Effect of Hydrodynamic Interactions on the Lifetime of Colloidal Bonds

We use analytical theory and numerical simulation to study the role of short-range hydrodynamics (lubrication forces) in determining the lifetime of colloidal bonds. Such insight is useful in understanding many aspects of colloidal systems, such as gelation, nucleation, yielding, and rejuvenation, and as a paradigm for diffusion-controlled dissociation reactions in liquids. Our model system consists of spherical particles with an attractive square-well potential of variable width δ. We find that the predicted colloidal bond lifetimes can be substantially increased upon the inclusion of lubrication forces, to an extent that depends on the attraction range. An analytical law is derived that predicts this enhancement as a function of the well width, in quantitative agreement with simulation data. For sufficiently short-ranged attraction, lubrication forces dramatically enhance the drag on two bonded particles, leading to reduced effective diffusion coefficients and, hence, longer bond lifetimes. This effect disappears upon an increase in the width of the attractive wells beyond a length scale comparable to the particle diameter. The simulation further suggests that the role of lubrication forces becomes less important as confinement is increased, i.e., upon approaching the supersaturation limit, φ ≈ 0.5, where caging effects become important. Our findings complement recent studies of the role of long-range hydrodynamic interactions, contributing to a comprehensive description of the subtle link between hydrodynamics and bonding in attractive colloids.