Fractal aggregation in relation to formation and properties of particle gels

The purpose of this study is to gain insight into the conditions determining whether small particles in a liquid are able to jointly occupy the total volume thus forming a gel network. In order to build a network the colloidal particles have to be 'sticky', unstable. In the unassociated state the particles move at random through the liquid due to collisions with solvent molecules. This movement, called thermal or Brownian motion or diffusion, depends on the temperature and on the size of the particles. By thermal motion particles may meet and subsequently stick, thus forming clusters or floes. This process is called perikinetic aggregation. Other transport mechanisms that lead to aggregation involve velocity gradients in the dispersion (orthokinetic aggregation) or sedimentation of the flocs.A model describing the formation of a gel out of aggregating floes is derived in chapter II. Floes that are formed by aggregation have in general a fractal geometry. This implies that repetitive levels of detail exist on all length scales between the size of the primary particles and the size of the floe. A floe is built up of smaller floes that, on their turn, are built of still smaller floes, etc. Each separate fractal floe has its own geometry, different from that of any other floe. However, all floes share a similar average structure characterized by a stochastic fractal nature, and are in this respect scale invariant. The efficiency with which floes fill the available space is expressed by the fractal dimensionality, D, which is the exponent in the power-law relation between the number of particles in a floe and the size of the floe. A low value of D implies a small number of particles needed to build up a floe of certain size, and thus a high spacefilling efficiency. In a three- dimensional system, D may attain values between 1 and 3. Computer simulations of the aggregation process yield D = 1.8 if all collisions lead to attachment (diffusion - limited cluster aggregation)