## 3 Results and Discussion
### Effect of Volume Flow Rate on Pressure Drop  
Pressure drop is a physical process in which flow energy dissipates due to frictional shear forces within the channel. A higher pressure drop in a reactor system requires higher pump power, tougher materials and as a result, increased financial operational and production costs [PERSON] _et al._ (2016). Therefore, pressure drop is an important parameter which should be considered in microfluidic systems [PERSON] _et al._ (2016). The mechanical energy in laminar flow in a reactor system dissipates mainly via two processes: the laminar flow wall friction \(\Delta\text{P}_{\text{wall friction}}\) and the chaotic secondary flow vortex structures \(\Delta\text{P}_{\text{chaotic advection}}\)[PERSON] _et al._ (2016):  
\[\Delta\text{P}_{\text{total}}=\Delta\text{P}_{\text{wall friction}}+\Delta \text{P}_{\text{chaotic advection}} \tag{11}\]  
The first term is proportional to the volume flow rate, while the second term shows a quadratic dependency of the volume flow rate. The simplified model, which is based on the model seem in the article by [PERSON] et al. [PERSON] _et al._ (2016), can be formulated as follows:  
\[\Delta\text{p}=\text{a}\text{Q}+\text{b}\text{Q}^{2} \tag{12}\]  
where a denotes the term which relates to the wall friction, and b characterizes the secondary vortices intensity. The experimental and calculated pressure drop values over the volume flow rate in different reactor systems are shown in Figure 12. The flow which consumes the least energy in the reactor system is based on the T-shaped reactor because it has the simplest structure and the largest characteristic lengths of 2.8 mm, compared to other microreactors. In this reactor type, pressure drop is less than 0.1 bar at flow rates of up to 10 mL/min. At higher volume flow rates, the formation of hydrodynamic vortices dramatically increases the pressure drop within this type of reactor. Therefore pressure drop dependency of the volume flow rate becomes quadratic. In the microreactor system with an interdigital microreactor, the pressure drop is much higher since the characteristic length of the microchannels is several times smaller. The extremely small dimensions of microchannels cause higher wall friction due to their larger wall area. This leads to a higher flow of mechanical energy consumption, which is shown by the pressure drop. The highest-pressure drop is observed in the microreactor system with a chicane microreactor. The reason for this is found in the structure of the chicane mixing channel, which is specially designed for building vortices. Increasing the volume flow rate causes a significant growth in the vortices' intensity in flow, resulting in higher energy dissipation due to larger frictional losses via chaotic advection. The wall friction and secondary chaotic friction factors of the model used are listed in Table 6. The reactor system with a T-shaped reactor provides the lowest values of both factors. The relatively small wall area of this reactor causes low wall friction. Due to the structure of the reaction system, an intense vortex pattern only appears in the T-shaped reactor. A slight growth in pressure drop in the system with a T-shaped reactor is observed at flow rates higher than 15 mL/min. This is because the intensity of chaotic advection greatly depends on the volume flow rate. In the interdigital microreactor, a high number of parallelly combined microchannels inside the microreactor provides a large area-to-volume ratio. Therefore it is possible to achieve a much higher value for the wall friction factor in this microreactor compared to other reactor systems. At the same time, the small channel dimensions provide a more intensive formation of vortex structures within an interdigital microreactor than seen in the setup with a T-shaped reactor. Consequently, both wall friction and chaotic advection play a similar role with regard to pressure drop in the interdigital microreactor.