## 1 Introduction  
Micro/nanofluidics are usually employed to manipulate and study properties of single DNA molecules, such as stretching [1], separation [2], concentrating [3], amplification [4], sequencing [5], and interactions between DNA molecules [6, 7]. To manipulate single DNA molecules accurately, researchers have developed various channel structures, including T-shaped [8], S-shaped [9], cross-shaped [10], tapered [11], hyperbolic [12], serrated [13] structures, etc. At the same time, nanopillar arrays [14], micro-nanochannel arrays, and nanoscale slits [15] are also integrated into fluidic channel systems. The combination of single-molecule imaging with micro/nanofluidics enables the visible research of the dynamic behavior of individual biomolecules. For instance, [PERSON] et al. used microparticle image velocimetry (\(\upmu\)PIV) to measure the velocities of two particles with different electrical surface properties. By subtracting the velocity component due to the effects of electrophoretic force from the velocity of the particles, the distribution of electro-osmotic flow velocity and electric field intensity was measured [16]. [PERSON] et al. observed the stretching of DNA molecules in semicircular and quarter-circular microchannels using the PIV (particle image velocimetry) technique. The effects of centrifugal force,electric field strength, and solution viscosity on the stretching efficiency were analyzed [17]. [PERSON] et al. studied the nonlinear rheological behavior of concentrated double-stranded (ds) and single-stranded (ss) DNA solutions under standard oscillation and large amplitude oscillatory shear (LAOS) deformation. Insights into the nonlinear response of the DNA solutions were achieved by performing PIV at a wide range of imposed strain amplitudes and two angular frequencies [18]. To drive DNA molecules within micro-/nano-fluidic channels, there are usually four kinds of methods: electrically driven [19; 20; 21], pressure driven [22], capillary force driven [23], and shear driven [24]. Of these, the electrically driven method is the most commonly used to guide the movement of DNA molecules within micro-nano channels. When an electric field drives the migration of DNA molecules, their velocity and direction are influenced by various factors, including electro-osmotic force [25], electrophoretic force [26], Stokes force [27], and Saffman force [28]. Additionally, the impact of the double electric layer [29] near the channel wall's surface on DNA molecules and the constraining effect of the channel structure's shape on DNA molecules cannot be ignored. To manipulate the movement of DNA molecules accurately, researchers have designed and prepared micro-/nanofluidic channels with specific functional structures. For example, [PERSON] et al. invented a hyperbolic microfluidic channel, which generates a constant strain rate along the flow centerline over a long distance, and it was used to extend and compress DNA molecules [12]. [PERSON] et al. developed a device to successfully screen DNA molecules by using electric field force. The device regulates the deflection direction of DNA molecules at the channel exit by varying the magnitude and frequency of the voltage [30]. [PERSON] investigated the significant effect of the micro-funnel shape on DNA fragmentation using both microfluidic experiments and numerical simulations. The funnel shape controls the flow fields, especially the magnitude and distribution of the extension rate. Recently, [PERSON] et al. designed a kind of tapered microchannel entrance structure to prevent DNA molecules from accumulating at the entrance and to achieve a uniform distribution of DNA molecules in the microchannel. It is found that the tapered microchannels with gradually changing inner diameters can solve the problem of DNA molecules accumulating and clogging at interfaces when channels with different inner diameters are spliced together [31]. In this investigation, soft lithography was employed to prepare microfluidic chips that contained tapered fluidic channels.