## 3 Results and Discussion
Figure 17: Pressure profile across the stenosed arteriole segment without graphene layer. Figure 18: Blood flow across aneurysm arteriole segment without graphene layer. Figure 32: Water flow across the graphene layer with 6.5% porosity (Case: Blood flow). Figure 37: Pressure distribution for graphene layer with 6% porosity (Case: Blood flow). Figure 38: Pressure distribution for graphene layer with 7% porosity (Case: Blood flow). Figure 39: Pressure distribution for graphene layer with 10% porosity (Case: Blood flow). Figure 16.0 Pressure distribution for graphene layer with 4.5% porosity (Case: Blood flow). Figure 16.1 Pressure distribution for graphene layer with 6.5% porosity (Case: Blood flow). Figure 16.2 Pressure distribution for graphene layer with 3.5% porosity (Case: Blood flow). Table 3 displays the results of simulating the flow of water and blood across a graphene layer of varying porosity. The critical porosity values are shaded in red. The critical porosity \(C_{\varepsilon_{p}}\) value is defined as the value of porosity of a material corresponding to which the flow of a fluid is possible across the material. For water, until 7.1% porosity, there is no flow through the layer. Hence, the solutions never converged. From 7.2% porosity, flow occurs across the sheet. For blood, until 5.6% porosity, there is no flow through the layer. Hence, the solutions never converged. From 5.7% porosity, flow occurs across the sheet. The above results are taken by considering a healthy arteriole segment that is devoid of any pathologies. Similar observations were made for blood flowing across stenosed or aneurys arteriole segments. For water flow, it has been observed that with the increase in porosity, the number of iterations and the linear error values decrease due to the increased pore capacities. The reverse is seen to happen in the case of blood due to the complexity of blood composition. The flow of water is executed just to compare the porosity values for two different fluids with different compositions. Figure 16.3 Pressure distribution for graphene layer with 4.5% porosity (Case: Blood flow). Figure 16.4 Pressure distribution for graphene layer with 6.5% porosity (Case: Blood flow). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Condition**} & \multirow{2}{*}{**Fluid**} & \multicolumn{2}{c}{**Porosity**} & \multirow{2}{*}{**DoF**} & \multirow{2}{*}{**Number of iterations**} & \multirow{2}{*}{**Linear Error**} & \multirow{2}{*}{**Linear Residue**} \\ \cline{5-6}  & & & & & & & \\ \cline{5-6}  & & \multicolumn{1}{c}{**Layer**} & & & & \\ \hline \multirow{5}{*}{Healthy} & \multirow{2}{*}{Water} & \(\mathcal{C}_{\varepsilon_{p}}=7.2\%\) & \multirow{5}{*}{2820} & 42 & \(7.5\times 10^{-12}\) & \(7.9\times 10^{-14}\) \\ \cline{3-6}  & & \multicolumn{1}{c}{} & \(10\%\) & 24 & \(4.3\times 10^{-12}\) & \(1\times 10^{-14}\) \\ \cline{3-6}  & & \multicolumn{1}{c}{} & \(\mathcal{C}_{\varepsilon_{p}}=7.2\%\) & \multirow{5}{*}{2820} & 34 & \(8.1\times 10^{-12}\) & \(2.7\times 10^{-14}\) \\ \cline{3-6}  & & \multicolumn{1}{c}{} & \(6\%\) & 22 & \(2.4\times 10^{-12}\) & \(2.6\times 10^{-14}\) \\ \cline{3-6}  & & \multicolumn{1}{c}{} & \(7\%\) & 21 & \(1.6\times 10^{-12}\) & \(6.3\times 10^{-14}\) \\ \cline{3-6}  & & \multicolumn{1}{c}{} & \(10\%\) & 14 & \(1.4\times 10^{-12}\) & \(3.4\times 10^{-14}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Linear error, linear residue, number of iterations, and the degrees of freedom (DoF) details.