# Energy-Efficient AC Electothermal Microfluidic Pumping via Localized External Heating
## 4 Discussion  
### Results Discussion  
The results above demonstrate the significant versatility of our platform, a diagram of which is shown in Figure 1. With this simulation configuration, we can effectively use heat and apply an alternating current to move solutions while modulating several parameters for the fluids within microchannels. A mesh study (Figure 2) confirms that our platform can maintain a stable volumetric flow rate throughout the tested range, a crucial factor for ensuring fluid integrity and transport. Surface velocities can be controlled by pressure-driven flow, as seen in (Figure 6a,b), but further simulations using COMSOL software in subsequent sections reveal novel innovations for moving fluids, managing heat and controlling pressure in microchannels. Channel height created meaningful changes to the capacity of several parameters in microchannel simulations as heights of 100 \(\upmu\)m, 200 \(\upmu\)m, 400 \(\upmu\)m and 500 \(\upmu\)m returned meaningful changes in three sets of simulations (Figures 7-9). As expected, changes to channel height elicited pressure gradients, which brought about increased flow rate and changing configurations of four-lobed pattern vortices at the site of the electrode array (Figure 7). This has been explained in prior work connecting papers [2; 3; 6]. Figure 8a,b shows that varying height can increase or decrease pressures across the architecture. Figure 8a,b demonstrate the potential for alteration of pressure (Pa) distribution across the channel, noting the qualitative change in pattern presented in Figure 8a. In the final height-based set of simulations, recorded temperatures decreased with channel height, as presented in Figure 9.  
Figure 12: Graph of volumetric flow rate (\(\upmu\)m\({}^{3}\)/s) as a function of increasing power (W). The remaining simulations were conducted with a consistent channel height of 100 \(\upmu\)m. Increases in conductivity (S/m) increased flow rate as well as temperature in our simulations as seen from the graphs plotting the results in Figure 10a,b. We note that while the relationship appears slightly super-linear in the plot of conductivity vs. flow rate (\(\upmu\)m\({}^{3}\)/s) in Figure 10a, it was very slightly sub-linear for the plot of conductivity vs. temperature (K) in Figure 10b. Another set of simulations were run gradually increasing the voltage (V) applied at the electrode array while monitoring flow rate (\(\upmu\)m\({}^{3}\)/s) in the microchannel. We found that not only is the configuration of vortices in the channel affected, as can be seen in Figure 11, but a super-linear relationship became apparent for simulations of 1 V to 6 V.  
Figure 6a shows fluid velocity increases when inlet velocity increases, this is due to the conservation of mass phenomena in the microchannel. A pressure difference is created inside the microchannel when the inlet velocity increases because fluid moves at higher velocity. The equation of continuity plays an important role for maximum velocity inside the channel and ACET are responsible for fluid flow. This study shows flow rate increases when channel height increases in Figure 7, this is due to higher channel height providing additional space for fluid flow. Fluid velocity is proportional to the height of the channel squared. At the same pressure gradient, fluid experiences less resistance, hence the microchannel observed higher fluid velocity with increasing channel height. This study shows that the flow rate increases when fluid conductivity increases, as shown in Figure 10a, due to electro thermal force. Higher-conductivity fluid interacts with electric fields, increasing the driving force and, consequently, the fluid velocity. The fluid flow rate increased when the electric field strength was increased, as shown in Figure 11, due to the AC Electrothermal Flow. This work shows that the maximum temperature is decreased when channel height is increased in Figure 9. Here, the hot spot was placed in between the electrodes and applied power was 2 W in the hop spot.