Correlation length by measuring empty space in simulated aggregates

Department of Physics and Astronomy, University of Edinburgh Edinburgh EH9 3JZ, UK

Received: 17 May 2002
Accepted: 13 August 2002

Abstract

We examine the geometry of the spaces between particles in diffusion-limited cluster aggregation, a numerical model of aggregating suspensions. Computing the distribution of distances from each point to the nearest particle, we show that it has a scaled form independent of the concentration ϕ, for both two- (2D) and three-dimensional (3D) model gels at low ϕ. The mean remoteness is proportional to the density-density correlation length of the gel, ξ, allowing a more precise measurement of ξ than by other methods. A simple analytical form for the scaled remoteness distribution is developed, highlighting the geometrical information content of the data. We show that the second moment of the distribution gives a useful estimate of the permeability of porous media.