  In this dissertation we analyzed the double-layer force interaction between
two dielectric charged colloidal spheres of different radii immersed in a
solution of ions in water and in thermal equilibrium. In the limit of low
electrostatic potential the interaction is governed by the Linearized
Poisson-Boltzmann Equation (LPBE). We obtained an analytical solution from the
LPBE for the electrostatic interaction via multipole expansion, considering a
uniform and fixed surface charge density on the spheres. A code in the
Mathematica platform was developed, allowing us to calculate the force between
the spheres as a function of their separation. In order to validate the code,
we compared our numerical results with the analytical ones in the limits of
Linear Superposition Approximation (LSA) (valid for sphere separations much
greater than the Debye length) and Proximity Force Approximation (PFA) (valid
for sphere separations and Debye length much smaller than the radii of the
spheres).
