Evaluation of residence time distribution for bubble train flow in a square mini-channel by direct numerical simulation

This paper presents an original method for evaluating the liquid phase residence time distribution in bubble train flow using data from direct numerical simulations. The method is a particle method and relies on the uniform introduction of virtual particles in the volume occupied by the liquid phase within a single flow unit cell. The residence time distribution for such a volumetric introduction is obtained by statistical evaluation of the time needed by any particle to travel an axial distance equivalent to the length of the flow unit cell. Residence time curves are evaluated from DNS data of bubble train flow in a square mini-channel for different length of the flow unit cell. The curves obtained can well be fitted by a simple exponential relationship. The latter has been developed on the basis of a compartment model which consists of two tanks in series, the first tank being a plug flow reactor and the second being a perfectly stirred vessel. It is argued that the model derived may also be a good representation for the real liquid phase residence time distribution in bubble train flow with flux introduction and measurement.