In this paper, the free energy based Lattice Boltzmann Method (LBM) which has been recently extended by the authors for modeling and simulation of Electrowetting (EW) phenomenon is applied to another application of EW, i.e., droplets merging. The results were compared with experimental data and the results show good accuracy of the numerical simulation. Also, the stability of a droplet in a finite system was studied analytically and numerically (by LBM) and it was shown that the droplet stability is a function of system size and droplet contact angle. The simulation results were in good agreement with analytical solution and it has been concluded that in the finite systems an unstable droplet can be stabilized by applying a voltage (i.e., using EW). Based on this observation, a new method for droplets merging in finite systems has been proposed. (C) Koninklijke Brill NV, Leiden, 2011