# Energy-Efficient AC Electothermal Microfluidic Pumping via Localized External Heating
## 3 Simulations and Results
### Fluid Velocities  
Seven inlet velocities were tested with a voltage of 5 V supplied to the electrode array. ACET produces modest fluid movement in the absence of any inlet flow by interaction of normal forces generated in the fluid. The resulting flow pattern depends on factors such as electrode dimensions and layout, as well as variables like voltage and frequency, among others, that we have used as variable parameters in this study. This resulting non-uniform electric field in the fluid is examined herein. This flow is visible in areas of higher velocity and a corresponding lower pressure consistent with the Navier-Stokes and continuity equations described above. Inlet velocities and flow rate are given in \(\upmu\)m/s and \(\upmu\)m\({}_{3}\)/s alone and our channel height remains constant at 100 \(\upmu\)m. To properly understand Figure 6a we need to point out that these images show color-coded velocities in the microchannel using relative mapping and are more for quantitative purposes, meaning that we are interested in the velocity difference within the channel and not representing the actual measured velocities. The actual measured velocities are visible, however, in Figure 6b, where flow rate (\(\upmu\)m\({}^{3}\)/s) is plotted against inlet velocity (\(\upmu\)m/s). We would like to note that this pairing of qualitative surface graphics with quantitative graphs is used throughout this study for a more wholistic understanding of the results. Figure 5: Plot of velocity (\(\upmu\)m/s) and channel height (\(\upmu\)m) relative to electrode sizes 20 \(\upmu\)m, 40 \(\upmu\)m, 60 \(\upmu\)m and 80 \(\upmu\)m.  
At an inlet velocity of 0 \(\mu\)m/s, shown in the uppermost graphic in Figure 6a, the asymmetrical electrode array produces distinct areas of higher velocity just above the array in two multi-lobed vortices on either side of the array. It can also be seen that of the lobed regions, the lower two have a greater velocity than all other regions in these 0 \(\mu\)m/s inlet velocity trials. The flow rate in the channel was recorded as 0 \(\mu\)m\({}^{3}\)/s. Figure 6: (**a**) Relative surface velocity magnitude (\(\mu\)m/s). (**b**) Graph of measured volumetric flow rates in the microfluidics channel. The lowest active inlet flow of 0.5 \(\upmu\)m/s can be seen as the second from the top graphic in Figure 6a. Now we can see that the bulk fluid in the channel has a slight increase in velocity as indicated by the change in color from the 0 \(\upmu\)m/s graphic above it, and the flow pattern created from the ACET begins to become distorted. Now we see velocity in the lower right lobe decrease while the upper right region expands, elongating slightly. Meanwhile, the lower lobe of the left vortices has a similar elongation with a distinctly higher velocity than anywhere else in the channel. Outside the electrode-affected region, the bulk fluid remains constant with the inlet velocity. In the 0.5 \(\upmu\)m/s trial, we that the distortion in the ACET flow pattern beginning to occur in the previous trial is exaggerate further. Here, the upper left and lower right lobes have diminished significantly as their measured velocities near that of the bulk fluid flow initiated by the inlet velocity where a flow rate of 49.83 \(\upmu\)m\({}^{3}\)/s was recorded. With an inlet velocity of 1 \(\upmu\)m/s there is considerable movement in the bulk fluid throughout the channel, indicated by the lighter region in the surface graphic in Figure 6a, and the ACET flow pattern is entirely altered from its original symmetrical 5-lobed pattern. Here, with a recorded flow rate of 99.65 \(\upmu\)m\({}^{3}\)/s, we notice that the lower left region remains an area of highest velocity, but the down-current lower lobe is effectively gone. We can see that at 1 \(\upmu\)m/s inlet velocity the ACET phenomenon just moderately manipulates the flow of the bulk fluid through the channel.