  In this thesis we study the lateral electrostatic interaction between a pair
of non-identical, moderately charged colloidal particles trapped at an
electrolyte interface in the limit of short inter-particle separations. Using a
simplified model system we solve the problem analytically within the framework
of linearised Poisson-Boltzmann theory and classical density functional theory.
In the first step, we calculate the electrostatic potential inside the system
exactly as well as within the widely used superposition approximation. Then
these results are used to calculate the surface and line interaction energy
densities between the particles. Contrary to the case of identical particles,
depending upon the parameters of the system, we obtain that both the surface
and the line interaction can vary non-monotonically with varying separation
between the particles and the superposition approximation fails to predict the
correct qualitative behaviours in most cases. Additionally, the superposition
approximation is unable to predict the energy contributions quantitatively even
at large distances. We also provide expression for the constant (independent of
the inter-particle separation) interaction parameters, i.e., the surface
tension, the line tension and the interfacial tension. Our results are expected
to be of use for modelling particle-interaction at fluid interfaces and, in
particular, for emulsion stabilization using oppositely charged particles.
