Collaborative Research: Diffusion of foreign particles in complex fluids

复杂流体在日常生活中随处可见。它们出现在食品、化妆品和先进材料生产的工业应用中;它们自然地以粘液、血液和生物膜等生物液体的形式存在。复杂流体具有奇异的性质，有时像固体一样，有时像液体一样自由流动。这些都是宏观尺度的观测，但粒子追踪技术的最新进展已经揭示了发生在微观尺度上的迷人动力学。准确表征和理解复杂流体中杂质颗粒的行为对于某些应用至关重要。 例如，了解为什么一些颗粒可以穿透生物液体，而另一些则不能，这对于开发成功的药物输送技术至关重要。此外，它已被证明，浸没粒子路径的统计数据可以携带重要的大尺度材料特性的签名，使其有可能研究昂贵的复杂流体与微升大小的样品。虽然在描述复杂流体中单个粒子的运动方面取得了成功，但为相互作用的粒子群开发模型已经证明令理论家感到沮丧。值得注意的是，例如，没有数学模型来描述粒子的行为，这些粒子单独地根据分数布朗运动，但是当它们靠近在一起时，它们通过流体环境定律所介导的力相互作用。这个合作项目解决了复杂流体中外来颗粒扩散研究中出现的随机，数值和实验问题。具体来说，我们将考虑两个流体模型，放大流体和粒子路径的机械性能之间的基本关系。模型为（1）线性粘弹性流体和（2）粘性流体中的运动悬浮体。除了开发数学工具来有效和准确地模拟这些模型外，我们还将使用这些模拟来解决使用粒子跟踪技术的工程师所面临的基本理论挑战。

Complex fluids are seen everywhere in everyday life. They appear in industrial applications in the production of food products, cosmetics, and advanced materials; and they occur naturally as biological fluids like mucus, blood, and biofilms. Complex fluids are known to exhibit exotic properties, sometimes acting like solids, while at other times flowing freely like liquids. These are macroscale observations, but recent advances in particle tracking techniques have shed light on fascinating dynamics that occur at the microscale as well. Accurately characterizing and understanding the behavior of foreign particles in complex fluids is vital for certain applications. For example, learning why some particles penetrate biological fluids, while others do not, can be critical for the development of successful drug delivery techniques. Furthermore, it has been shown that the statistics of immersed particle paths can carry the signature of important large scale material properties, making it possible to study expensive complex fluids with microliter sized samples. While there has been success in describing the motion of individual particles in complex fluids, developing models for interacting particle populations has proven frustrating for theoreticians. It is remarkable, for example, that there is no mathematical model for particles that individually behave according to fractional Brownian motion, but when close together, interact with each other through forces mediated by the laws of a fluid environment. This collaborative project addresses stochastic, numerical, and experimental issues arising in the study of diffusion of foreign particles in complex fluids. Specifically, we will consider two fluid models that amplify the fundamental relationships between mechanical properties of the fluids and particles paths. The models are (1) a linear viscoelastic fluid and (2) a motile suspension in a viscous fluid. In addition to developing the mathematical tools to efficiently and accurately simulate these models, we will use these simulations to address fundamental theoretical challenges that confront engineers who use particle tracking techniques.