pathogenic viruses, saving lives and economy is evident. A new competitive numerical platform specifically for designing microfluidic-integrated biosensors is developed and presented in this work. Properties of the biosensor, sample, buffer fluid and even the microfluidic channel can be modified in this model. This feature 20 provides the scientific community with the ability to design a specific biosensor for requested point-of-care (POC) applications. First, the validation of the presented numerical platform against experimental data and then results and discussion, highlighting the important role of the design parameters on the performance of the biosensor is presented. For the latter, the baseline case has been set on the previous 25 studies on the biosensors suitable for SARS-CoV, which has the highest similarity to the 2019 nCoV. Subsequently, the effects of concentration of the targeted molecules in the sample, installation position and properties of the biosensor on its performance were investigated in 11 case studies. The presented numerical framework provides an insight into understanding of the virus reaction in the design process of the biosensor 30 and enhances our preparation for any future outbreaks. Furthermore, the integration of * 1. Introduction
The current pandemic, the coronavirus disease is known as "COVID-19" (WHO, 2020) . According to the Coronaviridae Study Group (CSG) of the International 40 committee on Taxonomy of viruses' studies, this virus is as forming a sister clade to the severe acute respiratory syndrome coronaviruses ("SARS-CoVs"). It is named as "SARS-CoV-2" by the CSG (Gorbalenya et al., 2020) (Previously named "2019 nCoV"). Figure 1 (step 1) presents illustration of the structure of the coronavirus. It uses its spikes protein to enter the cell and delays the immune system response so that 45 when immune system responses, the infection is progressed enough that fighting it would be hard (Guevara-Carrion et al., 2011) . The three spill-over of animal to human coronaviruses are Middle East respiratory syndrome coronavirus ("MERS-CoV"), severe acute respiratory syndrome coronavirus ("SARS-CoV") and 2019 nCoV ("SARS-CoV-2'). 50 Since these viruses have the same origin, scientists are using the studies on MERS-CoV and SARS-CoV in order to reach to a faster solution for the SARS-CoV-2. SARS-CoV and SARS-CoV-2 both use angiotensin converting enzyme II (ACE2) as a cellular entry receptor and facilitate entry into the same panel of cell lines (WHO, 2020; Hoffmann et al., 2020; Seo et al., 2020) . Antibodies, vaccines, and drug 55 candidates are being developed throughout the world with the aim of preventing virus from entering the cell, viral replication or delaying the immune system.
The quantitative real-time polymerase chain reaction (qRT-PCR) test has been used broadly to detect SARS-CoV-2, SARS and MERS guides has been employed as a help for this test (WHO, 2020) . Although the conventional technologies such as 60 quantitative J o u r n a l P r e -p r o o f Figure 1 Schematic view of the four stages of designing a biosensor with the use of computational fluid dynamics. In stage 1, the virus is studied, and a conceptual design is prepared in stage 2. In stage 3, numerical analysis takes place and the design is 65 enhanced in stage 4 based on the results of the simulation.
J o u r n a l P r e -p r o o f -real-time polymerase chain reaction (qRT-PCR) are cost, labour, and time consuming, they have a higher sensitivity and specificity, hence they are the gold standard for biosensor design (Choi, 2020) .
Biosensors are sensitive, fast, low-cost, and easy-to-use pathogenic virus detection systems which are one of the best solutions for the reduction of death in pandemics (Amritsar et al., 2020) . Microfluidic integrated biosensors have been designed and developed for these means, in which a microfluidic channel is linked to electrical chips as micro-scale laboratories for analyzing reaction results. In Figure 1 (step 2), a 75 schematic view of microfluidic channel equipped with a biosensor is illustrated.
Targeted molecules flow into the channel and have chemical reactions with biological recognition element on the surface of the biosensor. Designing a reliable, e cient, a ordable and quick biosensor for point-of-care (POC) testing still remains a challenge . 80 The most important part in designing a procedure is related to the transport of targeted molecules to the functionalized surface of the biosensor (Luka et al., 2015; Nair and Alam, 2006) . Robust simulation (fast, reliable, and stable numerical modelling) of these systems and their chemical reactions would be a huge help in designing e cient biosensor. Computational fluid dynamics (CFD) is one of the best 85 solutions for this matter. In recent years, CFD has successfully been applied to numerous biomedical-related projects involving design, validation and proof-ofconcept; some examples from the present authors include McElroy and Keshmiri, 2018; Ruiz-Soler et al., 2017; Swanson et al., 2020) .
