<span id="lblAbstract">This paper deals with the simulation of single-component two-phase fluid flows in two dimensions using the lattice Boltzmann method. We start by describing the theory of the free energy multiphase lattice Boltzmann model. After showing how the formulation of the particles interaction fits into the framework of the lattice Boltzmann simulation, numerical results of a droplet falling and spreading are presented to highlight the capability of this approach to simulate the dynamics of a droplet.</span>