Abstarct: In this study, the lattice Boltzmann method is used to simulate the droplet formationand breakup process from mixing of immiscible fluids. The dimensionless numbers such as Capillary, viscosity ratio and velocity ratio are most important dimensionless numbers in determination of fluid flow characteristics in micro-channel. Two medels is used to simulation: The intermolecular potential model of the lattice Boltzmann method and free-energy model. In this research free-energy model is used to simulate Newtonian phase droplet in Newtonian continuous fluid in a T-junction micro-channel and explaine the dynamics of problem and importan parameters that effect on the droplet formation are investiged. Flow pattern is divided into three different regimes such as sqeezing, dripping and jetting. The influence of capillary number, velocity ratio, viscosity ratio and contact angle on the detachment time and length of droplet are investiged. We found that by increasing the capillary number and velocity ratio, droplet detachment time decreases and detachment length increase, and by increasing the viscosity ratio, droplet detachment time and detachment length increases. also at low capillary number that named squeezing regime, Capillary number doesn’t have significant effect on droplet size and droplet size number is heavily dependent on the ratio of flow rates and increases with increasing flow rate but in dripping regime , capillary number has significant effect on droplet length and droplet size is almost independent of flow rate ratio. at next part, the intermolecular potential model of the lattice Boltzmann method is used to simulate the non-Newtonian droplet formation in Newtonian continuous phase in a co-flowing micro-channel. the influence of capillary number, the non-Newtonian fluid carrio-yasuda exponent and velocity ratio on the droplet formation. The final droplet size, droplet generation frequency, and detachment point of the droplet has been studied.The results reveal that with the increasing carrio-yasuda exponent n, the viscosity of the fluid is increased, the time of starting of detachment point of the droplet is decreased and length of starting of detachment point of the first droplet is decreased. also increasing of the Capillary number leads to a reduction in the detachment point of the drop. The size of drop decreases, due to reducing the velocity ratio and Capillary number and increasing Carrio-yasuda exponent n. The effect of Carrio-yasuda exponent n on the distance of droplets is studied. The droplet generation frequency increases with the decreasing of the droplet length and this leads to reduction in the distance of droplets.