Inertial particle trapping in viscous streaming

Abstract

The motion of an inertial particle in a viscous streaming flow of Reynolds number order 10 is investigated theoretically and numerically. The streaming flow created by a circular cylinder undergoing rectilinear oscillation with small amplitude is obtained by asymptotic expansion from previous work, and the resulting velocity field is used to integrate the Maxey-Riley equation with the Saffman lift for the motion of an inertial spherical particle immersed in this flow. It is found that inertial particles spiral inward and become trapped inside one of the four streaming cells established by the cylinder oscillation, regardless of the particle size, density and flow Reynolds number. It is shown that the Faxén correction terms divert the particles from the fluid particle trajectories, and once diverted, the Saffman lift force is most responsible for effecting the inward motion and trapping. The speed of this trapping increases with increasing particle size, decreasing particle density, and increasing oscillation Reynolds number. The effects of Reynolds number on the streaming cell topology and the boundaries of particle attraction are also explored. It is found that particles initially outside the streaming cell are repelled by the flow rather than trapped.

Three-dimensional streaming flow in confined geometries

“…It is interesting to note, though, that the xy-projection of a tracer particle on such a trajectory shows a spiralling motion towards the two-dimensional vortex centre, an observation commonly made in cylinder streaming (Lutz, Chen & Schwartz 2005;Lutz et al 2006) and ascribed to inertial forces on the particles (as supported by numerical computations, cf. Chong et al 2013). Finally, figure 8 confirms that the pattern of motion over long time scales τ ∼ 1000T s is also modelled successfully: both the pattern of slow displacement along the z-axis and the pattern of widening and tightening radial extent of trajectories are confirmed in experiments, as is the strong correlation between the two motion patterns.…”

Streaming-enhanced flow-mediated transport

“…In this work we characterize the impact of viscous streaming in the context of passive two-and three-dimensional particle transport by capitalizing on our previous work [26] (fig. 1a), and drawing inspiration from previous studies [48,49]. We thus consider the simple yet representative setting of fig.…”

Steady streaming viscometry of Newtonian liquids in microfluidic devices

“…The steady streaming regime of an oscillating cylinder [29][30][31] is dictated by the magnitude of the Reynolds number, Re = ωa 2 /ν, and the streaming Reynolds number, Re s = ωs 2 /ν. Microscale streaming flows and applications have previously focused on ultrasonic frequencies and above (f ≥ 10 kHz), typically induced by the interaction between a liquid and surface acoustic waves generated by piezoelectric transducers [1,32].…”