Collaborative Research: Diffusion of foreign particles in complex fluids

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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.