SIMULATION OF BRIDGING FLOCCULATION AND ELASTIC PERCOLATION IN SUSPENSIONS

The suspensions flocculated by bridging show elastic responses at low frequencies when both the particle and polymer concentrations are increased beyond some critical levels. Boundaries for elastic percolation were determined in terms of the site-bond percolation. In bridging flocculation, many bridges are formed by one polymer chain, and a series of bridges cannot be broken down to noninteracting bonds. Therefore, the critical probability for bond percolation, p(c)B, varies with number of bridges formed by one polymer chain, N(b), whereas the critical site probability, p(c)S, is independent. As a result, scaling analysis is not applicable to the bond process. Flocs in which particles are connected by polymer chains were generated on the computer and p(c)B was geometrically determined as a function of N(b) in a two-dimensional square lattice. For random-bond percolation at N(b) = 1, the simulation gives the same value as the theoretical prediction, but p(c)B decreases with increasing N(b). The discrepancy between the experimental results and simulation appears in the N(b) dependence of p(c)B when N(b) is large. In strongly interacted systems, the formation of infinite flocs in the geometrical sense does not necessarily lead to the appearance of susceptible elasticity. The fractal dimension of percolating floc decreases with increasing N(b). The elastic properties above the percolation threshold may be closely connected with the inherent structure of flocs.