Effect of Hydrodynamic Interactions on the Lifetime of Colloidal Bonds

Abstract

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 inclusion of lubrication forces, to an extent which depends on the attraction range. An analytical law is derived which 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 increasing 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.

Radial distribution function of Lennard-Jones fluids in shear flows from intermediate asymptotics

“…We model the hydrodynamic disturbance of the flow field around the reference particle due to the presence of the target one through the adoption of two functions A(r) and B(r) derived by Batchelor [18] which influence v(r) (see Appendix A for more details). Instead, to describe the effect of lubrication forces we use the widely used parameterized function [4,20]: where h = (r − 2a)/a represents the surface-to-surface distance between the particles. Next we pack the two effects of interparticle potential and shear flow into an external force term K(r) acting on the target particle:…”

Probing the protein corona around charged macromolecules: interpretation of isothermal titration calorimetry by binding models and computer simulations

“…The two top ones still exhibit a global binding minimum but also a significant barrier for crossing at r 6 nm, kinetically hindering the binding of the corresponding proteins. (Note that for radial crossing of barriers in 3D space, the effective free energy landscape has to be corrected by a distance-dependent entropic factor [56,57].) We see also from Fig.…”

Pair correlation function of charge-stabilized colloidal systems under sheared conditions

“…If the particles are getting closer to each other as in the compression sectors, then the squeezing of the liquid between them creates a force which opposes the mutual approach [25]. In this case we model G(r) through a polynomial [18,26] which is a polynomial fit to the rigorous solution to the Stokes equation for the specific case of two particles approaching each other [17]:…”