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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).

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In this article, an immiscible two-phase flow in two dimensional ordinary and modified T-junction microchannels is numerically studied. To this approach, the Lattice Boltzmann method with Pseudo-Potential model is used. The accuracy of the present model is examined by the Laplace test, drop contact angle, and drop formation in an ordinary T-junction microchannel. The comparison shows that the present results have good agreement with previous numerical and experimental data. The effects of various parameters including Capillary number, flow rate ratio, width ratio, and drop contact angle on the width of the drop and on the distance between drops for ordinary and modified T-junction microchannels are investigated in details. The results reveal that by simple modifications to the ordinary T-junction, smaller drops and lower distances between them are generated in the comparison of ordinary T-junction geometry under the same conditions. On the other hand, this study demonstrates that the multiphase flows in micro-devices are very sensitive to even small changes in the channel geometry. It also indicates that lattice Boltzmann method with Pseudo-Potential model is an effective numerical technique to simulate the generation of drops in microchannels.