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，其中单个颗粒具有各向异性（例如，棒状）并具有自己的推进机制。例如，在自然界中，鞭毛推动的杆状细菌悬浮液，在活细胞中，肌动蛋白丝提供结构完整性，分子马达推动细丝实现细胞功能，在高性能材料中，催化纳米棒悬浮在活性溶剂中，由化学反应推动。这些系统在空间和时间尺度上的自组织的显著特征远远大于单个粒子，转化为跨许多尺度的功能。这些不同的活性颗粒-流体系统之前已经建模。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，这提供了多种好处。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性可以最有效地指导和优化系统，实现所需的特性，允许一个共同的计算平台，并允许人们加入额外的自由度或干扰现有的颗粒和流体特性，并预测它们的后果。这些进展可以应用于增强有益菌落和破坏有害菌落，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。研究生也参与了该项目的工作。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、游动细菌悬浮液和马达驱动的肌动蛋白丝凝胶），迄今为止，这些系统的模型、分析、算法和模拟都是独立发展的。该数学平台统一了之前的结果，跨越了动力学到连续空间和时间尺度，并在每个描述尺度上确定了一个共同的先导级数学结构，以及区分不同活性、各向异性流体的低阶结构。这种结构指导分析和算法开发，以理解和预测控制这些流体系统的显著观察行为。该项目旨在区分对颗粒尺寸、纵横比、浓度和活化能的敏感性，并直接应用于受限和自由表面流动中的活性纳米棒分散体、肌动蛋白丝凝胶和细菌悬浮液。

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.