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Numerous models have been proposed to incorporate various equations of state (EOS) into the pseudo potential model. This paper presents an investigation of different EOS types based on the Gong and Cheng model in multiphase-single component flows by the lattice Boltzmann method. Primarily, it is conducted to investigate eight EOS’s classified in four categories; the Shan- Chen EOS, the cubic EOS, the non-cubic EOS, and the cubic and non-cubic combination EOS. The results show that each EOS type results in producing relatively similar spurious currents and has a maximum achievable density ratio. Although by choosing a proper beta parameter for every EOS the simulation errors decrease dramatically, our results show it is impossible to set a constant parameter for the non-cubic EOS. Therefore, a new equation is introduced to predict an efficient beta for the cubic and the Shan- Chen EOS’s. It is also found that the non-cubic, cubic, and non-cubic and cubic combination EOS’s have a wider temperature range and larger density ratios respectively. Hence, we determine a temperature dependent function for the beta parameter prediction instead of using a fixed value for the non-cubic EOS. The results are noticeably in better agreement with those of the Maxwell construction (theoretical results).

Keywords: Lattice Boltzmann method (LBM), Multiphase flows, Pseudo Potential Model, Equation of state

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