## 3 Measurement Results
### Further Research
#### 3.2.3 Viscosity Measurement (Pipe Visometer)  
With the measurement facilities it is also possible to carry out traceable inline viscosity measurements of single and multi-component liquids at constant flow rates by means of a pipe visometer. The pipe visometer is based on the measurement of the pressure drop over a certain length of a straight tube, the flow rate and the liquid temperature. The pressure, flow rate and temperature can be selected to meet clinical requirements. For laminar flow, the dynamic viscosity is determined according to the Hagen-Poiseuille law.  
\[Q=\pi\times D^{4}\times\frac{\Delta p}{128\times\eta\times L} \tag{1}\]  
In a first step, the diameter of a capillary tube (glass or stainless steel) is determined by measuring the pressure drop across the capillary tube with water or oils of known temperature-dependent viscosity (Equation (1)).  
Figure 11: Results of the dynamic flow test. The green curve shows the (predefined) flow rate of the Cetoni pump, the blue curve, the measured data from the Sensirion flow meter (DUT) and the red curve, the flow rate of the scale converted from the mass data.  
The viscosity measurements at RISE were mainly carried out using a pre-cut stainless steel capillary tube with a length of 300 mm and a nominal ID of 0.18 mm. To get a deeper understanding of the influence of the connections and tubing, additional measurements were carried out with a pre-cut stainless steel capillary tube of 50 mm length with the same ID (Figure 12). The determination of the ID is important because most manufacturers of stainless steel tubing, as used here as capillary tube, give a tolerance of \(\pm\)0.05 mm OD and \(\pm\)0.025 mm ID for a tubing OD of 1/16\". As soon as the experimentally determined diameter of the capillary tube is known, the (unknown) dynamic viscosity of other liquids can be determined by simply determining the pressure loss \((\Delta p=p_{1}-p_{2})\). It should be noted that, in addition to the viscosity, the capillary properties (length and diameter) are also temperature-dependent and therefore the experiments are carried out under approximately the same conditions as when determining the diameter with the reference liquids. The determined ID with reference liquids at RISE resulted in a value of 0.1904 mm, which is within the manufacturer's tolerance for pre-cut stainless steel capillary tubes. Within the scope of the MeDDII project, eight Newtonian and two non-Newtonian test liquids with a very wide viscosity range were produced and investigated.  
Figure 13 shows a typical dynamic viscosity measurement, i.e., the measurement of the pressure drop at five different flow rates on the example of a solution consisting of 0.45 wt% sodium chloride (NaCl) and 5.54 wt% glucose (C\({}_{6}\)H\({}_{12}\)O\({}_{6}\)) using the 300 mm capillary tube. The measurements resulted in a dynamic viscosity of 1.113 mPa s at a temperature of 22.0 \({}^{\circ}\)C. Compared to reference calibration measurements in viscosity (NQIS/EIM, kinematic viscosity: 1.0952 mm\({}^{2}\) s\({}^{-1}\)) and density laboratories (IPQ, density: 1.0219 g cm\({}^{-3}\)) of project partners at the same temperature, a measurement deviation of \(-\)0.55% results. In summary, a target uncertainty U\((k=2)\) of less than 2.0% was achieved with the pipe viscometer for all test liquids investigated. The uncertainty value was chosen conservatively because it is known that a fluid with normally Newtonian behaviour can show non-Newtonian behaviour in microflow due to high shear rates [29]. With some effort, this value can certainly be halved, especially for Newtonian fluids.  
Figure 12: Capillary tubes of length 300 mm and 50 mm with matching holders used for viscosity measurements at RISE.