Is the water flow more or less than that predicted by the Navier-Stokes equation in micro-orifices?
Authors: Hasegawa Tomiichi , Ushida Akiomi , Narumi Takatsune , Goda Masaki 
Published: September 2016

Micro-fluid mechanics is an important field in modern fluid mechanics. However, flows through microscale short tubes (micro-orifices) are not yet fully understood. Thus far, experiments on the flow through micro-orifices have been conducted by two methods: the pressure-given method (PGM), in which the pressure is given and the rate of flow is measured, and the flow-given method (FGM), in which the flow rate is given and the pressure is measured. According to conventional fluid mechanics, these two methods should give the same result; however, studies have found lower fluidity (lower flow rate) in PGM and higher fluidity (lower pressure drop) in FGM than that predicted by the Navier-Stokes equation, suggesting that the difference is caused by the method used. To clarify the cause of this difference, we examined the flow of ultra-pure water (UPW) with elapsed time by PGM. UPW was passed through Ni or Ti micro-orifices with 20-μm diameter at applied pressures of 50-1000 Pa. The difference in the shape and material of the orifices did not have a great effect on the flow property. The flow rate was frequently higher than that predicted at the start of the flow experiment; however, it subsequently fell and finally reached zero as time elapsed. This fact suggests that UPW inherently flows at velocities higher than those predicted by the Navier-Stokes equation; however, the flow is then resisted by something that develops over time. We removed an orifice in which flow had stopped from the experimental apparatus, observed it by phase contrast microscope and electron probe micro analyzer, and revealed that a visible membrane, a transparent lattice-like structure, or nothing existed in the orifice. Dissolved air was reduced by deaerating the air from UPW (deaeration), bubbling UPW with Ar (Ar-bubbling), or preventing UPW from contact with air after UPW production (air-prevention). Deaeration, Ar-bubbling, and air-prevention reduced the probability of formation of the visible membrane. UPW treated by a combination of air-prevention and Ar-bubbling showed no visible membrane. Furthermore, we passed UPW through an electrically grounded orifice (grounding) and found that grounding also reduces the probability of formation of the visible membrane. These findings suggest that the membrane formation was related to the presence of air dissolved in UPW and the action of charges generated in the flow. The reduction of the dissolved air by Ar-bubbling and air-prevention provided a higher flow rate, although deaeration provided a slightly lower flow rate than seen in the case without deaeration. Grounding yielded a higher average flow rate. A combination of Ar-bubbling and grounding provided flow rates considerably larger than the predicted ones. We found a correlation between the probability of the membrane formation and the magnitude of the fall in flow rates. We concluded that the membranes, whether visible or invisible, came from the dissolved air by the action of charges generated at the orifice by the flow. Furthermore, the membrane developed naturally in PGM; in contrast, the membrane, even if it developed, was flushed away from the orifice in FGM because of the constant flow supplied. Therefore, the UPW flows in PGM with fluidity lower than the predicted value owing to the resistance of the membrane, whereas the UPW flows in FGM with fluidity higher than the predicted value owing to the inherent characteristics of UPW.