Nonlinear Dynamics of Polymeric Fluids: From Molecular Models to Turbulence Flow Prediction—A Systems Rheology Approach

Abstract Polymeric fluids exhibit Elastic Turbulence (ET) and Turbulent Drag Reduction (TDR) in strong flow fields far from equilibrium. These two phenomena are extreme manifestations of multiscale coupling mechanisms in rheology and fluid mechanics. They constitute two sides of the same coin for the turbulent dynamics of polymeric fluids. This paper reviews the evolution of dynamic theories from dilute solutions to highly entangled melts, elucidating the theoretical pathway toward constructing universal constitutive equations within the framework of Edwards’ self-consistent field theory, integrating the FENE bead-spring chain model and the Doi-Edwards model. To address the challenges posed by concentration fluctuations, conformational heterogeneity, and flow-induced phase separation in semi-dilute unentangled and entangled systems under strong flow, this review focuses on key advances in developing thermodynamically consistent multiscale coupled models of chain dynamics and macroscopic fluid dynamics based on the two-fluid model. Building upon this foundation, a new paradigm of Theory-Computation-Experiment-AI integrated systems rheology is proposed and elaborated. Centered on overcoming the technical bottlenecks of large-scale parallel direct numerical simulation (DNS) for multiscale coupling, and combined with in-situ multiphysics experimental characterization using rheological chips, this paradigm could construct a dynamic phase diagram of polymeric fluids in the Wi-Re coordinate space from both thermodynamics and fluid dynamics dimensions. By analyzing the influence of key state variables (such as the elasticity number El , concentration, and molecular weight), universal laws of multiscale coupled dynamics could be revealed, and the intrinsic connections and distinctions between the dynamic mechanisms of ET and TDR could be explored in depth. This paper aims to provide theoretical support and technical pathways for revealing the generation and evolution mechanisms of turbulent structures in complex fluids, thereby enabling precise engineering control of turbulence.