Liquid-liquid slug flow capillary millireactor has been suggested to carry out mass transfer limited and strongly exothermic reactions. The benefits include the ability to adjust the individual transport mechanisms i.e. convection inside the slug and diffusion between two slugs. The mass transfer rate is enhanced by internal circulation which arises due to the shear between slug axis and continuous phase or capillary wall. State-of-the-art assumes that there is no significance of the presence of film on the internal circulations within the slugs. During these studies, it had been assumed that there was no distortion in slug geometry at same average flow velocity and no significant shear stress between two fluids. The computational fluid dynamics (CFD) simulations were carried out considering each slug as single phase domain and solved for decoupled individual slugs. These circulation patterns were visualised with the help of virtual particle tracing methods in post processing. More detailed studies on liquid-liquid slug flow revealed that more viscous slug exerts a considerable shear on the film. As a result, it moves with a slightly higher rate than the less viscous fluid and thereby yields an asymmetric geometry of the slug at the same average liquid flow velocity. To examine this phenomenon, we are developing a two-phase CFD methodology. Volume of Fluid (VOF) and levelset are two of the best possible interface reconstruction methods. As a first approach, VOF methodology is considered because it is relatively simple and naturally conservative. The flow of each fluid is governed by the incompressible Navier Stokes equations. It was assumed that there is no interphase mass transfer between the fluids. The equations are discretized with a Finite Element method and realised in the CFD package FEATFLOW. The obtained results give qualitative information about the slug flow behaviour at different operating conditions. Future work will address the mass transfer between the two fluids. The aim is to obtain a fundamental understanding of the hydrodynamics and mass-transfer mechanisms to design an appropriate reactor concept exhibiting best possible conversion and selectivity for a given liquid-liquid reaction.