# Brownian motion of colloids at high density

Colloidal particles in dilute suspensions tend to perform a universal type of Brownian motion at finite temperature, according to the Stokes Einstein relation $D\approx\frac{k_BT}{6\pi \eta r}$ in the case of spherical colloids at low density. When the concentration is high enough and the colloids start to aggregate, however, the diffusion constant of colloids within the aggregate will change. This is true not only because of confinement of colloids by their neighbors, but also because of the fact that proximity of colloids to a stationary aggregate should actually change the diffusion constant from its value when colloids are isolated. This can be seen from the fact that the liquid phase is essentially incompressible, and also that the effects of viscosity would be amplified. My questions are, is this effect well understood, and if so, what would be some illuminating resources to learn about it in more detail? Full answers would also be much appreciated.

• Most of the colloid stuff is old but of interest again because of nano-particles. One place to start might be Collins & Kimball, Journal of Colloid Science, Volume 4, Issue 4, August 1949, Pages 425-437 which gives what is now the standard theory of diffusion controlled reactions so deals with the topics you mention. – porphyrin Apr 26 '17 at 8:27
• Thanks for the reference. I read the paper, but couldn't find where it addresses my specific question. Note that I'm asking how the diffusion constant of colloids changes when they are very close to a large aggregate. There are no reactions involved, just Brownian motion and hydrodynamics. – TotallyRhombus Apr 26 '17 at 14:22
• Have a look at Derjaguin approximation for the forces between two spheres, there is some discussion on this in Israelachvilli 'Intermolecular and Surfaces Forces' – porphyrin Apr 26 '17 at 15:25
• Again, the question isn't about the forces between two spheres (at least, not the standard depletion, electrostatic/ionic, and Van der Waals forces), but rather about how the proximity of two particles influences their individual types of Brownian motion. I assume that when particles are close enough to an aggregate, the approximations made in the derivation of Stokes-Einstein break down. I'm asking about an indirect and somewhat unusual interaction between particles that influences the rate and amplitude of their meandering. – TotallyRhombus Apr 26 '17 at 15:38
• so you are looking at brownian motion with sphere of differing sizes, sounds as if you are getting towards percolation where small particles move along channels formed by larger slow moving or static particles. – porphyrin Apr 26 '17 at 16:55