Planar Brownian motion in the presence of an attractive force

The two-dimensional Brownian motion of circular disks is considered where these join to form groups whenever they touch. The total number of groups Nt is considered as a function of time. An upper bound for Nt-1 is derived and compared to the experimental movement of erythrocytes. Cells at pH = 7.4 and pH = 6.3 are shown to have a group count that respectively exceeds and falls below the plotted bound. This provides evidence that live cells have a tendency to coalesce that is not explained by Brownian motion only.