In the previous works, di erent software packages and codes were utilized to 90 model the flow inside the microfluidic channel. Discretization method is the key component in these numerical solutions. There are three different discretization methods; finite element method (FEM), finite volume method (FVM) and control volume-based finite-element method (CVFEM). FEM has geometrical flexibility, CVM has physical intuition and CVFEM is a powerful combination of these two 95 methods (Tombarevic et al., 2013) . In some of them, the control-volume method is employed in the microfluidic flow simulation using software packages such as CFD-J o u r n a l P r e -p r o o f ACE+, Ansys-CFX, Ansys-Fluent and Flow3D, however, to avoid numerical di usion (when algorithm aggregates numerical errors through the simulation) the actual di usion constant from the experiments has not been used (Glatzel et al., 100 2008). Another common numerical study reported for this application is based on using an analytical velocity profile (assuming fully developed Poiseuille flow) in the convective-di usive transport equation instead of using the converged velocity from Navier-stokes equations. Gelarkin finite-element method (Selmi et al., 2017) and COMSOL commercial code (Hu et al., 2007; Liu et al., 2019) , (including FEMLAB, 105 MATLAB subsidiary of COMSOL) are in this category, in which it has been reported that numerical results has more than 2 orders of magnitude di erence with the experimental data (Squires et al., 2008) .
It is, therefore, the aim of the present work to introduce a reliable and stable 110 numerical model that has been developed to solve full Navier-Stokes equations coupled with convection, di usion and reaction of targeted molecules based on CVFEM. The model can simulate microfluidic-integrated biosensor without the need to modify the input values (properties of the real experimental samples) and the results will have good agreement with already existing experimental data from the 115 literature.
The next section presents the description of the methods, governing equations, and boundary conditions. As was alluded to earlier, Figure 1 demonstrates the four stages of designing a microfluidic-integrated biosensor with the proposed numerical platform. In step 1, the virus and its origins is studied, which is critical for step 2, for 120 preparing a conceptual design of a microfluidic-integrated biosensor. In the next step, the numerical model simulates the bu er fluid flow, convection, di usion and reaction of the targeted molecules in the biosensor. Finally, in step 4, design optimization takes place, based on the results and analysis. As a result, the present study will focus on studying the e ects of varying the most design parameters on the 125 performance of the designed biosensor.
J o u r n a l P r e -p r o o f
In the proposed new approach for modelling virus detection in a microfluidicintegrated biosensor, full Navier-Stokes equations (Equations (1)-(3)) coupled with convection, di usion and reaction of targeted molecules (Equations (4)-(6)) are 130 solved implicitly with the CVFEM.
Step 3 in Figure 1 demonstrates the numerical domain and boundaries. Since variation of velocity in the span wise direction of this channel is negligible (due to negligible side wall e ects on sensor surface), 2D simulation is valid for this case (Liu et al., 2019) .
In the micro-scale, any parameter proportionate to the scale of the surface area 135 becomes more important and viscous forces dominate over inertial forces. In order to avoid numerical di usion or suppression of small numbers during numerical loops, high-order discretization methods are needed (Glatzel et al., 2008) , which have been implemented in the proposed model. In addition, di usion and reaction are coupled and solved fully implicitly using CVFEM (Karimian and Schneider, 1995) . 140 Furthermore, instead of using an analytical velocity profile inside the channel, full Navier-Stokes equations are solved for a comprehensive numerical model.
The proposed numerical platform solves the two-dimensional Navier-Stokes equations (Equation 1 to 3) to simulate the bu er fluid flow.
Where u and v are the velocity in the x and y direction, respectively, while ρ is the density and µ is the molecular viscosity. The fluid is considered as continuum and incompressible, because of its negligible changes in density. In the present test cases, the concentration of biological species is significantly low, and they do not have any e ect on density or viscosity of the carrier fluid (Berthier and Silberzan, 2001) . By 
Where c is the concentration of the targeted molecules, D is the di usion coefficient and S is the source/sink term which is assumed zero in this study. Kinetics of heterogeneous biosensors (which are used for DNA hybridization, virus detection 155 etc.) is modelled using Langmuir-Hinshelwood mechanism (Berthier and Silberzan, 2001) . Ligands constantly trap targeted bio-species and they dissociate at a smaller rate (Equation 6):
Where k on is the adsorption rate, k off is the dissociation rate of the sensor, b is the surface concentration of bound analyte (Sevenler et al., 2019) , c 0 is the inlet 160 concentration and b max is the density of binding sites on the sensor. For discretizing the convection term, the upwind di erencing scheme is used, while for the di usion term, improved skewed upwind di erencing (SUD) is used (Karimian and Schneider, 1995) , which helps generate accurate and robust results. Upwind di erencing scheme (UDS) is first order accurate and gives high level of false di usion. SUD scheme uses 165 flow direction which provides more realistic results. In the improved SUD scheme, e ects of the di usion and source term are included in the di erencing procedure.
