Utilizing a recently developed numerical technique, known as the lattice-Boltzmann method, we study 2D immiscible three-phase Bow at the microscopic scale. In this paper, the spreading of a droplet on a fluid-fluid interface has been investigated. Different spreading regimes, depending on the governing forces, are identified. It has been found that the spreading rates derived from simulations agree with analytically obtained spreading rates for both capillary- and gravity-driven flow. In the gravity driven case, a formula can be derived for the drop shape. The numerical results regarding the drop shape turn out to resemble the predicted shape.