In the last years, the lattice Boltzmann method (LBM) have been widely used as a solver for simulating hydrodynamicsproblems. Thus ,this method is used to simulate two-phase flows in a 2D computational domain by using the pseudo-potential model proposed by Shan-Chen in (1993) which iscalled Shan-Chen LBM model. In the present study, wepresent a comparative study to Huang et al. carried out in (2009) for simulating the wettability phenomenon of a liquiddrop by adjusting the density of the wetting surface. On the other hand a simulation of the natural thermal convection in a square cavity will be presented by giving the densities of coexisting fluids the same value. The present results agreewell with those obtained by Mezrhab et al. in (2010) and givea good precision of this method. in the last study a coupledsystem is used to study the effect of natural thermal convection on a liquid drop by adjusting the density of the wetting surface.

In this study, We have considered a 2D square cavity placed in a gravity field and filled with gas. The horizontal walls are perfectly insulated while the vertical wallsare maintained at different temperatures Th = 0.5 and Tc =-0.5 respectively, midway between them a liquid drop is placed. For the fluid flows the solid wall is considered for the upperand lower boundaries, the bounce-back condition is selectedfor side walls.The laminar gas flow can be described by assuming that the fluid is Newtonian, incompressible and satisfies the Boussinesq approximation. Based on the abovestudy, it was concluded that For all Rayleigh numbers, the heated gas rises along the left wall, encounters the top adiabatic wall, travels towards the cold wall, comes down and recirculates inducing a steady clockwise rotational flow. This recirculation pushes the liquid drop towards the left wall. As Rayleigh number becomes higher, the flow moves faster as natural convection is intensified. The liquid drop moves to take place on the hot wall and it deforms under the effect of gas pressure. It is also noted that for low values of Rayleigh number, the gas's motion is slow and the drop keeps the sameshape while moving. However its radius decreases owing to the heat exchange between the gas trapped in the cavity and the liquid droplet, Indeed, the drop is evaporated and itbecomes smaller than its initial shape.