Traceability of the primary Nano-flow measurement System: Measuring the local inner diameter of a glass capillary

•A new method for measuring the local inner diameter of glass capillaries has been developed.•The method ensure metrological traceability and high accuracy.•The method has been validated by comparison to another method.•A full uncertainty budget is provided. As part of the Metrology for Drug Delivery (“MeDD II”) European joint research project, a primary method for the measurement of liquid flow rates at the nanolitre per minute scale has been developed. This primary standard allows the calibration of flow meters and flow generators such as infusion pumps, pressure controllers and syringe pumps, for flow rates ranging from 10 nl/min to 1500 nl/min with relative expanded uncertainties (k=2) of 12 % and 0.15 %, respectively. The system is based on the measurement of the displacements over time of a liquid/air interface moving inside a cylindrical glass capillary tube. The flow rate is obtained by multiplying the resulting flow velocity by the cross-sectional area of the tube which depends on the square of the capillary’s inner radius. In order to ensure the traceability of flow rate measurements to International System of Units, camera and frame rate calibration procedures have been established. However, the measured flow rates depend on the local value of the inner diameter which must also be traceable. In this paper, we present a method to measure the inner diameter of cylindrical thin-walled capillaries by confocal microscopy. The method allows visualizing the inside of a tube by filling it with a fluorescent solution and acquiring z-stacked images along its full height. The mean inner diameter is deduced from the widths of the fluorescent signal in the obtained images which are measured by image processing. The method was applied on capillaries with different inner diameters and the results were compared with the values given by manufacturers. The relative expanded uncertainties (k=2) were estimated to a maximum of 4 %, which is two times lower than the one provided by manufacturers.