Boundary conditions implemented in this model are summarized in Table 1 J o u r n a l P r e -p r o o f CoV-2 (Seo et al., 2020) .
Then for enhancing the performance of the biosensor and studying the e ect of important parameters, 11 cases has been studied. Details of these numerical simulations is demonstrated, and color scaled in Table 3 At the start of stage 2, targeted molecules are injected into the bu er fluid and they start to be adsorbed and immobilized temporarily by the available sites of the sensor.
In this stage, the detection of surface concentration will begin. When concentration 220 reaches its asymptotic value (i.e. stage 3), an analyte free fluid passes through the channel and the desorption of ligands takes place (i.e. stage 4).
Details of the numerical simulations. Group A (cases 1 to 5), which is for studying the e ects of the position of the biosensor and case 3 is the base case. Group B (cases 6 to 8) for studying e ect of varying dissociation and adsorption rates (but 225 keeping the a nity the same) of the biosensor and case 7 is the base case. Group C (cases 9 to 11) for studying the e ect of concentration of the targeted molecules in the sample and case 10 is the base case in this group. 
For a better analysis of the changes in the performance of the biosensor, saturation time versus the position of the sensor is illustrated in Figure 3(b) . As the biosensor 230 transfers from the inlet, its saturation time increases As Figure 3(b) shows, the variation of the saturation time with respect to the location of the sensor reduces as the biosensor gets far from the inlet or outlet. Displacements happen at the same rate, although changes in binding cycle and saturation times are not at the same rate. As tₛ= -0.0054xₛ 2 + 11.352xₛ + 3294.1
Where t s represents the saturation time and x s is the position of the sensor from the inlet boundary.
Next, we study the e ect of functionalized surface with the same a nities but The fundamental rule of biosensors in fighting against pandemic is proven in previous studies Morales-Narváez and Dincer, 2020; Zhu et al., 2020) . As it is shown above, design and optimization of an e ective, low cost and At last, concentration of the targeted bio-species that is an important factor in the improvement of the mass transport. The performance of the biosensor can be 295 improved based on an appropriate choice of these three design parameters.
Time is of paramount importance in the fight against a pandemic. The crucial role of biosensors in containing highly pathogenic viruses in saving lives and the economy is evident. The challenge is to design a biosensor for each specific for point-of-care 300 (POC) applications.
To address this challenge, a new numerical solver for competitive biosensors is developed and presented in this work. The model is based on the control-volume J o u r n a l P r e -p r o o f finite-element method (CVFEM) and all the convective-di usive-Langmuir equations are solved fully coupled together with a high order discretization scheme. 305 The first part of the study presented the validation test of the preliminary results against the experimental data. Unlike previously published numerical studies, the present model makes use of the exact flow parameters, adsorption/dissociation rate and di usion constant, that shows the reliability and robustness of the developed approach. 310 The next part of the study showed the e ect of 3 design parameters on the performance of the biosensor. It was found that the installation position of the biosensor has a significant e ect on its e ciency; it can reduce the detection time by over 50% with only 500-µm displacement. It was also found that the reaction rates would lead to a considerable increase in the total time of the binding cycle when they 315 reach a specific order of magnitude, thus it would be better to avoid using such ligands in reaction surfaces. Furthermore, changing the inlet concentration was also shown to have a significant impact on the saturation time and shape of binding cycle stages (which demonstrates the behavior of targeted molecules through time). These variations take place in a non-linear manner. 320 Since May 2020 until the time of writing this paper (July 2020), more than 20 diagnostic tests have been approved by FDA by receiving the emergency use authorization (EUA) (BioCentury, 2020). The sample-to-answer tests are chip-based biosensors (nucleic acid test) and paper-based (antibody test) biosensors. Because of complicated procedure of nucleic acid tests in comparison to the antibody test, recent 325 studies show that antibody tests are playing an important role in reducing the overall diagnostic time and help in a fast decision making. (Choi, 2020; Du et al., 2020; Li et al., 2020; Sheridan, 2020) .
The presented computational model would provide a valuable insight into The current tests have the potential to produce wrong negative results and they have different sensitivity (BioCentury, 2020). Most of the FDA approved tests are qRT-PCR, which has lower limit of detection (LoD), hence higher level of sensitivity.
Limit of detection (LoD) is one of the crucial performance characteristics that 340 describes the lowest concentration of the target that can be reliably measured by the test (Lavín et al., 2018) . This numerical platform can in understanding operational behavior of designed biosensors and reducing their limit of detection.