Direct measurements of colloidal friction coefficients

The time-independent hydrodynamic forces operating between two hard spheres were studied as a function of the interparticle separation $r.\mathrm{}$ Two colloids were positioned a distance $r$ apart using a dual-beam optical tweezer similar to that described by Meiners and Quake [Phys. Rev. Lett. 82, 2211 (1999)]. Brownian fluctuations in the positions of the two spheres were followed by recording the intensity of forward scattered laser light. The two particles move cooperatively as a result of hydrodynamic forces. The strength of the correlation increased strongly with decreasing separation $r.\mathrm{}$ We show that the temporal and spatial correlations in the particle displacements are determined by the distance dependence of the pair friction tensor ξ. The distance and geometry dependence of the measured friction tensor is found to be in excellent agreement with the predictions of low-Reynolds number calculations.