Double Layer Interaction Between Two Aggregates

This section addresses the calculation of the double layer interaction energy between aggregates. A numeric calculation scheme is described in detail and further employed for a qualitative analysis on the factors that determine the strength of the double layer interaction. Finally, the benefit of rigorous numerical methods and the application of approximate solutions are discussed. 

1 Modelling the Electric Double Layer for Particle Aggregates 

but of less mathematical rigour, is the singularity method (SM), which reconstructs the potential field by a superposition of singularity fields from point charges (Phillips 1995). Additionally, it is possible to approximate compact, isometric aggregates as porous spheres (PS), for which analytical expressions of the double layer structure are available (Ohshima 2008). Some of the mentioned methods assume a certain shape of the aggregates or primary particles, some of them are based on the Unearised PBE (BEM, ME, PS). Only a few have already been employed for particle clusters (CoeUio et al. 1996 Kwon et al. 1998 Schiefil et al. 2012). 

2 Calculation of Double Layer Interaction with the Singularity Method 

The singularity method is based on the linearised PBE (Eq. (3.17)) and on the simple analytical expression of the radially-symmetric potential field y/ r) around a point charge  

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