# Numerical Modelling of Erythrocyte Sticking Mechanics
## 4 Numerical Experiment
\begin{table}
\begin{tabular}{c c c c} \hline
**Objects** & **Initial Parameters** & **Values** & **References, Sources** \\ \hline Arteriole & Diameter, \(d_{blood\ vessel}\) & \(100\) μm & [PERSON] and Yoshida [50] \\ Surface potential, \(\psi_{j}\) & \(-48.3\) mV & [PERSON] et al. [52] \\ \hline Blood clot & Poisson ratio, \(\
u_{j}\) & \(0.5\) & [PERSON] et al. [53] \\ \hline Simulation & Time step & \(5\) ps (picoseconds) & - \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 2: Interaction of an erythrocyte with a blood clot (fibrin and platelets). Without drag force. Dependence of the normal force on displacement (**a**) and time (**b**); dependence of displacement (**c**) and velocity (**d**) on time. In the process of sticking, during oscillations, the values of the normal velocity change; positive and negative values are observed. Such obtaining results are likely if, for example, a dry particle or a drop of water interacts with a certain surface in the air. It should be noted that oscillations of an ultrafine object are difficult to physically detect, especially if the deformation occurs only in the contact zone ([PERSON] and Kruggel-Emden [34]). The results of the second part of the experiment are presented in Figure 3a-d. The graphs show the corresponding points of the interaction process path S-L-U(E); the values of force, displacement, and velocity at these points are given in Table 2. In the case of such an interaction, the drag force is considered. The results obtained (Figure 3) are completely different from Figure 2. Not only do the achieved values of forces, displacements, and velocities differ, but so does the behavior of the erythrocyte itself. During oscillations, the sticking process is absent. The movement of an erythrocyte stops when it is deformed at the point E on the corresponding surface. The values of force and velocity (Figure 3) of the adhered cell, as in Figure 2, are equal to zero. Moreover, when comparing the results (Figures 2 and 3), it can be noted that until the erythrocyte movement stops under the action of the drag force (Figure 3), the interaction time lasts longer. In the case of sticking (Figure 3), the velocity value remained negative until it decreased and reached zero. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Parameter**} & \multicolumn{6}{c}{**Values at Certain Points**} \\ \cline{2-7}  & & **S** & **L** & **U** & **A\({}^{\prime}\)** & **E** \\ \hline Without & \(t\), \(\mu\)s & 0 & 11.59687 & 15.120995 & 19.679315001 & \(\approx\)150 \\ drag & \(F\), pN & \(-\)5.78593 & \(-\)34.27663 & 104.69451942 & \(-\)66.7513884 & 0 \\ force & \(h\), nm & \(-\)20 & 0 & 14.3479743 & 1.806173644 & 7.71084038 \\  & \(v\), mm/s & \(-\)0.10783 & \(-\)4.6735475 & 0 & 0 & 0 \\ \hline With drag & \(t\), \(\mu\)s & 0 & 107.64 & \(\approx\)250 & - & \(\approx\)250 \\ force & \(F\), pN & \(-\)5.78593 & \(-\)0.18155 & 0 & - & 0 \\  & \(h\), nm & \(-\)20 & 0 & 7.562478 & - & 7.562478 \\  & \(v\), mm/s & \(-\)0.10783 & \(-\)0.30232 & 0 & - & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Properties of the movement of an erythrocyte during interaction at certain points S-L-U-A\({}^{\prime}\)-E.  
Figure 3: Interaction of an erythrocyte with a blood clot (fibrin and platelets) with drag force. Dependence of the normal force on displacement (**a**) and time (**b**); dependence of displacement (**c**) and velocity (**d**) on time. During the sticking process, adhesion effects are quickly suppressed but sufficient for the erythrocyte to approach the surface and adhere. It was also observed that the unloading process did not occur; point U, which should describe the beginning of unloading, coincided with point E, indicating the end of the erythrocyte sticking process. If the interaction of an erythrocyte in air is modeled, then point U must coincide with the maximum force achieved.