Low Bond number open capillary channel flows have been shown to exhibit collapsing free surfaces when a critical flow rate is exceeded, a phenomenon that is referred to as choking. As shown in this work, the critical flow rate can be pre-determined with sufficient accuracy for the presented channel geometry when certain boundary conditions are known a priori. The presented model that describes the flow rate limitation of stable liquid flow through the open channel is examined and compared to numerical simulations and experimental studies. In addition, the characteristics of the supercritical domain, in which bubbles are ingested passively into the flow in the channel, are described and a new model for bubble formation via choking is proposed.