Enhancement of mixing by chaotic advection with diffusion

Abstract

The role of diffusion in the mixing of particles by chaotic advection produced in a Stokes flow in an eccentric annulus is studied numerically and experimentally. It is observed that the mean square separation of diffusing particles initialized in a chaotic region after flow reversal is a few times greater than that in a regular region, and that the separation increases exponentially with the duration of stirring. The main causes of enhancement of separation are identified to be stretching and folding of material lines. We find that the greater the degree of stretching in a region, the greater is the separation of particles in that region. Experimental observations are made by taking photographs of blobs before and after stirring and analyzing the images. There is good qualitative agreement between the numerical results and the experimental observations for a few cycles of stirring, but for longer stirring, if the blob undergoes multiple folds, the final distribution of particles after flow reversal predicted numerically using the Stokes flow assumption deviates from the experimental results. The main cause of this deviation is believed to be the irreversibilities other than diffusion such as inertial effects and vibration.