The two-fluid formulation with closure models for interfacial forces and turbulence is applied to the evaluation of a meandering plume in a rectangular bubble column. In literature there is some discussion about how precisely the models should be in order to capture the dynamics as is observed experimentally. Furthermore, this type of flow has shown to be quite sensitive for the degree of diffusion (physical and numerical) introduced in the model equations. The focus is on the necessity and influence of certain interfacial closure models in above type of bubbly flow. The influence of the drag, turbulent diffusive, and added mass force will be highlighted. TVD schemes are used for the computations to obtain accurate results against low costs, that is, coarse grid approximation and to reduce the amount of numerical diffusion as much as possible. Still these schemes have to be "tuned" in their properties in order to obtain the desired accuracy. Nonproper choice of certain parameters, that is, "flux-limiters" introduces errors in the final solution, with the same order of magnitude as physical phenomenon, which are introduced by interfacial forces.