Water collection techniques at very low flow rates including strong capillary effects
Introduction
Milli-, micro- and nano-flow calibrations are important in several areas of pharmaceutical, flow chemistry and health care applications where volumetric dosage, delivery of constant volumes at given time intervals or continuous delivery at given flow rates are crucial for the process. Calibration is required to achieve high flow rate accuracy or to verify the repeatability and the reproducibility. Although most of the flow devices are measuring flow rates of process oriented liquids, their calibrations are often performed with water as calibration liquid. It is recommended to perform the calibrations of the flow devices with process-oriented liquids as the liquid itself might influence the performance of the flow devices.
METAS has upgraded the Microflow facility and developed the Milliflow facility with METAS flow generators to address the issue of measuring with process-oriented liquids and to extend its international traceability for flow rates from 50 nL/min up to 400 mL/min with uncertainties from 0.9% to 0.07% (k = 2) [1,2]. The METAS flow generators are homemade piston provers, which allow measurements with liquids other than water in this range. Traceability is guaranteed through the calibration of the generated flow rates of the METAS piston provers by means of the dynamic gravimetric method where a liquid of well-known density and a well-controlled evaporation rate is used. As the METAS piston provers are volumetric flow generators, they can be operated with any liquid acting as a transfer standard to perform calibrations of flow devices. The advantage of traceable calibrations of a flow device with the process-oriented liquid is to enhance the quality of the measurements results of the flow device during the production process.
In this paper, we describe the newly developed METAS piston provers and focus on the water collection techniques used for the flow rate determination of very low flow rates going as low as 50 nL/min by means of the dynamic gravimetric method.
One water collection technique that is widely applied is the immersed outlet needle into the water collected in the beaker on the balance [3,4]. To prevent evaporation, the beaker is either in a humidity-controlled environment or the water layer is protected by a layer of oil on top of the water. Force interactions between the outlet needle and the collected liquid (or the covering layer of oil) in the beaker such as capillary and buoyancy effects create instabilities in the weighing data.
Another approach is using a constant level of the liquid at the outlet needle [5]. The outlet needle is immersed in an inner overflow vessel, which is fixed in the main vessel. The liquid in the inner vessel flows over a notch along the wall into the main vessel. The constant level of liquid at the outlet needle is minimizing instabilities to the weighing data.
A similar method is used to minimize instabilities in weighing data collection, where the outlet needle is placed inside a capillary, which is fixed to the cover of the beaker [6]. A water meniscus is formed around the outlet needle at the top of the capillary, where the capillary force remains constant as the water level in the capillary remains constant. The water flows through the capillary to fill the beaker from the bottom.
The METAS facilities apply the water collection technique, where the outlet needle is positioned just over glass filters on top of the beaker [1,2]. The flowing water is building a water bridge, which leads to a constant capillary force for steady flow rates. The building of the water bridge occurs at each flow rate and the formation of droplets is disabled. The magnitude of the capillary force might depend on the flow rate due to the shape of the water bridge, but the capillary force remains constant once the steady state of the flow rate is reached. Thus, during the collection of water, the increase in weight is only due to the increase of water in the beaker as the capillary forces contribute with a constant force.
The immersed outlet needle technique and the water bridge technique are investigated at the Microflow facility for comparison of the stability of the flow rate determination and the influence of the capillary forces acting due to the water or water-oil surface on the outlet needle and on the water bridge between the outlet needle and glass filters. The effects of buoyancy forces and capillary forces are reported in this paper highlighting the different effects that can occur during the water collection.
Section snippets
METAS facilities
METAS has updated the Microflow facility and developed the Milliflow facility for flow rates applied in microfluidics covering flow rates from 50 nL/min up to 400 mL/min [[1], [2], [3]]. The scheme of the facilities is shown in Fig. 1. The METAS piston prover presses the water through the device under test (DUT) in the beaker on the balance, where it is continuously collected. The two main components being the piston prover and the beaker for continuous water collection are emphasized in this
Different water collection techniques
Four methods of water collection at the Microflow facility are characterized with the focus on stability of flow rate determination, uncertainty and deviation with respect to the METAS piston prover.
The main water collection technique (a) was specially developed for the Microflow facility being a special measurement beaker shown in Fig. 6a [1]. The cover of the beaker has a hole to place the outlet needle for the water close to the glass filter in the beaker. The glass filter has a flat top
Third water collection technique (c)
For the third water collection technique (c), the buoyancy correction factor was determined with the simple experiment of moving the immersed needle several steps up and then several steps down by steps of 5 μm and collecting the weighing data. The needle was moved step by step downwards and after each step, the needle is kept in position again to collect the weighing data in stable conditions. The result is shown in the blue data curve in Fig. 7. The same procedure was done with the motion of
Stick-slip effect on outlet needle
As mentioned earlier, another important contribution to the stability of the flow determination of the third and fourth water collection technique is the stick-slip effect of the water or water-oil on the outlet needle. This effect leads to strong variations of the capillary force in time. To illustrate this stick-slip effect at 40 μL/min, we show two series of pictures taken of the outlet needle immersed in water-milk mixture (one drop of milk in a glass of water) to increase the contrast
Stability in flow rate determination
After discussing the buoyancy and the stick-slip effect on the outlet needle, we can compare the stability in the flow rate determination for the four water collection techniques (a – d) in this paragraph. The first (a) and the second water collection techniques (b) reveals to be very reproducible as can be seen in Fig. 16, Fig. 17. To illustrate the randomness of the stick-slip effect two representative data sets of the third (c) resp. the fourth (d) water collection technique are shown in
Misleading flow rate determination
These strong fluctuations in the flow rate data due to the stick-slip effect of the third (c) and fourth (d) water collection technique could lead to a misleading flow rate determination. In Fig. 15, the flow rate data at 200 μL/min for the third (c) water collection technique are shown. The data of the piston prover are shown in red illustrating the stable data in this case. We determine the deviations of the piston prover with respect of the gravimetric method with averages over a time window
Instabilities of the water-oil interfaces in the collection beaker
When the outlet needle is immersed into water with an oil layer on top to minimize the evaporation rate, it can happen that the water-oil layer is not stable and the oil is filling up the center of the beaker made of aluminium and pushing the water to the border. For this case, water droplets are formed in an oil layer while water is flowing out of the outlet needle immersed in the water-oil layer (see Fig. 18 on the right). This behavior adds other uncertainty contributions to the method and
Conclusions
The Microflow and Milliflow facilities consisting of METAS piston provers and dynamic gravimetric methods for the determination of volume flow rates have been described in this paper. The advantages of the piston provers are the ability to measure with any process-oriented liquids and the shorter calibration time compared to the dynamic gravimetric method.
The main issue for the dynamic gravimetric method is the continuous collection of the flowing water in a beaker on the balance. Four
CRediT authorship contribution statement
Hugo Bissig: Writing - original draft, Conceptualization, Investigation, Methodology. Martin Tschannen: Methodology, Writing - review & editing. Marc de Huu: Supervision, Writing - review & editing.
Declaration of competing interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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