The great advantages of micro–reactors are associated with an extremely high surface–to–volume ratio. Hence, micro–reactors permit promising operating conditions, such as almost perfect heat or mass transfer. The hydrodynamics of a liquid/liquid slug flow in a micro–channel is characterized by complex vortex structures in both the disperse and the continuous phase. The disperse phase, in our investigations, is not wetting the walls and, thus, a thin film of the continuous phase persists between the disperse phase and the wall. Due to this phenomenon, a relative movement between disperse and continuous phase is possible and, indeed, observed. Understanding of these complex phenomena allows for a control of the hydrodynamics, and thus, to tailor the heat and mass transport in a desired manner. To study the physics of this complex liquid/liquid system, a modified level–set method in conjunction with an immersed–boundary formulation is engaged. The mesh resolution represents a challenge, as the spatial resolution has to resolve the thin film between the disperse phase and the wall adequately. All simulations are implemented within the software OpenFOAM. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)