Capillary driven flow in oval tubes under microgravity

Abstract

The capillary driven flow of a liquid in a tube of elliptical cross section under microgravity is studied in this paper. All the factors including the dynamic contact angle between the liquid and the tube wall, the pressure loss caused by convection, the viscous resistance in the tube and the reservoir, and the curved liquid surface in the reservoir are considered. The equation of capillary driven flow in the tube of elliptical cross section is derived. The flow equation can be transformed into an equation that combines external forces on the control body in the tube. In the case of low Ohnesorge (Oh) numbers, the flow behavior is divided into three time domains by using the capillary force as the driving force that balances with the inertial force in the reservoir, the convective pressure loss in the reservoir, and the viscous resistance in the tube in the three domains, respectively. The liquid climbing height in these three sections is proportional to t2, t, and t, respectively. However, in the case of high Oh numbers, the flow is divided into two regions, something which has not been proposed in previous work about capillary driven flow in cylinder tubes. This study is verified by drop tower experiments and numerical simulation with the volume of fluid method.