Chaotic advection using passive and externally actuated particles in a serpentine channel flow

Chaotic advection due to the presence and external actuation of rigid particles in a two-dimensional serpentine channel flow has been numerically investigated. The motion of a freely suspended particle in this flow is time periodic and the streamlines from the perturbed velocity are hyperbolic in nature. From Poincaré sections we observe two chaotic zones separated by Kolmogorov–Arnold–Moser (KAM) boundaries along the path of the particle. In the case of a time-periodic flow of two particles, two interacting hyperbolic perturbations are present, which give rise to three chaotic zones. The efficiency of the mixing process can be greatly enhanced by adding a periodic external force working on a single rigid particle, which changes the trajectory of the particle. The larger the force, the larger the strength of the perturbation of the flow strongly influencing the existence of chaotic mixing zones. As demonstrated by the Poincaré sections, a proper external actuation indeed makes the separating KAM boundaries disappear leading to almost global chaotic advection in a two-dimensional continuous flow with just a single particle moving in a periodic manner. The enhanced rate of mixing is computed via the deformation of a material strip undergoing stretching and folding around the particle. A measure of mixing, based on the information entropy, has been used to quantify the progress of mixing with time. It is shown that within a reasonable number of periodic units we can achieve mixing in the channel flow with an externally actuated particle.