This paper is concerned with forced flow through partially open capillary channels under microgravity conditions. The investigated channel consists of two parallel plates and is bounded by free liquid surfaces along the open sides. The curvature of the channel’s gas-liquid interface, which is exposed to the ambient pressure, adjusts to the pressure difference across the interface in accordance with the Young-Laplace equation. Flow within the channel becomes unstable when the free surface collapses and gas ingestion into the flow path occurs—a process that is also referred to as the “choking” phenomenon. During stable flow, the behavior of the free surface is influenced by flow conditions, geometric properties of the channel, and the pre-defined system pressure. In this work, a previously published stability theory is verified for a wide range of model parameters. A detailed study is provided for stable flow in capillary channels, including static and dynamic solutions. The results of the Capillary Channel Flow (CCF) experiment are evaluated and are found to agree well with numerical predictions. A clear limit is determined between stable and unstable flows. It is shown that the model can predict the shape of the free surface under various flow conditions. A numerical tool is employed to exploit the mathematical model, and the general behavior of free surfaces in said capillary channels is studied. Studies are conducted in both viscous and convective flow regimes and in the transition area between the two. The validity of the model is confirmed for a wide range of geometrical configurations and parameters.