On the Permeability of Colloidal Gels

We reexamine and refine analytical theories for permeability in colloidal networks, with particular focus on constants and identification of approximations. The new theories are compared against numerical simulations of Stokes flow through the networks and reveal nearly quantitative power-law predictions for both pore size and permeability at low volume fractions, with systematic deviations observed only at high volume fractions. Comparison with two previously published experimental data sets yields mixed results: in one case, very good agreement is found, while in the other, only the scaling is correctly predicted. In fractal gel networks, the permeability is commonly modeled as a power-law function of volume fraction, with the fractal dimension of the network determining the power-law exponent. To quantitatively probe the influence of gel structure on permeability, we investigate this relation in structures generated by diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA) and, for contrast, non-overlapping uniform random dispersions of particles. Geometric analyses are used to determine network pore size distributions, fractal dimensions, and percolation characteristics. High-fidelity simulations of the slow viscous flow of Newtonian fluids are used to obtain first-principles-based velocity and fields and hence network permeabilities. Interestingly, the effective pore size that determines permeability is found to be somewhat larger than that measured by a method based on the insertion of spherical probes. Empirical inclusion of a fractal dimension dependence on volume fraction is found to yield quantitative results for permeabilities over the entire volume fraction range studied, in both DLCA and RLCA materials. Published under license by AIP Publishing.