Collaborative Research: Diffusion of foreign particles in complex fluids

复杂的液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；它们以粘液、血液和生物膜等生物液体的形式自然存在。复杂的流体表现出奇异的特性，有时表现得像固体，而在其他时候像液体一样自由流动。这些都是宏观尺度的观察结果，但最近粒子跟踪技术的进步也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外来颗粒的行为对某些应用至关重要。例如，了解为什么有些粒子能穿透生物流体，而另一些却不能，对于开发成功的药物输送技术至关重要。此外，研究表明，浸没颗粒路径的统计数据可以携带重要的大尺度材料特性的特征，从而可以用微升尺寸的样品研究昂贵的复杂流体。虽然在描述复杂流体中单个粒子的运动方面已经取得了成功，但为相互作用的粒子群开发模型却让理论家们感到沮丧。值得注意的是，例如，对于那些按照分数布朗运动单独运动的粒子，没有数学模型，但当它们靠近时，它们通过流体环境定律所调节的力相互作用。这个合作项目解决了在复杂流体中外来粒子扩散研究中出现的随机、数值和实验问题。具体来说，我们将考虑两种流体模型，它们放大了流体力学特性和颗粒路径之间的基本关系。模型是(1)线性粘弹性流体和(2)粘性流体中的运动悬架。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.