Chaotic dynamics of particle dispersion in fluids

Abstract

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.

Settling and asymptotic motion of aerosol particles in a cellular flow field

“…One of the observed features in these primarily computational studies is that for particles with a relatively fast inertial response, the particle trajectories asymptotically merge into a set of preferred paths. This settling and subsequent convergence is in contrast to the observed response for particles without inertia [Stommel (1949)] or the results of Crisanti et al (1990) or Wang et al (1992), who found chaotic motion for spherical and more general particles with large response times.…”

Calculating effective diffusivities in the limit of vanishing molecular diffusion

“…Various extensions of this basic model have been considered in the literature, in particular by Maxey and collaborators [14][15][16][17]29,37]. The equation of motion for a particle subject to the force (1.3) and molecular diffusion is…”

Whole-wavelength description of a wave boundary layer over permeable wall

“…16), the sign of the Stokes drift changes and the particles net displacement is directed toward the wave motion from left to right. At a distance lower than 5 mm from the bottom, the interaction between particle path and vorticity layer becomes intense and the mixing process is largely enhanced because of the chaotic nature of the Lagrangian advection and because of an anomalous dispersion (Wang et al 1992).…”