Lab-on-a-Chip (LOC) is a new technology focused on analyzing and controlling flows of fluids, ions, and (bio) particles on the nanometer and micrometer scales, allowing us to shrink a complete fluid-based laboratory into a coin-sized instrumentation. In this thesis, we study a novel fluidic structure with a "branched U-turn" geometry, investigating its potential to perform size-based sorting and characterization on DNA single-molecules. The fluid flow and the DNA molecule motion within the fluidic structure are controlled using electric fields and analyzed with quantitative fluorescence microscopy. The channel depth is less than 1 micrometer, while the channel lengths and widths are in the range of 100 micrometers. Due to these dimensions, the fluidic structure can be simplified as a quasi-two-dimensional system when we perform digital image analysis and numerical simulation. Using these channels, we pose the following research questions: 1. How does the fluid flow behave when various types of electric fields are applied across these channels? 2. How do the pathlines of individual DNA molecules behave inside the confining nanofluidic channels? 3. Can we use these channels as novel devices to sort and characterize single DNA molecules? In Chapter 2, we review the concepts of electrokinetics. Chapter 3 describes the nanofluidic channels studied in this research. In Chapter 4 we studied the first research question by investigating and analyzing the electro-osmotic flow inside the nanofluidic channels. In the experiments, we use distilled water as the liquid in which we add 110 nm diameter fluorescent beads employed as tracer-particles inside 150 nm deep nanofluidic channels. From the results we can characterize the pathlines and velocity distribution of the fluid flow. Due to the complex geometry of the channel, the electro-osmotic flow cannot be calculated analytically. Therefore we use numerical flow simulations to build our model. Comparison between the experimental data and the simulation results give a very good agreement, where the deviation can be explained by the measured Brownian motion of the tracer-particles which was not incorporated in the simulation. The second research question was investigated in Chapter 5. Experiments are performed with two types of dsDNA molecules, λ (48.5 kbp) and T4GT7 (165.6 kbp), using channels with depth of 400 nm. We observe that the electrokinetic pathlines of the DNA molecules depends on the DNA size. We use numerical simulation to calculate the distribution of electrokinetic forces in the channels, which can explain the observed experimental phenomena. The results of Chapter 5 also indicate that, for the first time, size-based separation of DNA molecules can be done in a continuous, sieve-less, manner. This is related to our third research question. By using the nanofluidic channel geometry, we can configure the electric field distribution in the channels and manipulate the electrokinetic forces to influence the pathlines of the DNA molecules. The same results can be expected not only on DNA molecules, but also on any other polarizable biological molecules that can be manipulated using dielectrophoresis.