In unstable colloidal gels, the viscous flow through the non-neutrally buoyant colloidal network determines the initial rate of collapse. The resistance to this flow through the network is characterized by the permeability. 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. However, in high-volume-fraction gels the "fractal" nature of the gel structure is questionable, and dependence of the permeability on finer structural details of the gel network is as yet unknown.
We investigate permeability in model gel structures using coarse-grained numerical simulations. Our approach is based on assigning a "local" permeability to each point in the volume based on geometric considerations, in particular a geometrically defined local pore size and the distance to the nearest point on the gel network. The relationship between permeability and local pore size is established with supplementary finite-element simulations of pressure-driven flow past an array of cylinders.
In calculations on model gel structures generated by diffusion-limited cluster aggregation (DLCA), this approach is found to be insensitive to the "coarse" grid size used, and reasonable agreement with available experimental data is obtained over a wide range of gel volume fraction. Subsequent calculations consider the effects of gel connectivity, polydispersity and pore size distribution on permeability, as investigated using model gel networks prepared using several different simulation algorithms.
See more of this Group/Topical: Engineering Sciences and Fundamentals