Nonlinear Physics Lab


Transport of Finite-sized Particles
in Two-Dimensional Flows


Understanding the dynamics of particulate matter in fluid flows is a longstanding problem with wide applicability in droplet dynamics in clouds, fuel injector sprays, diagnostic techniques (e.g. PIV), etc. By extending traditional particle tracking techniques, we study the dynamics of neutrally buoyant finite-sized particles in a spatiotemporally chaotic flow. We simultaneously measure the flow field and the trajectories of millimeter-scale particles so that the two can be directly compared. While the single-point statistics of the particles are indistinguishable from the flow statistics, the particles often move in directions that are systematically different from the underlying flow. These differences are especially evident when Lagrangian statistics are considered.

Particle Tracking

Particle motion may deviate from the underlying flow due to density differences or finite size effects (or both), where the latter is less well studied. Quasi-2D flows (10<Re<300) are generated by driving a thin layer of an electrolytic fluid electromagnetically. The fluid contains 80 μm tracer particles and two sizes of larger, inertial particles (1 mm and 2 mm); all particles are density matched to float at a single layer (Fig. 1).

Particle tracking techniques allow us to simultaneously measure the flow field from the tracer particle motion along with the the Lagrangian trajectories of the inertial particles (Fig. 2), which are compared statistically.



Fig. 1 Sample image containing tracer particles and two sizes of large, inertial particles.



Fig. 2 Velocity field determined from Eulerian measurements of tracer particle motion.

Inertial Effects

Surprisingly, single point velocity and acceleration statistics for the large particles show no discernable deviation from the underlying flow (tracers). However, the velocity difference magnitude and velocity vector angular difference between the large particles and flow shows clear deviations (Fig. 3) even for small Stokes numbers (St<0.1). (Note: flow statistics are solid lines, 1 mm particles are open symbols, 2 mm particles are closed symbols)

In addition to single-time statistics, the time dependence of inertial effects is quatified by creating virtual trajectories of fluid elements through integrating time-resolved velocity field measurements (Fig. 4).



Fig. 2 Velocity difference magnitude (top) and velocity vector angular difference (bottom) between large particles (symbols) and the flow (lines) for different Reynolds numbers.



Fig. 4 A sample inertial partile trajectory (red line) along with several possible virtual trajectories of corresponding fluid elements (blue lines).

Anisotropic Particles

Unlike spherical particles, which have been studied extensively due to their mathematical simplicity stemming from a high degree of symmetry, the dynamics of anisotropic particles are largely unexplored. We use a similar experimental setup and analysis techniques to those described above to study the dynamics of rods in two-dimensional, spatio-temporally chaotic flows with moderate Reynolds numbers (80-200) where the particle aspect ratios range from 1.5-12. This allows us to study not only the translational deviations from the underlying flow, but also rotational and alignment effects.



Movie 1 Anisotropic particles (plastic rods, 1 cm long) in a two-dimensional chaotic flow (Re~180).


Nicholas T. Ouellette, P. J. J. O’Malley, and J. P. Gollub, Transport of Finite-Sized Particles in Chaotic Flow. Physical Review Letters 101, 174504 (2008)