Investigation of apparent correlated motion of Brownian particles

We, as well as other workers, have noticed using light microscopy that particles undergoing Brownian motion can appear to linger around each other for long periods of time, The question arises as to whether this lingering is a product of interparticle interactions, or is an artifact due to random thermal motion and projection onto a two-dimensional image plane. To answer this question, we produced digitized animations of colloidal particles using light microscopy images of a system composed of mii micrometer-sized latex spheres suspended in water. Sis observers, unfamiliar with the experiment. watched these animations for lingering among the particles. Control animations were also generated from these data sets in which correlations due to particle-particle interactions had been destroyed. but the probability of the aforementioned artifactual correlations remained unchanged. We found that the differences in what people observed in the real and control data were not statistically significant. Thus, we conclude that any lingering observed on the time scale or 10 s and the length scale of 5 mu m is the result of the random motion of the particles and projection effects. By way oi explaining this result theoretically, we find that on this length and time scale, hydrodynamic interactions dominate over electrostatic and van dsr Waals forces. Accordingly, we present numerical and analytical calculations of the enhanced lingering associated with the decrease in hydrodynamic mobility of closely separated particles. These calculations give results which are consistent with the conclusion that the enhanced lingering effect is too small to he seen bq an individual observer.