Ferrofluids

Abstract

A colloidal suspension is an example of a mixture containing species characterized by different length and time scales. It consists of mesoscopic particles with a diameter σ ranging between 1 nm and 1 μm dispersed in a microscopic molecular liquid solvent (water, organic solvent, etc.). The interaction between two spherical colloidal particles can be derived by summing van der Waals attractions between pairs of atoms distributed uniformly over the spherical volumes. This summation yields the Hamacker potential [128]

$${u_{Ham}}\left( r \right) = - \frac{A}{{12}}\left[ {\frac{{{\sigma ^2}}}{{{r^2} - {\sigma ^2}}} + \frac{{{\sigma ^2}}}{{{r^2}}} + \ln \left( {1 - \frac{{{\sigma ^2}}}{{{r^2}}}} \right)} \right]$$

(14.1)

where A > 0 is the Hamacker constant (of the order of k _B T), and r the distance between centers of the particles. Due to the long-range nature of the Hamacker potential, particles have a tendency to coagulate. In order to prevent irreversible coagulation induced by singularity of u _Ham at r → σ, stabilization is needed. The latter can be achieved by means of two mechanisms.