向又由模具中发生的流动引起。另一个重要的应用是通过电泳分离大分子。现代应用包括蛋白质重量测定、DNA测序和遗传疾病诊断。电泳涉及带电粒子(大分子)在电场影响下在溶液中的运动。分子的取向发挥着重要作用,因为它是导致稳定场凝胶电泳期间分离性丧失的原因。颗粒取向的最后但并非不重要的应用发生在血流中,其中血细胞在某些流动条件下倾向于以某些优选角度(倾斜角)沿着动脉的轴线沿着将其自身链接。

项目成果

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Giovanni Galdi其他文献

Giovanni Galdi的其他文献

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{{ truncateString('Giovanni Galdi', 18)}}的其他基金

Two Problems in Liquid-Solid Interaction
液固相互作用的两个问题
  • 批准号:
    2307811
  • 财政年份:
    2023
  • 资助金额:
    $ 12万
  • 项目类别:
    Standard Grant
On the Occurrence of Resonance in Elastic-Dissipative Coupled Systems
关于弹性耗散耦合系统中共振的发生
  • 批准号:
    1614011
  • 财政年份:
    2016
  • 资助金额:
    $ 12万
  • 项目类别:
    Standard Grant
Analytical and Numerical Study of Two Problems Arising in solid-Liquid Interaction
固液相互作用中两个问题的解析和数值研究
  • 批准号:
    1311983
  • 财政年份:
    2013
  • 资助金额:
    $ 12万
  • 项目类别:
    Standard Grant
Mathematical Analysis of Some Fundamental Problems in Solid-Liquid Interaction
固液相互作用若干基本问题的数学分析
  • 批准号:
    1009456
  • 财政年份:
    2010
  • 资助金额:
    $ 12万
  • 项目类别:
    Continuing Grant
Mathematical Problems in Liquid-Particle Interaction
液体-粒子相互作用的数学问题
  • 批准号:
    0707281
  • 财政年份:
    2007
  • 资助金额:
    $ 12万
  • 项目类别:
    Standard Grant
Mathematical Analysis of Some Problems of Particle-Liquid Motion
质液运动若干问题的数学分析
  • 批准号:
    0404834
  • 财政年份:
    2004
  • 资助金额:
    $ 12万
  • 项目类别:
    Standard Grant

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