Thermal Agitation and the Force of Gravity

If the particles are small enough, diffusion due to thermal agitation opposes sedimentation or creaming and an equilibrium state is set up. This is why, in a tube of height H, the concentration profile for a dispersion of identical particles can be described by Boltzmann s law in the form 

The general expression for C h) shows that if the thermal agitation kT is large compared with mgH, the concentrations at the top and bottom of the tube will be more or less the same (C h) = Co). On the other hand, when kT is much smaller than mgH, a phase separation occurs, either through sedimentation or through creaming. 

As an example, consider small spheres of density 2 x 10 kg/m dispersed in water (so that Ap = 10 kg/m ), at room temperature (T = 300 K), in a container of height 10 cm H = 0.1 m). The ratio between the particle concentration near the surface and that near the bottom of the container is of order zero for particles of diameter 100 nm (eventual sedimentation), whereas it is 0.88 for particles of diameter 10 nm (almost no sedimentation occurs). This clearly illustrates the effect of particle size on phase separation, but it gives no idea of the rate at which it happens. The sedimentation speed can easily be estimated by formulating the fact that it is the limiting speed at which the force of gravity is balanced by frictional forces with the suspension fluid (Stokes law)  

---