Particles were identified and trajectories were linked from the fluorescence micrographs following the same procedure, as described previously (30). The azimuthal velocity in Fig. 3D was calculated by first dividing the micrograph along the line of symmetry (y = 0) and analyzing only one half (to reduce computation time). Instantaneous particle velocities in the radial and tangential directions were obtained from frame-to-frame displacements, and velocity profiles were calculated by averaging the velocities within angular regions of 5° width with the origin fixed at the center of the source. The velocity profiles were further averaged over an interval of 500 s. The space average velocities in Figs. 4C and 5C were extracted by first cropping the micrograph in the space between the two beacons into rectangular regions with approximate dimensions, 320 by 250 pixels, and then measuring the displacement of the particles in the x direction (and, hence, the x component of the velocity). The velocity profiles were calculated independently over 10-s intervals throughout the experiment, and averaged over all of space. Velocity for single-source systems in these cases refers to the average velocity of particles in the space between source-sink beacon pairs of corresponding solutes. The time average velocities in Fig. 6B were also extracted in the same way as the space average velocities. The velocity profiles in this case were, however, calculated by averaging the velocities within spatial bins of 10-pixel width and further averaged over the given time interval. Splitting the experiment into chunks in this way provides more samples in each bin, improving the statistics of averaging and suppressing noise in the velocity profiles. The particle flux in Fig. 3 (E and F) was calculated by directly counting the number of particles entering and exiting a region of radius r ≈ 300 μm ≈ 1.5*Rbeacon around the sink. This number was then normalized by the total number of particles counted in that region at the beginning of the experiment. The particle flux for a single source (blue points in Fig. 3, E and F) was calculated by counting the number of particles entering an imaginary ring (of r ≈ 300 μm), situated at the same location as the sink in the source-sink experiments.

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