The hydrodynamics of a liquid-liquid slug flow in a capillary microreactor is characterized by a complex vortex structure in both the disperse and the continuous phase. In order to study the complex flow physics of this two-phase liquid-liquid system, a finite-volume method is engaged, in combination with a modified level set method for the representation of the interface. The movement of small catalytic converter particles is additionally captured by means of an Euler-Lagrange method. The catalytic converter particles appear to perfectly follow the streamlines as long as gravitational forces are neglected. In presence of gravity, though, a relative movement of fluid and particles is observed.