(519b) Numerical Computation of Permeability in Unstable Colloidal Gels

In unstable colloidal gels, the viscous flow through the non-neutrally buoyant colloidal network determines the initial rate of collapse[1]. 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. To test this with direct numerical simulations, randomly generated diffusion-limited-cluster-aggregated networks of spheres are generated periodically. These networks will be characterized using the fractal dimension by measuring the length of the network strands with different sized measurement scales[2]. The permeability is then determined using finite element solutions of Darcy’s Law of pressure-driven flow of Newtonian fluids through the networks. An effective permeability of small sections of the network is calculated with analytic expressions that have been shown to be in good agreement with FEM solutions to Stokes equations. The results are in reasonable agreement with the available experimental data. [1] S. Manley, J. M. Skotheim, L. Mahadevan, and D. A. Weitz, “Gravitational Collapse of Colloidal Gel,” PRL 94, 218302 (2005). [2] B. Mandelbrot (1967). "How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension", Science 156 3775, 636(May 5, 1967).