## 2 Materials and Methods
### Classical Rheological Measurements
Static pressure values at the beginning and at the end of the measuring section were made using piezoelectric pressure transducers (PBMN, Baumer Germany type). Transducer had analog voltage output (0-10 V). Output values were aquired and converted by a 12-bit analog/digital converter at a rate of 1 Msps (PCI NI-646445 card, National Instruments, England). The sensors were used to measure pressure losses in both chemically inert and aggressive liquids, hence the measuring heads were small and enclosed in an acid-resistant steel housing. All used measuring elements that had been calibrated by the manufacturer before their assembly on the measuring section. All measurements were carried out at 21 \({}^{\circ}\)C.  
The first measurements in the changes of static pressure drop during flow as, a function of flow rate, were made for glycerol (99.5%). It acts like a Newtonian fluid and the viscosity value against temperature is well known (Figure 3). This experiment allowed to validate measurement setup and provided useful information about temperature stabilisation during this type of measurements. A temperature 20 \({}^{\circ}\)C was kept with \(\pm\)0.15 \({}^{\circ}\)C deviation over the time of experiment. The measurement of pressure drop \(\Delta p\) across the measuring section of length \(L\) allows to determine the value of the tangential stress \(\tau_{w}\) on the wall of the pipe:  
\[\tau_{w}=\frac{\Delta p\cdot D}{4L}. \tag{1}\]  
In this equation, \(D\) denotes the diameter of the pipe where flow took place. The above linear dependence of the tangential stress on the distance from the bore axis results from the general balance of forces for the laminar flow through the bore. It is correct for both Newtonian and non-Newtonian fluids. Additionaly the knowledge of the volumetric flow rate is necessary to determine the shear rate \(\dot{\gamma}_{w}\) at the capillary wall:  
\[\dot{\gamma}_{w}=\frac{32\cdot\dot{V}}{\pi\cdot d^{3}}. \tag{2}\]  
Knowledge of these fluid flow parameters in a capillary-pipe viscometer allows the determination of flow curves-the dependence of the tangential stress on the shear rate. It  
Figure 2: Electromagnetic flowmeter and static pressure piezoelectric sensor. is worth noting that both the shear rate and the stress change with the distance from the bore axis. For this reason, it is necessary that both the shear rate and the tangential stresses are determined under the same conditions-in the discussed case, at the bore wall. The knowledge of the shear rate and stress values allows determination of apparent viscosity, according to the equation:  
\[\eta_{app}=\frac{\tau_{w}}{\dot{\gamma}_{w}}. \tag{3}\]  
The accomplishment of a research program allowing the determination of flow curves requires appropriate planning of the experiment. It is necessary to be able to monitor the pressure drop \(\Delta p\) over/across the measuring section \(L\) as a function of the volumetric flow rate \(\dot{V}\). In the described experiment, the flow rates were selected so that the shear rates determined on its basis were in the range from 5 s\({}^{-1}\) to 65 s\({}^{-1}\). The experiment was carried out in analogy to the classical equilibrium experiment described in the work of [PERSON] and [PERSON] [15]. The following scheme of operation was adopted:  
1. Stage I, conditions for increasing volumetric flow rate: * assignment \(\dot{V}\), which corresponds to a shear rate of 5 s\({}^{-1}\), * measurement \(\Delta p\) in a 10-min time range, * Increase the volumetric flow rate to the next \(\dot{V}\) value (corresponds to next selected shear rate value), * measurement \(\Delta p\) in a 10-min time range, *...
2. Measurement \(\Delta p\) in a 10-min time range, for volumetric flow rate corresponding with 65 s\({}^{-1}\) shear rate. 3.