Electrostatic double layer force between two spherical particles in a straight cylindrical capillary: Finite element analysis

A numerical solution of the nonlinear Poisson-Boltzmann equation based on finite element approximation is developed to assess the interaction force between two identical spherical particles located inside a straight cylindrical capillary. The interaction forces for constant potential and constant charge particle surfaces are calculated for different surface potentials on the cylinder wall, various particle sizes, and different cylinder radii. The interaction force between the spheres was affected significantly by the proximity of the charged cylinder wall, particularly for constant surface potential particles. The influence of the cylinder wall on the particle-particle interaction force was most pronounced when the particle radius was comparable to the cylinder radius. The results suggest that when the cylinder and the particle surfaces are like-charged (bearing the same sign of the charge or surface potential), the electrostatic repulsion between the two spherical colloids is considerably suppressed. Conversely, the interparticle repulsion is more pronounced when the cylinder wall is oppositely charged with respect to the particles. The possibility of inducing a force modulation between two charged particles by altering the surface potential of the confining cylindrical wall appears to be viable on the basis of these simulations.