## 2 Materials and Methods
### Linear Polarization Resistance  
In this model, the corrosion process is assumed to be controlled by the kinetics of electron transfer reaction at the metal surface, and the electrochemical reaction can be expressed using the Tafel equation,  
\[I=I_{o}e^{\frac{2.300(I-I_{o})}{\beta}} \tag{1}\]  
where \(I\) is the current resulting from the reaction, \(I_{o}\) is a reaction-dependent constant called the exchange current, \(E\) is the electrode potential, \(E_{o}\) is the equilibrium potential, and \(\beta\) is the Tafel constant (volts/decade).  
Figure 5: The microstructure of the steel is studied using optical microscopic images of the metal sample and shown (a) 20-micrometer (b) 100-micrometer (c) SEM images of the surface.  
Figure 6: (**a**) Projection of sensor electrodes into the flow (**b**) isometric view of the sensor (**c**) side view. The orange rubber cap keeps the reference sensor (Ag/AgCl) from drying out.  
The Tafel equation is generally used to express the behavior of one reaction, and it is modified to Butler-Volmer equation, which can express both anodic and cathodic reactions, and it is given by,  
\[I=I_{corr}e^{\frac{-2.300(E-E_{corr})}{\beta_{a}}}e^{\frac{-2.300(E-E_{corr})}{ \beta_{c}}} \tag{2}\]  
where \(I\) is the current (amperes), \(I_{corr}\) is the corrosion current, \(E\) is the electrode potential, \(E_{corr}\) is the corrosion potential, and \(\beta_{a}\) and \(\beta_{c}\) are the anodic and cathodic Tafel constants in volts/decade.  
From the Tafel analysis shown, the current-voltage curve at \(E_{corr}\) can be considered as linear, and Equation (2) can be modified to obtain the Stern-Geary equation.  
\[I_{corr}=\frac{1}{R_{P}}\times\frac{\beta_{a}\beta_{c}}{2.303(\beta_{a}+\beta _{c})} \tag{3}\]  
The corrosion current can be related to the corrosion rate using [PERSON]'s law,  
\[Q=n\times F\times M \tag{4}\]  
where \(Q\) is the charge in coulombs, \(n\) is the no of electrons transferred, \(F\) is [PERSON]'s constant (96,485 coulombs/mole), and \(M\) is the number of moles equal to \(M=m/AW\), where \(AW\) is the atomic weight. Substituting the equivalent weight in terms of \(M\) in Equation (4), the mass of the species \(m\) can be written as,  
\[m=\frac{(EW)Q}{F} \tag{5}\]  
where \(EW\) is the equivalent weight. Modifying Equation (5) and substituting the value of [PERSON]'s constant, the corrosion rate (\(CR\)) is found to be:  
\[CR=\frac{I_{corr}\times K\times EW}{d(A)} \tag{6}\]  
where \(d\) is the density (g/cm\({}^{3}\)), \(A\) is the sample area in cm\({}^{2}\), and \(K\) is a constant.  
Electrochemical measurements are performed using Gamry Reference 600 potentiostat. The experiments were conducted till the system reached the open circuit potential (OCP) before linear polarization resistance was measured. Figure 7 shows the OCP measurement where potential is plotted against time for 1%, 2%, and 3.5% NaCl concentrations at 25 \({}^{\circ}\)C when the flow velocity is kept at zero. OCP, also called corrosion potential, is the Potential difference between the working and reference electrode when no external current is flowing in the cell. OCP measurement allows us to determine the \(E_{corr}\) and gives a broad view of the stability of the system. The plot shows the OCP value becomes stable after 3600 s for three concentrations, and the test time for the experiments are kept at 1 h throughout the study. The area of the cylindrical electrode is 1.6 cm\({}^{2}\) with a density of 7.87 g/cm\({}^{3}\), the potential was swept between \(-0.02\) Volts to 0.02 volts with a scan rate of 0.2 mV/s. The sample period was kept as 2 s, and Tafel analysis is conducted to determine the Tafel constants by running a potentiodynamic scan from \(-250\) mV to 250 mV.