Choked flows in open capillary channels: theory, experiment and computations

Abstract

This paper is concerned with flow-rate limitations in open capillary channels under low-gravity conditions. The channels consist of two parallel plates bounded by free liquid surfaces along the open sides. In the case of steady flow the capillary pressure of the free surface balances the differential pressure between the liquid and the surrounding constant-pressure gas phase. A maximum flow rate is achieved when the adjusted volumetric flow rate exceeds a certain limit leading to a collapse of the free surfaces.

In this study the steady one-dimensional momentum equation is solved numerically for perfectly wetting incompressible liquids to determine important characteristics of the flow, such as the free-surface shape and limiting volumetric flow rate. Using the ratio of the mean liquid velocity and the longitudinal small-amplitude wave speed a local capillary speed index $S_{ca}$ is introduced. A reformulation of the momentum equation in terms of this speed index illustrates that the volumetric flow rate is limited. The maximum flow rate is reached if $S_{ca}\,{=}\,1$ locally, a phenomenon called choking in compressible flows. Experiments with perfectly wetting liquids in the low-gravity environment of a drop tower and aboard a sounding rocket are presented where the flow rate is increased in a quasi-steady manner up to the maximum value. The experimental results are in very good agreement with the numerical predictions. Furthermore, the influence of the $S_{ca}$ on the flow-rate limit is confirmed.