About the Effects of Flow Rate Limitation in Open Capillary Channels

Abstract

We consider a forced liquid flow in an open capillary channel with free liquid surfaces under low gravity. The channel consists of two parallel plates and is shown in Figure 1. The liquid flows along the x-axis from the inlet to the outlet and forms free surface at the sides between the plates. The flow is maintained by external pumps and the free surface deforms according to the pressure along the flow path. Since the free surface can only withstand a certain difference between the liquid pressure and the ambient pressure the flow rate in the channel is limited. The maximum flow rate is achieved when the surface collapse and gas ingestion occurs at the outlet. The aim of the consideration is also to determine the shape of the free surface, to find the maximum or critical flow rate without a collapse of the free surface and to understand the mechanism of the flow rate limitation. The critical flow rate depends on the geometry of the channel and the properties of the liquid, specified by the three dimensionless parameters, the Ohnesorge number Oh = √ ρν2/(2σa), the aspect ratio Λ = b/a and the dimensionless length l = Oh l/(4a) (ρ is the density, ν the kinematic viscosity and σ the surface tension of the fluid). The right picture in Fig. 1 shows the cross section area A perpendicular to the flow direction.