Collaborative Research: Kinetic to Continuum Modeling of Active Anisotropic Fluids

主要研究人员使用数学和计算来模拟流体颗粒混合物，其中单个颗粒是各向异性的（例如，杆状）并具有它们自己的推进机构。 实例出现在自然界中，具有杆状鞭毛推进细菌的悬浮液，在活细胞中，其中肌动蛋白丝提供结构完整性并且分子马达推进丝以实现细胞功能，以及在高性能材料中，其中催化纳米棒悬浮在反应性溶剂中并通过化学反应推进。 这些系统都具有显著的自组织特征，其空间和时间尺度远远大于单个粒子的尺度，并在许多尺度上转化为功能。 这些不同的活性粒子-流体系统先前已被建模。 在这里，研究人员为这些问题提供了一个统一的理论和计算平台，它提供了多种好处。 一个共同的数学结构揭示了这些系统如何实现其功能特性，告知哪些物理和化学特征允许系统最有效地转向和优化所需的属性，允许一个共同的计算平台，并允许一个纳入额外的自由度或扰动现有的粒子和流体属性，并预测其后果。 这些进展可用于增强有益的细菌菌落并破坏有害的菌落，修复受损的细胞功能，以及设计具有最佳性能的纳米复合材料。 主要研究人员为活性各向异性流体开发了一个建模和计算平台，统一了三种明显不同的流体系统（催化纳米棒分散体，游动细菌悬浮液和电机驱动的肌动蛋白丝凝胶），迄今为止，模型，分析，算法和模拟都是独立发展的。 数学平台统一了以前的结果，跨越动力学连续空间和时间尺度，并确定了一个共同的领导阶数学结构在每个尺度的描述，以及低阶结构，区分不同的活性，各向异性流体。 这种结构引导分析和算法开发，以理解和预测控制这些流体系统的显著观察行为。 该项目旨在区分颗粒尺寸，纵横比，浓度和活化能的敏感性，直接应用于活性纳米棒分散体，肌动蛋白丝凝胶和细菌悬浮液在受限和自由表面流动。

The principal investigators use mathematics and computation to model fluid-particle mixtures in which the individual particles are anisotropic (e.g., rod-like) and have their own propulsion mechanism. Examples arise in nature with suspensions of rod-like, flagella-propelled bacteria, in living cells where actin filaments provide structural integrity and molecular motors propel the filaments to achieve cellular function, and in high performance materials where catalytic nano-rods are suspended in a reactive solvent and propelled by chemical reactions. These systems share the remarkable feature of self-organization on scales in space and time far greater than those of the individual particles, translating to functionality across many scales. These diverse active particle-fluid systems have been previously modeled. Here the investigators undertake a unified theoretical and computational platform for such problems, which offers multiple benefits. A common mathematical structure reveals how these systems achieve their functional properties, informs which physical and chemical features allow the most efficient steering and optimization of the system toward desired properties, allows for a common computational platform, and allows one to incorporate additional degrees of freedom or perturb existing particle and fluid properties and predict their consequences. These advances have applications to enhance beneficial bacterial colonies and to disrupt harmful ones, to repair damaged cellular functions, and to design nano-composite materials with optimal properties. Graduate students are involved in the work of the project.The principal investigators develop a modeling and computational platform for active, anisotropic fluids, unifying three apparently diverse fluid systems (catalytic nano-rod dispersions, swimming bacterial suspensions, and motor-driven actin filament gels) for which models, analysis, algorithms, and simulations have so far evolved independently. The mathematical platform unifies previous results, spans kinetic to continuum spatial and temporal scales, and identifies a common leading-order mathematical structure at each scale of description as well as the lower-order structure that distinguishes among different active, anisotropic fluids. This structure guides analysis and algorithm development toward an understanding of, and predictive control over, the remarkable observed behavior of these fluid systems. The project aims to distinguish sensitivity to particle dimensions, aspect ratio, concentration, and activation energy, with direct application to active nano-rod dispersions, actin filament gels, and bacterial suspensions in confined and free surface flows.