Micro-fabrication techniques are developed rapidly because they offer numerous benefits for chemical and biological industries. Numerical simulations (based on incompressible Navier–Stokes equations) are presented of the two-phase flow in a cross-flowing T-junction micro-channel using the phase field method and the results are in agreement with experimental measurements. The leakage rate in the gap between the droplet and lower wall decreases during the droplet formation, the relationship between the leakage rate and the derivative of the up-stream droplet size is obtained, which is applicable when the droplet contacts with the lower wall on the wetted conditions or expands to the up-stream in the main channel. The droplet formation is related to several factors, including the capillary number, the contact angle, the flow rate ratio, and the micro-channel shape. The critical capillary number could distinguish between the squeezing and dripping regimes for the generation of different kinds of droplets. The simulations show that the critical capillary number is 0.012. Influence of those factors on the droplet length is related to the leakage rate. The leakage rate of the continuous phase decreases slowly as the flow rate ratio decreases or contact angle increases. In the squeezing regime, the leakage rate is weakly influenced by the contact angle at the small flow rate ratio and is different in three type micro-channels, the droplet length increases with the increase in contact angle which intensifies growth at the big flow rate ratio, and the longest droplet is obtained in the Y-junction micro-channel. In the dripping regime, at the big flow rate ratio the leakage rate is almost independent to the contact angle and micro-channel shape, and the droplet length also is same.