Force- and torque-free hard spheres, with radius a and positions , are confined between two parallel planar plates with distance 2W. A Poiseuille flow is applied.
Two identical spherical colloids with an initial axial distance y 21 = y 2 − y 1 and initial lateral positions z 1 and z 2.
Trajectories for different initial conditions plotted in the center-of-mass frame. In the unbound state the spheres move on either (a) swapping trajectories (ST) or (b) cross-swapping trajectories (CS). In the bound state they move on trajectories (c) forming the pattern of an eight (8P) or (d) with an oval shape (OT).
State diagram for the different types of trajectories of a two-particle system. It is plotted when the initial lateral positions z 1 and z 2 are varied, while the initial axial distance y 21 is fixed. The particle radius is a/W = 0.6. (a) y 21/W = 1.3, (b) y 21/W = 2.0, (c) y 21/W = 3.0, and (d) y 21/W = 4.0. The frequencies ω of the oscillatory states [oval trajectory (OT) and pattern of eight (8P)] are color-coded. Outside the colored region, unbound states with swapping- (ST) or cross-swapping (CS) trajectories occur. The trajectories in the gray shaded areas show binary encounters of either ST or CS type when they are traced back into the past.
State diagrams in z 1, z 2 for an initial axial distance y 21/W = 2.0 and different particle sizes: (a) a/W = 0.4, (b) a/W = 0.6, and (c) a/W = 0.8.
Passing trajectories of two identical spheres with radius a/W = 0.4 turn into cross-swapping trajectories (plotted in the center-of-mass frame): sphere 1 starts at a lateral position of z 1/W = 0.005 while the lateral coordinate z 2 of sphere 2 is gradually decreased. The transition to cross-swapping occurs when v 0y (z 1) < v 0y (z 2).
Oscillation frequency ω in the bound states plotted versus particle radius a for different initial axial distances y 21. The lateral coordinates are set to (a) z 1/W = 0, z 2/W = 0.1 and (b) z 1/W = 0.3, z 2/W = −0.3.
Snapshots of a linear array of particles with radius a/W = 0.6 at different times t. In addition, the lateral coordinate z and the relative axial displacement y − y C in the center-of-mass frame is plotted versus time for the blue colored particle. (a) Initially, the spheres are placed close to the centerline with a small random offset Δz i relative to z = 0. (b) Initially, the spheres are arranged in a zig-zag pattern, where the particles have a small random offset Δz i relative to z j + 1 = −z j = ±0.25W.
Same setting as in Fig. 8 . Now the offset of the blue colored particle is larger so that neighboring particles belong to the unbound state.
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