Alternately trapping and releasing the spheres allowed us to sample their dynamics efficiently in a range of configurations. Because optical tweezers form in the microscope's focal plane, their height relative to the coverslip's surface can be adjusted from 1 to 30 m with 0.5 m accuracy by adjusting the microscope's focus. For a given height, we continuously varied the spheres' initial separation between 2 m and 10 m at 0.025 Hz for a total of 20 minutes. These trajectories were decomposed into cooperative motions and relative motions either perpendicular or parallel to the initial separation vector, and binned according to the initial separation, . 1 shows typical data for one mode of motion at one height and starting separation.
Diffusion coefficients extracted from least squares fits to Eq.
Dashed curves result from linear superposition of drag coefficients. Solid curves result from the theory described here, with no adjustable parameters. Horizontal dashed lines indicate the asymptotic self-diffusion coefficient from Eq. In the absence of other interactions, the observed trends reflect hydrodynamic coupling between the spheres and the bounding surface. These flows couple distant particles' motions, so that each particle's dynamics depends on the particular configuration of the entire collection.