Relation of EDL Forces between Clay Particles Calculated by Different Methods

Calculation of the electrostatic double layer force (EDL force) between clay particles is relevant as it is closely related to important macroscopic mechanical behaviors of clays. The popular method to calculate the EDL force is to integrate the electric potential and Maxwell stress along the boundary enclosing a simply connected domain within which a clay particle resides. The EDL force has also been calculated by the integration of the electrostatic force density over the preceding domain. However, the subtle relation of the EDL forces calculated by the different existing methods has not yet been investigated. By means of theoretical analysis and finite element simulation, it was shown that the force calculated by the integration of Maxwell stress along the complete boundary enclosing a multiply connected domain in which the clay particle is excluded, and that along the partial boundary enclosing the preceding simply connected domain represents the electrical attractive force and osmotic repulsive force, respectively, while the integration of the potential along both the same complete and partial boundary denotes the osmotic force. Numerical results showed that the calculated EDL force deviates from its actual value significantly with the decrease in distance between the chosen integral boundary and particle surface, and the deviation varies with surface potential and angle between particles. Moreover, the recommended minimum distance was proposed to be 10 times the thickness of the particle based on the present simulation results.