## 4 Discussion
To further investigate the trajectory and velocity of DNA molecules translocating through the tapered microchannel (region II), we analyzed the distribution of electric field strength in the region between the two neighboring tapered microchannels as marked in the black dashed box of Figure 10a, ranged 28 \(\upmu\)m \(\times\) 28 \(\upmu\)m with point O located in the center of the channel wall. Figure 10b displays the distribution of \(E\) in the region with \(\theta\) = 30\({}^{\circ}\), while Figure 10c shows that with \(\theta\) = 60\({}^{\circ}\). Figure 10d shows that the distribution of \(E\) at different \(\theta\) in the OP direction is 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\) (U = 20 V). As shown in Figure 10b, the \(E\) decreases as it approaches point O, and the strength decreases to 0 in point O, which affects the velocity of DNA molecules translocating through the region. As DNA molecules translocate through this area and approach region II, the effect of decreasing electric field strength and the channel wall slows the DNA molecules down. Additionally, the channel wall restricts the movement of DNA molecules and results in it deflecting to the tapered microchannels (Figures 4b and 5b). When \(\theta\) changed to 60\({}^{\circ}\) as Figure 10c depicts (the blue dotted line area), the distance between spacing tapered microchannels decreases and the electric field intensity in the selected area increases overall. It can be seen from Figure 10d that for each \(\theta\), the \(E\) is monotonically increasing, and the difference in \(E\) increases and then decreases in different \(\theta\). Figure 10d shows the variation of \(E\) along the OP direction with different \(\theta\) values. When \(0<x<22.3~{}\upmu\)m, the \(E\) is monotonically increasing, and the difference in \(E\) increases and then decreases in different \(\theta\), and the value of \(E\) increases faster with smaller \(\theta\). When \(x\) = 22.3 \(\upmu\)m, the values of \(E\) with different \(\theta\) become equal. When \(x\) > 22.3 \(\upmu\)m, the strength of \(E\) also increases as \(\theta\) decreases. Figure 9: Electric field distribution inside the tapered microchannel: (**a**) schematic of the tapered channel (\(\theta\) = 30\({}^{\circ}\)); (**b**) local electric field strength inside the tapered microchannel; (**c**) distribution of \(E\) in different directions (\(\theta\) = 30\({}^{\circ}\)). Figure 11 illustrates the distribution of \(E\) within the tapered microchannel in the OP direction under different applied voltages (20 V, 40 V, 60 V, and 80 V, respectively). It can be seen that the \(E\) at all locations increases with the applied voltage U increase. Therefore, \(v_{\rm d}\) and \(v_{\rm D}\) increase when U increases (Figure 7b). Comparing the three cases shown in Figure 5, it can be found that the velocity of DNA molecules near the wall of the large microchannels (Figure 5c) in region I is smaller than that of the other two cases (Figure 5a,b). This difference might have another influence, i.e., the interaction between the DNA molecules and the channel wall besides the EDL has an effect on the DNA molecule. The surface of the PDMS channel is not completely smooth, thus the tangled-mass-thread DNA molecules around the channel wall interact with the rough part of the surface. The interactions between DNA molecules and the microchannel wall and the adsorption of the EDL led to a decrease in the velocity. Figure 11: The distribution of \(E\) within the tapered microchannel in the OP direction under different applied voltages. Figure 10: Electric field strength distribution in the region between the two neighboring tapered microchannels: (**a**) location of the selected region (black dashed box); (**b**) distribution of \(E\) (\(\theta=30^{\circ}\)); (**c**) distribution of \(E\) (\(\theta=60^{\circ}\)); (**d**) the distribution of \(E\) at different \(\theta\) in the OP direction is \(30^{\circ}\), \(45^{\circ}\), and \(60^{\circ}\) (U = 20 V).