## 3 Results
### Properties of DNA Translocation in Tapered Microchannels from Different Original Positions  
Figure 4 shows the movement trajectories of three DNA molecules translocating through the tapered channel system from different starting locations. The channel boundaries are delineated by white dashed lines, and the locations of the DNA molecule are indicated with blue dashed boxes. As shown in Figure 4, the trajectories for the three \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Physical Parameter** & **Symbol** & **Unit** & **Value** \\ \hline Relative permittivity & \(\epsilon_{r}\) & 1 & 80 \\ Dynamic viscosity & \(\mu\) & Pa-s & \(1.1\times 10^{-3}\) \\ Wall potential & \(\zeta\) & mV & \(-30\) \\ Temperature & \(K\) & \({}^{\circ}\)C & 296 \\ Elementary charge & \(e\) & C & \(1.602\times 10^{-19}\) \\ Voltage & \(U\) & V & 0–100 \\ Conductivity & \(\sigma\) & S/m & \(5.5\times 10^{-6}\) \\ Boltzmann constant & \(K_{B}\) & J/K & \(1.381\times 10^{-23}\) \\ Density & \(\rho\) & kg/m\({}^{3}\) & \(1.05\times 10^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main physical parameters. Figure 3: Tapered microfluidic channels: (**a**) typical photograph of the microfluidic channel; (**b**) different positions of DNA molecules entering into tapered microchannels. scenarios are as follows: DNA molecules entered the tapered microchannel along the axis direction as shown in Figure 3b and did not have their trajectories deflected and always migrated along the channel axis (Figure 4a). DNA molecules entered from the location between the two neighboring tapered microchannels as shown in Figure 3b and after moving a short distance in a straight line and reaching the region II (Figure 3b), it altered the moving direction and turned towards the tapered channel wall and moving forward along the channel wall, and then moved inside the small diameter channel and translocating forward along the channel wall (Figure 4b). DNA molecules that enter from a location near the wall of the large microchannel consistently moved near the channel wall in all channels (Figure 4c). Figure 5 is the velocity change in DNA molecules translocating from three different starting locations as shown in Figure 4. Specifically, Figure 5a-c corresponds to the three cases of DNA molecule movement shown in Figure 4, and the corresponding velocities are defined as \(v_{1}\), \(v_{2}\), and \(v_{3}\), respectively. It can be seen from Figure 5 that the velocity of the DNA molecules as they are translocating through the tapered microchannel from three different starting locations. This can be divided into three similar stages: (1) the velocities were all relatively smaller when they moved within the large channel (region I as shown in Figure 3b); (2) the velocities for all DNA molecules had a significant increase (region II); and (3) the velocities of DNA molecules achieved almost the same maximum value at the tapered microchannel exit. Figure 4: The trajectories of DNA molecules translocating through tapered microchannels from different starting locations: (**a**) along the microchannel axis direction; (**b**) between two neighboring tapered microchannels; (**c**) near the wall of the large microchannel. Figure 5: Velocities of DNA molecules migrating through tapered microchannels from various starting locations: (**a**) along the microchannel axis direction; (**b**) between two neighboring tapered microchannels; (**c**) near the wall of the large microchannel. The velocity was maintained through the entire small channel (region III). However, the velocity characteristics of the three cases are obvious: (1) in region I, the average velocities were different in the three cases, \(v_{2}\) was the maximum, while \(v_{3}\) was the minimum; (2) \(v_{1}\) remained almost the same value and \(v_{3}\) kept fluctuating up and down, while \(v_{2}\) had a large change near the entrance (entering the region II), decreasing firstly and then increasing immediately; in addition, these velocity changes were different when DNA molecules translocated region II.