## 4 Discussion
As the DNA molecule translocates through the tapered microchannel along the microchannel axis direction, it is subjected to a stable electric field force in region I and keeps the distance from the channel wall constant in region II, resulting in a straight trajectory and stable velocity (Figures 4a and 5a). To further reveal the velocity change rule of DNA molecules in tapered microchannels, the distribution of electric field strength in the tapered channel system was studied in detail, as shown in Figure 9 (U = 20 V). Figure 9a shows a schematic diagram of the tapered microchannel, and the coordinate axes were established to test the change in \(E\). The axis of the channel is the x-axis, and the direction of the inner diameter is the y-axis. The trajectory of the DNA molecules may be deflected when approaching the tapered channel, so the origin is taken to be the O point 10 \(\upmu\)m away from the entrance of the tapered microchannel. From the simulation results shown in Figure 8, it can be seen that the \(E\) is stable after entering the small microchannel for about 2 \(\upmu\)m, so the point P (25.5, 0) is taken at a depth of 2.5 \(\upmu\)m inside the small microchannel. Then, points A (0, 12), B (0, 8), and C (0, 4), which are the same distance away from the entrance of the tapered microchannel as point O are also selected, and points A, B, C, and O are connected with point P to test the electric field intensity changes in the four paths. The corresponding results are shown in Figure 9c. Figure 9b displays locally the simulated distribution of electric field strength (\(\theta\) = 30\({}^{\circ}\), U = 20 V). As the inner diameter of the tapered microchannel decreases, the corresponding electric field strength increases rapidly. Figure 8: Electric field distribution inside the tapered microfluidic channel system. Furthermore, by combining the distribution of electric field strength in Figure 9b, the velocity changes in DNA molecules as shown in Figures 5 and 6 can be understood. The strength of the electric field is highest in the channel axis, and it reduces as the distance is far away from the channel axis. That is to say, the electric field force on DNA molecules in different positions of region II is different. DNA molecules moving along the axis of the tapered microchannel are under the largest electric field force (as the driving force), while DNA molecules in other places are under a smaller force. In addition, the \(E\) increases with decreasing inner diameter within the tapered microchannels, thus the velocity of the DNA molecules increases as the inner diameter decreases (Figure 6a,b). Figure 9c is the distribution of \(E\) in various directions. It can be seen from Figure 9c that along each direction, the \(E\) is monotonically increasing, and the disparity in the intensity of \(E\) in distinct orientations is exceedingly modest. There are about three stages of the distribution of \(E\) in four different directions (AP, BP, CP, and OP, \(\theta\) = 30\({}^{\circ}\)). At different stages the electric field strength (\(E\)) can be simply summarized as follows: When \(0<x<21.3~{}\upmu\)m, the region contains large channels and tapered microchannels as shown in Figure 9a, \(E_{\text{OP}}\)\(>E_{\text{CP}}>E_{\text{BP}}>E_{\text{AP}}\); that is to say, as the distance from the channel axis decreases, the \(E\) gradually increases. Moreover, the closer to the inner channel the higher the electric field strength, and the gap among the electric fields on different paths gradually decreases. When \(x\) = 21.3 \(\upmu\)m, \(E_{\text{AP}}\) = \(E_{\text{BP}}\) = \(E_{\text{CP}}\); when \(21.3<x<24~{}\upmu\)m, \(E_{\text{AP}}>E_{\text{BP}}>E_{\text{CP}}>E_{\text{OP}}\); and when \(x>24~{}\upmu\)m, \(E_{\text{AP}}\) = \(E_{\text{BP}}\) = \(E_{\text{CP}}\) = \(E_{\text{OP}}\), the electric field strength is equal in all directions, meaning the \(E\) inside the small microchannel is the same.