Abstarct: The lattice Boltzmann method (LBM) has gained increasing popularity among the most favorable numerical methods for simulating fluid flow in complex geometries. This method is used not only for single-phase simulations but also for multi-phase / multi-component simulations with a high-density ratio. However, it also has some limitations, so we must recognize and evaluate these limitations to have the highest efficiency. This study aimed to investigate droplet behavior and assess and identify instabilities of the pseudo-potential LBM model that can be used as a benchmark for future studies. Accordingly, spurious currents, thermodynamic inconsistency, parameters dependency, surface tension, two-phase diagram, and wettability were evaluated and examined. In this way, for the first time, four new equations were obtained to determine the contact angle with a maximum determination coefficient of 0.99. In addition, droplet behaviors analysis at different contact angles and interfacial tensions showed splitting of the droplet to lower volume in high interfacial tension and high adhesive force, which to the best of our knowledge was not reported yet and the theory needs more investigations and recommended for future studies. Moreover, we evaluated two kinds of equations of state and their properties. Besides, we investigated the instabilities, advantages, and disadvantages of the Van der Waals and Carnahan-Starling method. Then the fluid-solid interactions are presented and schemes to obtain different contact angles are discussed. Consequently, the contact angles and surface tension have been evaluated by these equations of state.