# Numerical and Experimental Investigations of a Micromixer with Chicane Mixing Geometry
## 3 Results and Discussion
### Pressure Drop  
The pressure drop \(\Delta\)p is the loss of energy of the flow that occurs due to viscous forces. In general, in the field of laminar flow the dependency between the pressure drop and the Reynolds number (or the volume flow rate) is linear because of the Hagen-Poiseuille equation:  
\[\Delta\mathrm{p}\ \propto\ \mathrm{Q}. \tag{5}\]  
However, if there is any vortex structure in the flow the above mentioned dependence becomes a square law [35].  
Using the CFD simulation, values of pressure drop were calculated for different volume flow rates (Figure 10).  
The square dependence can be approximated as given by:  
\[\Delta\mathrm{p}=\mathrm{aRe^{2}}+\mathrm{bRe} \tag{6}\]  
where a--is the quadratic coefficient, which is related to energy dissipated via chaotic advection, and b--the linear coefficient, which takes into account laminar flow wall friction. The form of the equation is similar to the Darcy-Weisbach equation, but it also includes a linear term. The pressure losses in each meander element of the microm mixer in the case of Re = 2.6 and Re = 26 are constant and equal; 0.31 Pa and 3.71 Pa, respectively. By Re = 259, the value of the pressure loss in each mixing element varies from 155 to 212 Pa.  
In comparison with a microm mixer with a relationship between the radius of the circular element and the characteristic length of the channel between elements ratio: w/d = 1/8 [28], the studied micromixer has approximately a 10 times smaller pressure drop at the same Reynolds number and similar mixing index.  
The mixing cost and mixing energy cost were calculated for the chicanes micromixer at different volume flow rates (Table 1) [36; 37; 38; 39]. The highest mixing cost was obtained at low volume flow rates. Mixing cost decreases at increasing Reynolds number. This indicates that the higher flow rates lead to higher pressure drop inside the micromixer and the intensity of mixing rises within the chicanes channel due to mixing intensification. Therefore, an overall reduction of mixing costs and mixing energy costs can be observed.  
Figure 10: Pressure drop by different Reynolds numbers.  
Mixing costs for different micromixers at Reynolds number of 50 are presented in Table 2. The chicanes micromixer stands out among other micromixers which consist of a straight channel and a mixing head with a simple geometry [40]. The serpentine micromixers with the T-joint and tangentially aligned inputs from [41] are much effective compared to T and Y-micromixer with the straight channel. The serpentine micromixers have lower mixing costs than the chicanes micromixer, because of higher pressure losses due to right-angle geometry, which leads to a moderate intensification of the mixing. The further increasing of the channel complexity, as shown for serpentine 3D splitting and recombination-type (SAR) micromixers [42; 43], causes higher energy dissipation and pressure drops up to 40 kPa at Reynolds number of 50. The generated saddle-shaped flow structure promotes chaotic advection and complete mixing at the micromixer outlet. Together with the extremely high pressure drop it provides low mixing costs, which are two orders of magnitude lower than the mixing costs of the serpentine micromixer.