Mixing dynamics and transport mechanisms during laminar stirring flows

Abstract

We investigate laminar mixing of a passive dye in an infinite, two-dimensional domain filled with a Newtonian fluid by simulating a cylindrical stirrer that rotates at constant speed along a circular path, stirring an initially quiescent fluid. The fluid is marked by a passive dye in the lower half of the domain, enabling a systematic analysis of dye-interface evolution and mixing dynamics. By varying the stirring Reynolds number within the laminar regime, we identify how transitions in flow topology govern mixing and distinguish three mixing regimes spanning diffusion-dominated and advective mixing. In the diffusion-dominated regime, mixing is characterized by the formation of a well-mixed central region and the development of a spiral dye pattern that evolves in an approximately self-similar manner. Advective mixing is marked by substantial deformation of the dye interface beyond the central region. We provide a mechanistic interpretation of advective mixing by relating mixing events to specific flow features: (i) direct interaction between the stirrer and the dye interface, and (ii) vortex shedding near the stirrer and away from the central region. Enhanced mixing occurs when vortical structures are able to escape the central region and transport scalar gradients nonlocally. When vortical activity remains confined near the stirrer's path, mixing per stirrer period exhibits only weak dependence on stirring speed despite increasing stirring intensity. Significant enhancement of mixing per period occurs only when escaping vortices introduce a new transport mechanism that carries scalar gradients far beyond the stirrer's path. Overall, we present a mechanistic link between flow topology and mixing by identifying the transport mechanisms through which flow features govern scalar evolution, providing a bridge between the kinematics of mixing and the underlying fluid dynamics.