Flow Rate Limitation in Open Capillary Channel Flows

Abstract

This paper reports the experimental and theoretical investigations of forced liquid flows through open capillary channels under reduced gravity conditions. An open capillary channel is a structure that establishes a liquid flow path at low Bond numbers, when the capillary pressure caused by the surface tension force dominates in comparison to the hydrostatic pressure induced by gravitational or residual accelerations. In case of steady flow through the channel, the capillary pressure of the free surface balances the pressure difference between the liquid and the surrounding constant-pressure gas phase. Because of convective and viscous momentum transport, the pressure along the flow path decreases and causes the free surface to bend inward. The maximum flow rate is achieved when the free surface collapses and gas ingestion occurs at the outlet. This critical flow rate depends on the geometry of the channel and the properties of the liquid. In this paper we present a comparison of the theoretical and experimental critical flow rates and surface profiles for convective dominated flows. For the prediction of the critical flow rate a one-dimensional theoretical model taking into account the entrance pressure loss and the frictional pressure loss in the channel is developed.

Laminar bubbly flow in an open capillary channel in microgravity

“…The cross section of the flow also evolves along the flow and can be calculated versus k(x), the distance of the free surface to the mid-plan of the channel (z = 0). Following Haake et al (2006), two situations can be observed. The liquid can be pinned at the edge of the channel when k > (b À a)/ 2, or the liquid separates from the edge of the channel when k < (b À a)/2.…”

“…The hydrodynamics and the stability of forced flows in open capillary channels were investigated by Rosendahl et al (2001Rosendahl et al ( , 2004, Haake et al (2006), Rosendahl and Dreyer (2007), Grah et al (2008). For an internal liquid pressure lower than ambient gas pressure the free liquid surface is bent inwards and concave at any cross section.…”

Experimental Investigation of a Bubbly Two-Phase Flow in an Open Capillary Channel under Microgravity Conditions

“…The forced liquid flow through open capillary channels was investigated experimentally, theoretically and numerically by Rosendahl et al (2004), Haake et al (2006), Rosendahl and Dreyer (2007), Grah et al (2008). It was found that for an internal liquid pressure lower than ambient gas pressure, the free liquid surface is bent inwards and concave at any cross section.…”

Flow Rate Limitation of Steady Convective Dominated Open Capillary Channel Flows Through a Groove

“…Again, if a constant radius at the mean curvature plane for R 1 is assumed, the principal radius of surface curvature R 1 is a function of k only (Haake et al 2006). …”

“…Therefore the cross-section area is a function of the minimal contour value k, one of the main variables of the following differential equation system. The detailed derivation of the governing equation for A(k) can be found in Haake et al (2006). The convective term of the Bernoulli equation (7) can be rewritten as…”