AbstractA 2D model with focus on field gradient effect is presented and explained. The numerical schemes to solve the time-dependent governing equations in volume-of-fluid (VOF) methodology are described. A model case of flow through a partially full exit-pipe between toroidal field coils, as it applies to the parameters of the APEX CLiFF-Sn concept, is explored using this tool. The results show that the field gradient restrains and destabilizes the flow, but that an applied streamwise current can propel the flow through the gradient region. A small change of the magnetic field variation with the streamwise coordinate may lead to large difference of flow behavior, and an increase in back wall electrical conductance may intensify the instability of the film flow.