  In this thesis, the electrostatic interaction between two chemically
identical colloids, both carrying constant surface potential is studied in the
limit of short inter-particle separation at the interface of two immiscible
fluids. Using an appropriate model system, the problem is solved analytically
within the framework of linearized Poisson-Boltzmann theory and classical
density functional theory. The governing equation of the electrostatic problem
is derived by minimization of the corresponding density functional, which leads
to the Debye-H\"uckel equation. Subsequently, the Debye-H\"uckel equation is
solved by exact calculations as well as by applying the widely used
superposition approximation, each providing expressions for the electrostatic
potential distribution inside the system. Furthermore, the obtained results of
the electrostatic problem are used to calculate surface and line interaction
energy densities between the colloidal particles. In all cases, the
superposition approximation fails to predict the interaction energies correctly
for both small and large separations. Additionally, analytic expressions for
the surface tensions, line tension, and interfacial tension, which are all
independent of the inter-particle separation, are obtained. The results of this
thesis are expected to enrich the description of electrostatic interaction
between colloids at fluid interfaces.
