## 5 Results and Discussion  
The geometries in Table 1 are used for conducting the present numerical simulations. First, a mesh independence study has been carried out to ensure adequate resolution. Based on the results, 443,000 tetrahedral elements would provide reliable and comparably fast results for this dimension. Subsequently, the validity of the numerical model is tested by modelling the experimental setup (case A-01) [28]. In this setup, a constant carrier fluid flow, which carries different sequences and lengths of DNA strands, starts at the time \(t_{0}\). After 50 min (\(t_{1}\)), the flow stops for the next 100 min (until \(t_{2}\)). The details of the experimental setup, the flow conditions, and the kinetics of oligonucleotide are presented in Tables 2 and 3. Figure 2 shows the surface coverage (\(\theta\)) over time for both numerical study and the experimental results [28]. The numerical model is validated based on the results since it shows a good agreement with the experimental data. For a better comparison, the surface coverage (\(\theta\)), the fraction of active sites occupied by adsorbed DNA strands (Equation (12)) are used for presenting the results. \[\theta=\frac{b}{b_{m}} \tag{12}\]  
Figure 3 shows the bulk concentration of DNA strands as the flow goes through the microchannel. As time passes, the bulk concentration around the functionalized surfaces reduces since the targeted DNA strands are binding with their specific ligand on the surface. This can be more evident in the surface coverage and surface concentration results in Figure 4, as it shows an increase in the surface coverage over time. After the validation, the numerical simulation is carried out for various cases of the three other setups: thin chamber (H series), suction (S series), and electroosmotic flow (E series). For each set, only the optimized values are presented in this paper. For instance, for the H series, the height H\({}_{\text{s}}\) varied from H/1.2 to H/20, but only case H-02 (H\({}_{\text{s}}=\text{H}/2\)) and H-03 (H\({}_{\text{s}}=\text{H}/4\)) are presented here since they have shown the best performance while not causing extra fabrication challenges. Figure 5 presents a comparison between cases H-02, H-03 and the original case for the first 50 min of the test. In the t\({}_{1}\) (50 min) case, H-02 has 24% more surface coverage than the original case (Figure 6). The surface coverage increases even further, by 9%, as the height of the channel on the functionalized surfaces halved in case H-03. However, this would put excessive pressure on the structure, which is evident from Figure 7, where the maximum pressure through the microchannel for all cases is shown. Figure 2: The time-dependent solution from the beginning of the test (\(t_{0}\)) to 50 min (\(t_{1}\)), and 150 min (\(t_{2}\)) [28]. Figure 4: The time-dependent solution for surface coverage of the original experimental setup (Case A) in comparison to cases H-03, S-04, and E06 for the whole surface (**a**), \(Pt_{f}\) (**b**) and \(Pt_{b}\) (**c**). A slide of surface concentration contour on the functionalized surfaces for cases A-01, H-03, S-04, and E06, after 100 \(s\) (**d**), 750 \(s\) (**e**), 2000 \(s\) (**f**) and 3000 \(s\) (**g**). Figure 3: Concentration contour for the original case (A-01) at the start of the time (**a**), after 50 s (**b**), after 150 s (**c**), and at the end of 50 min (**d**). Figure 5: The time-dependent solution for surface concentration in the first 50 min for the original experimental setup (Case A) in comparison to the: thin chamber (**a**), suction (**b**), and electroosmotic flow (**c**). A slide of bulk concentration on the functionalized surfaces for cases A-01, H-03, S-04, and E06, after 100 \(s\) (**d**) and 3000 \(s\) (**e**).