## 5 Conclusions  
In this study, we first fabricated highly uniform chips consisting of five sets of tapered microchannels by soft lithography, of which the major tapered structure is 13 \(\upmu\)m in length and gradually changed from 5 \(\upmu\)m to 20 \(\upmu\)m in width. Microchannels with widths of 5 \(\upmu\)m and 120 \(\upmu\)m were connected at two sides of the tapered structure, respectively. Then, by using single-molecule fluorescence imaging, we systematically investigated the dynamic characteristics (such as the trajectories and velocities) of \(\lambda\)-DNA molecules translocating the tapered microchannels driven by an external DC electric field and found some meaningful phenomena.  
The velocities of DNA molecules are relatively slow as DNA molecules translocate through large channels, and they increase as DNA molecules translocate tapered microchannels and reach the same maximum value at the place that connects tapered microchannels and small channels and then stabilized in the small channels. The velocity characteristics of DNA molecules in large channels are complicated. DNA molecules near the large channel walls translocate slowly and fluctuate, while the velocity of the DNA molecules translocating along the microchannel axis direction remains almost constant. DNA molecules between two neighboring tapered microchannels translocate the fastest, and the velocity of DNA molecules in these places decreases first but increases immediately as they approach the tapered channels. The velocity of the DNA molecule is inversely proportional to the diameter of the tapered channel, and the velocity of DNA molecules translocating through both large and small microchannels increases with the external applied voltage. The trajectory of DNA molecules around microchannels is near the wall surface, while DNA molecules translocating along the axis of the channel move in a straight line along the axis, and DNA molecules translocating between two neighboring tapered microchannels alter their moving directions and move forward along the tapered channel wall.  
All the above phenomena and characteristics can be well understood by simulating the distribution of electric field strengths when considering only the electrophoretic and electro-osmotic forces acting on DNA molecules.  
This study helps in the development of DNA molecular sensors and lab-on-a-chip systems. In future research, the \(\theta\) angle of the tapered microchannels can be adjusted to different degrees to guide the movement of DNA molecules. Additionally, we aim to combine the tapered microchannels and nanostructures to stretch DNA molecules and study their conformational changes in detail.  
Conceptualization, methodology, K.W.; software, Y.N., J.W., and Z.L.; data curation, Y.N., Y.L. ([PERSON]), Y.L. ([PERSON]), J.Z., and K.W.; formal analysis, writing--original draft preparation, Y.N. and K.W.; writing--review and editing, Y.N., Y.D., J.W., J.Z., and K.W.; supervision, project administration, K.W. and D.S. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the National Natural Science Foundation of China (No. 62275216, 61775181), the Innovation Capability Support Program of Shaanxi Province (grant No. S2018-ZC-TD-0061, TZ0393), and the National Key Scientific Instrument and Equipment Development Projects of China (No. 51927804).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.