In this thesis, the problem of droplet breakup at low Reynolds number flow regime and the other one with a high Reynolds number of the numerical simulation methods, have been investigated. In the first group of cases, the slippage of droplet on the slope, drop in tension between flat and groove and affects between two flat plates were considered. The second group of cases studied include: drop deformation in uniform flow field with assuming laminar flow and study of the effect of the dimensionless Weber number, Reynolds number, viscosity ratio and density ratio on the rate of strain, displacement, acceleration and change of drag and second drop deformation in uniform flow field with assuming turbulent flow and compared with laminar flow in the values of the break time, elongation at break time and the critical Weber number. in the study of the slippage of the droplet, the effect of slope angle, contact angle, surface roughness and surface tension coefficient on the surface wetted area, droplet elongation and slip velocity has been studied. The results were compared with experimental results and good agreement between experimental and numerical results of the study in this thesis there. The study of droplet confined between flat surface and groove under tension and the droplet confined between two flat surfaces, the same model of offset the impact of mobile phones with touch screen and touch shear are the two-dimensional simulations and VOF method of detection methods have been performed. Geometric parameters, surface conditions and functional parameters were examined and in each case the transfer rate drop, drop shape and decay time is calculated and presented. Then drop in a uniform flow is studied. This study investigated parameters retraction of the droplet, the droplet velocity, droplet drag coefficient is the change in position of the center of gravity. Weber of dimensionless numbers, Reynolds number, viscosity ratio and density ratio is. Laminar and turbulent flow regimes, are considered separately. A new model for the surface tension term in the Reynolds averaged equations was presented and the applied in numerical code OpenFOAM as a new and separate solver for simulation of turbulent flows. results show that modeling of surface tension term in RANS equations is in accurate orientation and compared with experimental results in three stages. Key Words: Breakup, VOF, Drag Coefficient, Droplet deformation