We discuss the theory of ligand receptor reactions between two freely rotating colloids in close proximity to oneother. Such reactions, limited by rotational diffusion, arise in magnetic bead suspensions where the beads are driveninto close contact by an applied magnetic field as they align in chainlike structures. By a combination of reaction-diffusion theory, numerical simulations, and heuristic arguments, we compute the time required for a reaction to occurin a number of experimentally relevant situations. We find in all cases that the time required for a reaction to occuris larger than the characteristic rotation time of the diffusion motion
rot. When the colloids carry one ligand only anda number
n of receptors, we find that the reaction time is, in units of
rot, a function simply of
n and of the relativesurface
![](/images/gifchars/alpha.gif)
occupied by one reaction patch
![](/images/gifchars/alpha.gif)
=
rC2/(4
r2), where
rC is the ligand receptor capture radius and
r is theradius of the colloid.