Influence of capillarity on nano-liter flowrate measuremet with displacemet method*

Nano-liter flowrate measurements in micro-tubes with displacement method were performed and the effect of capillarity force on the accuracy was investigated through lab experiments and theoretical analysis in this article. The experiments were conducted under the pressure drops ranging from 1 kPa to 10 kPa in a circular pipe with a diameter of 50 μm, to give the pressure-flowrate (P-Q) relation and verify the applicability of the classical Hagen-Poiseuille (HP) formula. The experimental results showed that there existed a discrepancy between the experimental data and the theoretical values predicted by the HP formula if the capillary effect was not considered, which exceeded obviously the limit of the system error. And hence a modified formula for the relation, taking the capillary effect into account, was presented through theoretical deduction, and after the HP formula had been modified the error was proved to be less than 3%, which was permitted in comparison with the system error. It was also concluded that only by eliminating the effect of the capillary force in experiments could the original HP formula be employed to predict the pressure-flowrate relation in the Hagen-Poiseuille flow in the micro-tube.