Chaotic dynamics of particle dispersion in fluids

An analysis of the Lagrangian motion for small particles denser than surrounding fluid in a two-dimensional steady cellular flow is presented. The Stokes drag, fluid acceleration, and added mass effect are included in the particle equation of motion. Although the fluid motion is regular, the particle motion can be either chaotic or regular depending on the Stokes number and density ratio. The implications of chaotic motion to particle mixing and dispersion are discussed. Chaotic orbits lead to the dispersion of particle clouds which has many of the features of turbulent dispersion. The mixing process of particles is greatly enhanced since the chaotic advection has the property of ergodicity. However, a high dispersion rate was found to be correlated with low fractal dimension and low mixing efficiency. A similar correlation between dispersion and mixing was found for particles convected by a plane shear mixing layer.