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，棒状)，并且具有自己的推进机制。例如，在自然界中，由鞭毛推动的杆状细菌悬浮；在活细胞中，肌动蛋白细丝提供结构完整性，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并由化学反应推动。这些系统共享一个显著的特征，即在空间和时间尺度上的自组织远远大于单个粒子的自组织，从而转化为跨越许多尺度的功能。这些不同的活跃粒子-流体系统之前已经被建模。在这里，研究人员为这类问题提供了一个统一的理论和计算平台，提供了多种好处。一个通用的数学结构揭示了这些系统如何实现它们的功能特性，告知哪些物理和化学特性允许系统朝着所需的特性进行最有效的操纵和优化，允许一个通用的计算平台，并允许一个人加入额外的自由度或扰动现有的颗粒和流体特性并预测其后果。这些进展在增强有益细菌菌落和破坏有害细菌菌落，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方面具有应用。研究生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，统一了三个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细丝凝胶)，到目前为止，模型、分析、算法和模拟都是独立发展的。该数学平台统一了以前的结果，跨越了动力学到连续的空间和时间尺度，并在每个描述尺度上确定了共同的前序数学结构，以及区分不同活动、各向异性流体的低阶结构。这种结构指导分析和算法开发，以了解这些流体系统的显著观测行为，并对其进行预测控制。该项目旨在区分颗粒尺寸、纵横比、浓度和激活能的敏感性，将其直接应用于受限和自由表面流动中的活性纳米棒分散体、肌动蛋白细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.