A particle's hydrodynamic coupling to other particles or a plane interface can strongly influence its motion even at relatively large separations. Crocker  extended the methods of the previous section to investigate hydrodynamic coupling between two micron-diameter spheres at micron-scale separations. Diffusion in this case can be separated into collective and relative components both along and transverse to line connecting the spheres' centers. The measured separation dependences of these four diffusion coefficients agree quantitatively with Batchelor's predictions  while revealing subtle effects up to sixth order in the particles' separation.
Hydrodynamic coupling to nearby walls is known to suppress colloidal diffusion both the normal and transverse directions . The effect on transverse diffusion has been examined indirectly in imaging experiments. Blinking optical tweezer measurements would provide useful quantitative tests for the transverse case, but have not been reported yet.