Collaborative Research on Mathematical Constructs for Multiphase Complex Fluids

多相复杂流体数学结构的合作研究

• 批准号: 0908409
• 负责人: Ruhai Zhou
• 金额: $ 17.17万
• 依托单位: Old Dominion University Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-01 至 2013-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0908409&HistoricalAwards=false
• 关键词: Collaborative; Research; Mathematical; Constructs; Multiphase; Collaborative; Research; Mathematical; Constructs; Multiphase

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).This research project will develop a suite of mathematical constructs for the hydrodynamics of multiphase complex fluids. Complex fluids are distinguished from viscous fluids (e.g., water, oil) in that they require resolution of microstructure to resolve behavior in even the simplest of experiments. For single-phase complex fluids, the signature phenomena of shear thinning (viscosity falls with increased shear rate) and normal stress generation in shear (oppositely translating parallel plates experience a force along their mutual normal) are not captured by the Navier-Stokes model for viscous fluids. Yet, these features are successfully predicted by the kinetic theory of single-phase polymeric liquids. When combined to form multiphase mixtures, either in Nature (biofilms or lung airway mucosal layers) or synthetically (nano-rods or nano-platelets dispersed in a polymer matrix), the different fluid phases are prone to separate. Other forces (chemical bonds and weaker attractive potentials) compete with phase separation to sustain the mixture, which are only reasonably understood for equilibrium states. Outstanding challenges arise, and predictive tools do not yet exist, in far-from-equilibrium conditions typical of biofilms in streams or pipes, lung airway mucus layers propelled toward the larynx by coordinated cilia and tidal breathing, and flow processing of polymer nano-composites into films or molds. A mathematically consistent kinetic theory for generic multiphase complex fluids, incorporating the physics and chemistry of individual phases, their mixtures and their hydrodynamics, will be developed in this research project. A kinetic theory is only useful when accompanied by clear protocols for the derivation of reduced models applicable to benchmark experiments, numerical algorithms for each model reduction, and direct simulations to test the predictive capability of the theory with blind experiments. These constructs will be developed, along with inference methods so that all physical parameters of a multiphase complex fluid model can be experimentally determined. The generality and diversity of the theory will be demonstrated by detailed specificity to hydrodynamics of biofilms, mucosal layers, and polymer nano-composites. Polymer nano-composites are new synthetic materials with extraordinary promise, consisting of a cocktail of a traditional polymer with property-boosting nano-rods or platelets. Insight into why nano-composites are truly special can be appreciated from a simple fact: one percent volume fraction of nano-platelets in a single raindrop of polymer matrix introduces an entire football field of new surface area! The novel features of number and size of particles together with new surface contact between the particle phase and the polymer phase overwhelm current experimental and theoretical capabilities. Flow is impossible to probe experimentally (particles are too small and too numerous to track orientation and position) and there is no predictive theory, and therefore no simulation tools, to guide material design. This project will develop the requisite theoretical and computational capabilities. Similar challenges and limitations exist for mixtures of multiphase complex fluids arising in Nature, such as biofilms in streams, ponds, and pipes and mucosal layers between the air and tissue in lung airways. This research project will develop a mathematical blueprint for theory and simulation of the hydrodynamics of generic multiphase complex fluid mixtures. In this strategy, details of each phase in the mixture and the chemical and physical interactions between phases serve as inputs, together with the necessary experimental data to test the theory. The formalism will produce the theory specific to the multiphase fluid, the approach to derive model reductions for benchmark experiments, and numerical methods and simulations. The general methods will be brought to bear on three diverse multiphase materials: biofilms, mucosal layers, and polymer nano-composites. These mathematical constructs will provide predictive tools for: the design of novel high performance polymer nano-composite materials for defense and the aerospace industry; remediation strategies for biofilms in industrial pipelines; and, improved pulmonary health through simulations of mucus transport prior to and during drug and physical therapies.

该奖项是根据2009年的《美国回收与再投资法》（公法111-5）资助的。本研究项目将开发一套数学构造，以用于多相复杂液体的水动力学。 复杂的流体与粘性流体（例如水，油）区分开，因为它们需要分辨出微观结构以解决最简单的实验中的行为。对于单相复杂的流体，剪切变薄的特征现象（粘度降低，剪切速率提高）和剪切中的正常应力产生（相对翻译平行的平板经历了沿其相互正常的力），并未被粘性流体的Navier-Stokes模型捕获。 然而，这些特征通过单相聚合物液体的动力学理论成功预测。 当组合形成多相混合物时，在自然界（生物膜或肺气道粘膜层）或合成（分散在聚合物基质中的纳米棒或纳米层状）时，不同的流体相容易分离。 其他力（化学键和较弱的吸引力）与相位分离竞争以维持混合物，仅在平衡状态下才合理地理解了混合物。 出现了杰出的挑战，并且尚不存在，在溪流或管道中典型的生物膜的典型平衡条件下，肺气道粘液层通过协调的纤毛和潮汐呼吸向喉向喉向，以及聚合物纳米 - 复合物的流动处理中的膜或模具。 该研究项目将开发出一种数学上一致的动力学理论，该学理论融合了单个阶段的物理和化学，它们的混合物和流体动力学。 动力学理论只有在伴随清晰方案的范围来推导适用于基准实验的模型，每种模型降低的数值算法以及直接模拟以通过盲目实验测试理论的预测能力的清晰方案。 这些结构将被开发，以及推理方法，以便可以通过实验确定多相复杂流体模型的所有物理参数。 该理论的一般性和多样性将通过对生物膜，粘膜层和聚合物纳米含量的水动力学的详细特异性来证明。 聚合物纳米复合材料是具有非凡诺言的新合成材料，由传统聚合物的鸡尾酒组成，并具有增强特性的纳米棒或血小板。 从一个简单的事实中可以欣赏到纳米复合材料为何真正特殊的信息：在单个聚合物基质中，纳米平台的一百分点纳米平台的一百分点会引入新的表面积的整个足球场！ 粒子数和大小的新颖特征以及颗粒相和聚合物相之间的新表面接触压倒了当前的实验和理论能力。 流量是不可能通过实验探测的（颗粒太小，太多而无法跟踪方向和位置），并且没有预测理论，因此没有模拟工具来指导材料设计。 该项目将开发必要的理论和计算能力。 对于自然界中产生的多相复合液的混合物，例如河流，池塘和管道中的生物膜以及肺气道中的空气和组织之间的粘膜层，也存在类似的挑战和局限性。 该研究项目将开发出一种数学蓝图，用于理论和模拟通用多相复杂流体混合物的流体动力学。在这种策略中，混合物中每个阶段的细节以及阶段之间的化学和物理相互作用作为输入，以及必要的实验数据以测试理论。形式主义将产生特定于多相流体的理论，即基准实验的模型减少的方法以及数值方法和仿真。 一般方法将在三种不同的多相材料上携带：生物膜，粘膜层和聚合物纳米 - 复合材料。 这些数学结构将为：防御和航空航天行业的新型高性能聚合物复合材料的设计提供预测工具；工业管道中生物膜的修复策略；并且，通过在药物和物理疗法之前和期间对粘液转运的模拟改善了肺部健康。