ON THE DYNAMICS OF BUOYANT AND HEAVY-PARTICLES IN A PERIODIC STUART VORTEX FLOW

In this paper, we study the dynamics of small, spherical, rigid partic les in a spatially periodic array of Stuart vortices given by a steady -state solution to the two-dimensional incompressible Euler equation. In the limiting case of dominant viscous drag forces, the motion of th e particles is studied analytically by using a perturbation scheme. Th is approach consists of the analysis of the leading-order term in the expansion of the 'particle path function' PHI, which is equal to the s tream function evaluated at the instantaneous particle position. It is shown that heavy particles which remain suspended against gravity all move in a periodic asymptotic trajectory located above the vortices, while buoyant particles may be trapped by the stable equilibrium point s located within the vortices. In addition, a linear map for PHI is de rived to describe the short-term evolution of particles moving near th e boundary of a vortex. Next, the assumption of dominant viscous drag forces is relaxed, and linear stability analyses are carried out to in vestigate the equilibrium points of the five-parameter dynamical syste m governing the motion of the particles. The five parameters are the f ree-stream Reynolds number, the Stokes number, the fluid-to-particle m ass density ratio, the distribution of vorticity in the flow, and a gr avitational parameter. For heavy particles, the equilibrium points, wh en they exist, are found to be unstable. In the case of buoyant partic les, a pair of stable and unstable equilibrium points exist simultaneo usly, and undergo a saddle-node bifurcation when a certain parameter o f the dynamical system is varied. Finally, a computational study is al so carried out by integrating the dynamical system numerically. It is found that the analytical and computational results are in agreement, provided the viscous drag forces are large. The computational study co vers a more general regime in which the viscous drag forces are not ne cessarily dominant, and the effects of the various parametric inputs o n the dynamics of buoyant particles are investigated.