Transport and mixing in Stokes flow: the effect of chaotic dynamics on theblinking stokeslet

Mixing and transport processes associated with slow viscous flows are studi ed in the context of a blinking stokeslet above a plane rigid boundary. Whi lst the motivation for this study comes from feeding currents due to cilia or flagella in sessile microorganisms, other applications in physiological fluid mechanics where eddying motions occur include the enhanced mixing whi ch may arise in 'bolus' flow between red blood cells, peristaltic motion an d airflow in alveoli. There will also be further applications to micro-engi neering flows at micron lengthscales. This study is therefore of generic in terest because it analyses the opportunities for enhanced transport and mix ing in a Stokes flow environment in which one or more eddies are a central feature. The central premise in this study is that the flow induced by the beating o f microscopic flagella or cilia can be modelled by point forces. The result ing system is mimicked by using an implicit map, the introduction of which greatly aids the study of the system's dynamics. In an earlier study. Blake & Otto (1996), it was noticed that the blinking stokeslet system can have a chaotic structure. Poincare: sections and local Lyapunov exponents are us ed here to explore the structure of the system and to give quantitative des criptions of mixing; calculations of the barriers to diffusion are also pre sented. Comparisons are made between the results of these approaches. We co nsider the trajectories of tracer particles whose density may differ from t he ambient fluid; this implies that the motion of the particles is influenc ed by inertia. The smoothing effect of molecular diffusion can be incorpora ted via the direct solution of an advection-diffusion equation or equivalen tly the inclusion of white noise in the map. The enhancement to mixing, and the consequent ramifications for filter feeding due to chaotic advection a re demonstrated.