**3. Results and discussion**

### **3.1 Model validation**

First, the numerical model was tested by comparison with experimental existing data of Berthier and Silberzan [18], as shown in **Figure 5**. The time-normalized surface concentration during the adsorption phase was calculated using the same experimental parameters [18], for a microfluidic of 10 mm in length and 1 mm in height without flow confinement. The flow rate of the transporter fluid is 10<sup>6</sup> m<sup>3</sup> /s, the inlet concentration of the target molecules is 2.5 <sup>10</sup><sup>6</sup> Mol/m<sup>3</sup> , the diffusion constant is 7 <sup>10</sup><sup>11</sup> <sup>m</sup><sup>2</sup> /s, and the density of ligands initially immobilized on the reaction surface is 1.668 <sup>10</sup><sup>8</sup> Mol/m<sup>2</sup> . The association and dissociation constants are, 75 m<sup>3</sup> /Mols and 10<sup>2</sup> 1/s, respectively. We can note that our results are in good agreement with the experimental data and that the average error between the two results is very small, which confirms the validation of the model.

### **3.2 Flow confinement impact**

Succeeding the successful model validation, this section aims to show how to flow confinement can improve the kinetic response of SARS-CoV-2. **Figure 6** shows the binding reaction with and without flow confinement for a biosensor configured, as shown in **Figure 1**. An enhancement of the binding reaction and thus the detection time (22%), was seen in the case where the flow confinement was employed (**Table 3**). This shows the effectiveness of confinement in improving biosensors immunoassays. Admittedly, this improvement can be explained by a local condensation of the analyte over the reaction surface. In fact, the flow confinement increases the fluid velocity in the vicinity of the sensitive membrane which decreases the thickness of the analyte concentration diffusion boundary layer formed at the adsorption phase, as illustrated in **Figure 7**. Also, it is noted that the thickness of the analyte concentration diffusion boundary layer decreases with increasing flow confinement rate.

**Figure 5.** *Confirmation of the present model with the experimental data of Berthier and Silberzan [18].*

*Enhancement of SARS-CoV-2 Detection Time for Integrated Flow Confinement Microfluidic… DOI: http://dx.doi.org/10.5772/intechopen.104802*

#### **Figure 6.**

*Impact of the flow confinement on the variation of the normalized surface concentration, AB , over time.*


#### **Table 3.**

*Detection time and drop percentage for the microfluidic biosensor with or without flow confinement.*

**Figure 7.**

*Analyte concentration diffusion boundary layers in the adsorption phase with and without flow confinement effect. (a): Without flow confinement. (b): With flow confinement (uconf* ¼ *uave) and (c): With flow confinement (uconf* ¼ 3*uave).*
