Flow Rate Limits in Surface Tension Dominated Open Channel Flows: An Efficient Design Tool

In the present study a forced liquid flow through an open capillary channel is investigated. Due to the interplay between inertial and viscous forces the pressure along the flow path decreases causing the free surface to bend inwards the open channel. Because the curvature of the free surface is in turn dependent on the channel pressure a maximum flow rate is achieved beyond which the free surface collapses and gas ingestion occurs. This critical flow rate depends intricately on the channel geometry and liquid properties. A new numerical method has been developed to predict the pressure, free surface curvature, and velocity parameters for such open capillary channel flows with constant flow rates. The solver is able to calculate the critical flow rate for various channel geometries and can be used as an efficient design tool for open channel flows in capillary systems. As a demonstration, the method is validated herein via parabolic flight and drop tower experiments.