Convective dominated flows in open capillary channels

This paper is concerned with convective dominated liquid flows in open capillary channels. 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. The convective dominated flow regime is a special case of open capillary flow, since the viscous forces are negligibly small compared with the convective forces. Flows of this type are of peculiar interest since the free surfaces possess a quasisymmetry in the flow direction. This quasisymmetry enables the application of a new effective method for evaluation of the flow limit. The flow limit is caused by a choking effect. This effect is indicated by the speed index, S, which is defined by the ratio of the flow velocity and the longitudinal capillary wave speed. The speed index is defined analogously to Mach number and tends toward unity in the case of flow limitation, i.e., when the maximum flow rate is reached. Utilizing the quasisymmetry, a new approach for a very precise determination of the speed index is presented. This approach uses a new approximation for the curvature of the surfaces by means of the empirical surface profiles. On the basis of empirical and theoretical data, the paper discusses the typical features of the stable flow. The experiments were performed under microgravity aboard the sounding rockets TEXUS 41 and TEXUS 42. The experiment setup enables the approach to the flow limit through either increase in flow rate or channel length. The theoretical data have been gained from numerical solutions of a one-dimensional flow model. The empirical and theoretical results are in good agreement and both confirm the choking effect as cause of the flow limitation. A general relation for the speed index as function of the flow rate and the channel length has been found which clarifies the fundamental behavior of the choking effect. (C) 2010 American Institute of Physics. [doi:10.1063/1.3379847]