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出现。众所周知，复杂的流体表现出奇异的性质，有时表现为固体，而另一些时候则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也揭示了微观尺度上发生的迷人的动力学。准确地表征和了解外来颗粒在复杂流体中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体液，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，研究还表明，浸没粒子路径的统计数据可以携带重要的大尺度材料性质的特征，这使得用微升大小的样品来研究昂贵的复杂流体成为可能。虽然已经成功地描述了单个颗粒在复杂流体中的运动，但开发相互作用的颗粒群体的模型对理论家来说是令人沮丧的。例如，值得注意的是，对于单独按照分数布朗运动行为的粒子，没有数学模型，但当它们靠近时，通过流体环境定律中介的力相互作用。这一合作项目解决了在研究外来颗粒在复杂流体中的扩散时出现的随机、数值和实验问题。具体地说，我们将考虑两种流体模型，它们放大了流体的力学性质和颗粒路径之间的基本关系。这些模型是(1)线性粘弹性流体和(2)粘性流体中的运动悬浮液。除了开发数学工具来高效、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.