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Inertial particle trapping in viscous streaming
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10.1063/1.4795857
/content/aip/journal/pof2/25/3/10.1063/1.4795857
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/3/10.1063/1.4795857

Figures

Image of FIG. 1.
FIG. 1.

(a) Lagrangian streamlines (top half) and instantaneous Stokes-layer vorticity (bottom half) of canonical streaming pattern for and (here, ). (b) Streaming regimes (adapted from Wang ).

Image of FIG. 2.
FIG. 2.

Inertial particle trajectory (solid line) and trajectory sampled once per cycle (shown as dots) for = 40, / = 0.175, and ρ = 1.

Image of FIG. 3.
FIG. 3.

Panels (a)–(c) Inertial particles trajectories (in dark gray, or blue), sampled once per cycle, for = 40, / = 0.175. Initial locations depicted with circles. Lagrangian streamlines are depicted in light gray. (a) ρ = 1.05, (b) 1, (c) 0.95. In (b), square symbols denote the instants / = 290 and 350. (d) Inertial (dark gray, or red) and fluid (light gray, or green) particle trajectories over one oscillation cycle, / ∈ [317, 318] for ρ = 1. Arrows depict the total hydrodynamic force vectors in Eq. (14) . Dots denote inertial particle trajectory sampled once per cycle.

Image of FIG. 4.
FIG. 4.

Comparison of trapping position from current results (squares) and experiments (circles) of Lutz, Chen, and Schwartz. Dashed and solid lines depict, respectively, inner streaming cell size δ/ and inner streaming cell center location.

Image of FIG. 5.
FIG. 5.

Illustration of the tendency of a inertial particle to deviate from a Lagrangian streamline. Note that α < 0 in the upper right portion of the streamline, and α > 0 in the lower left portion.

Image of FIG. 6.
FIG. 6.

(a) History of α during the cycle / ∈ [290, 350] for = 40, / = 0.175, ρ = 1. (b) Contributions to dα/d from each term in Eq. (21) : Stokes drag (solid black); convective term (dashed, cyan); Basset history (dashed-dotted, magenta); Saffman lift (dashed-dotted-dotted, blue); Faxén corrections (dotted, green); (solid light gray, or yellow).

Image of FIG. 7.
FIG. 7.

Hydrodynamic force (arrows) at sampled times along the inertial particle trajectory (dark solid line) during the intervals / ∈ [0, 485] and / ∈ [1300, 1370] for = 40, / = 0.175 and ρ = 1. All portions of the inertial particle trajectory not in these intervals are shown as a light gray line.

Image of FIG. 8.
FIG. 8.

Saffman lift force (black arrow), relative particle velocity, (light gray arrow, or green), and local profile of fluid velocity, , perpendicular to (gray arrows, or blue) at / = 317.5 and / = 318. Velocity vectors are plotted with the same scale. Solid line (red) denotes the inertial particle trajectory during the oscillation cycle / ∈ [317, 318]. Local fluid particle trajectory, sampled once per period, shown with dots.

Image of FIG. 9.
FIG. 9.

The final limit cycle for inertial particles of various sizes: / = 0.1 (blue); / = 0.115 (red); / = 0.13 (green); / = 0.145 (cyan); / = 0.16 (black); / = 0.175 (magenta), each plotted over one cycle for , ρ = 1. Mean Lagrangian streamlines shown in light gray for reference.

Image of FIG. 10.
FIG. 10.

(a) The sampled history of the position of an inertial particle (- - -) and an exponential fit to the envelope (—), for , ρ = 1, and / = 0.175. (b) Trapping timescale dependence on /, for , ρ = 1. This figure contains results for (green triangles), 0.2 (blue circles), 0.1 (red squares). (c) Trapping timescale dependence on ρ for , / = 0.175. (d) Trapping timescale dependence on for ρ = 1, with / varied so that Ω /ν is fixed at 1.2.

Image of FIG. 11.
FIG. 11.

Inertial particle trajectories at for particle of density ρ = 1 and radius / = 0.175, initially located at (1.2, 1.2) (circle), (1.8, 1.8) (square), (2, 2) (triangle), (2.2, 2.2) (diamond). Lagrangian streamlines are in light gray.

Image of FIG. 12.
FIG. 12.

(a) Mean Eulerian streamlines, and (b) mean Lagrangian streamlines, for .

Tables

Generic image for table
Table I.

Time averaged forces applied on the inertial particle during the interval / ∈ [4200, 4700] for = 40, / = 0.175, ρ = 1.

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/content/aip/journal/pof2/25/3/10.1063/1.4795857
2013-03-28
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Inertial particle trapping in viscous streaming
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/3/10.1063/1.4795857
10.1063/1.4795857
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