Relationships Between Structure and Permeability in Colloidal Networks

The resistance to flow through colloidal networks is characterized by the permeability. The permeability influences many practical applications of colloidal gels, and in particular controls the rate of (gravitational) collapse of non-neutrally buoyant networks. The permeability is generally accepted to be a power-law function of volume fraction, where the power is dependent on the fractal dimension of the network. To probe microscopically the influence of gel structure on permeability, we investigate permeability in structures generated by diffusion-limited cluster aggregation (DLCA) and related simulation techniques. We apply a geometric analysis to determine the local pore size associated with every point in the pore network, from which we then extract the pore size distribution. The overall network permeability is then computed by assigning permeabilities based on the local pore size field and applying Darcy's Law. Remarkably, predictions based on the full-field calculations and just based on the mean pore size agree extremely well for volume fractions from 0.2% up to 20%, indicating that there is no effect of void-space connectivity on flow. This modeling approach is shown to agree well with available experimental data at low volume fraction [1]. We then consider the effects of modifying the gel structure on pore size distribution and permeability. Reaction-limited cluster aggregation (RLCA) generates networks with a different power-law dependence of pore size on volume fraction and larger pores at any volume fraction. Incorporating some relaxation into the network-formation simulations likewise leads to larger pores and higher permeabilities. These findings have significant consequences for network stability: networks which can relax through Brownian motion will collapse faster than networks which cannot, both because they have lower moduli and because buoyancy forces have a greater effect due to their higher permeability. Finally, we discuss the relationship of permeability to volume fraction in networks composed of non-spherical particles, and consider the application of our numerical tools to determining a priori the permeability of network structures measured by 3D microscopy.

[1] S. Manley, J. M. Skotheim, L. Mahadevan, and D. A. Weitz, Gravitational Collapse of Colloidal Gels, PRL 94, 218302 (2005).