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.