Collaborative Research on Mathematical Constructs for Multiphase Complex Fluids

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。该研究项目将为多相复杂流体的流体动力学开发一套数学结构。 复杂流体与粘性流体（例如，水、油），因为它们需要微观结构的解析来解析即使是最简单的实验中的行为。对于单相复杂流体，粘性流体的Navier-Stokes模型没有捕捉到剪切稀化（粘度随着剪切速率的增加而福尔斯下降）和剪切中的法向应力产生（反向平移的平行板经受沿着其相互法线的力）的特征现象。 然而，这些功能是成功地预测单相聚合物液体的动力学理论。 当组合以形成多相混合物时，无论是在自然界（生物膜或肺气道粘膜层）还是合成（分散在聚合物基质中的纳米棒或纳米片），不同的流体相易于分离。 其他力（化学键和较弱的吸引势）与相分离竞争以维持混合物，这只能合理地理解平衡状态。 突出的挑战出现了，预测工具还不存在，在远离平衡的条件下，典型的生物膜在流或管道，肺气道粘液层推向喉的协调纤毛和潮汐呼吸，和流动加工的聚合物纳米复合材料成膜或模具。 在本研究项目中，将开发一种数学上一致的通用多相复杂流体的动力学理论，该理论结合了各个相、其混合物及其流体力学的物理和化学。 一个动力学理论是唯一有用的，当伴随着明确的协议，适用于基准实验，每个模型减少，数值算法的推导简化模型，并直接模拟测试预测能力的理论与盲实验。 这些结构将被开发，沿着推理方法，使多相复杂流体模型的所有物理参数可以通过实验确定。 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复合材料的流体力学的详细特异性来证明。 聚合物纳米复合材料是一种具有非凡前景的新型合成材料，由传统聚合物与性能增强纳米棒或片晶的混合物组成。 了解为什么纳米复合材料是真正的特殊可以从一个简单的事实欣赏：百分之一的体积分数的纳米片在一个雨滴的聚合物基质介绍了整个足球场的新的表面积！ 颗粒的数量和尺寸的新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。 流动不可能通过实验进行探测（颗粒太小，数量太多，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。 该项目将发展必要的理论和计算能力。 对于自然界中产生的多相复杂流体的混合物存在类似的挑战和限制，例如溪流、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。 该研究项目将为一般多相复杂流体混合物的流体动力学理论和模拟开发数学蓝图。在这种策略中，混合物中每个相的细节以及相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来测试理论。形式主义将产生特定于多相流体的理论，基准实验的模型简化方法，以及数值方法和模拟。 一般的方法将带来承担三个不同的多相材料：生物膜，粘膜层，和聚合物纳米复合材料。 这些数学结构将提供预测工具：用于国防和航空航天工业的新型高性能聚合物纳米复合材料的设计;工业管道中生物膜的修复策略;以及通过模拟药物和物理治疗之前和期间的粘液运输来改善肺部健康。

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.