Universal Transport Dynamics of Complex Fluids

Thermal motion in complex fluids is a complicated stochastic process but ubiquitously exhibits initial ballistic, intermediate sub-diffusive, and long-time non-Gaussian diffusive motion, unless interrupted. Despite its relevance to numerous dynamical processes of interest in modern science, a unified, quantitative understanding of thermal motion in complex fluids remains a long-standing problem. Here, we present a new transport equation and its solutions, which yield a unified quantitative explanation of the mean square displacement (MSD) and the non-Gaussian parameter (NGP) of various fluid systems. We find the environment-coupled diffusion kernel and its time correlation function are two essential quantities determining transport dynamics of complex fluids. From our analysis, we construct a general, explicit model of the complex fluid transport dynamics. This model quantitatively explains not only the MSD and NGP, but also the time-dependent relaxation of the displacement distribution for various systems. We introduce the concepts of intrinsic disorder and extrinsic disorder that have distinct effects on transport dynamics and different dependencies on temperature and density. This work presents a new paradigm for quantitative understanding of transport and transport-coupled processes in complex disordered media.