Dissipative particle dynamics (DPD) is an emerging method for simulating problems at mesoscopic time and length scales. In this thesis we present a DPD approach that describes the correct hydrodynamic behavior of a two-phase fluids system on a length-scale larger than an atom.To gain this end we mustreproduce the correct liquid viscosity and surface tension between the two phases in DPD system. The formulation is applied to a stationary drop in a multicomponent and free surface system in a wide range of drop radii (Nano and Micro scales). DPD fluids showed the correct hydrodynamic behavior and simulated results were in good agreement with the continuum formulation. We have shown, although DPD is a promising method, it should be used with some considerations. There are some limitations on the maximum and minimum viscosity and surface tension that can be modeled with DPD. However, a DPD simulation is carried out to study dripping flow from a nozzle. The results of this study are used to answer this question that whether DPD is capable of simulating the free surface fluid on all different scales. We also utilize a new method to capture the real-time instantaneous geometry of the drop. The obtained results are in good agreement with the macroscopic experiment except near the breakup time, when the fluid thread that connects the primitive drop to the nozzle, becomes tenuous. At this point, the DPD simulation can be justifiable by thermal length of DPD fluid and the finest accuracy of the simulation that is the radius of a particle. We conclude that in spite of the fact that DPD can be used potentially for simulating flow on different scales, due to the surface thermal fluctuations, it is restricted to the nanoscale problems. Also, in this thesis, we present a new algorithm to describe the hydrodynamics of a perfect conductive fluid in the presence of an electric field. The model is based on solving the electrostatic equations in each DPD time step for determining the charge distribution at the fluid interface and, therefore, corresponding electrical forces exerted by the electric field to the particles near the interface. The method is applied to a perfect conductive stationary drop which is immersed in a perfect dielectric and hydrodynamically inactive ambient. We have shown that when the applied voltage is sufficiently high, the drop shape is changed to a cone with an apex angle which is near to the Taylor analytical estimation of 98.6°. Our results show that the presented algorithm gives new capabilities to the conventional DPD method for simulating nanoscale problems in the presence of an electric field. Keywords : Dissipative Particle Dynamics, Electrospinning, Nano and micro flows, Two-phase flows, Nano-Jet, Nano-Drop and Taylor cone.