# Numerical Modelling of Erythrocyte Sticking Mechanics
## 4 Numerical Experiment  
In a numerical experiment, it is planned to study the interaction of an erythrocyte with the surface of the blood clot. The aim is to analyze the effect of fluid on the process of erythrocyte sticking. As a result, the study of the sticking process is divided into two parts. In the first part, when the influence of the liquid is partially evaluated, the drag force is not taken into account and the electrostatic double layer force is taken into account. In the second part, all the forces presented in this article acting on the erythrocyte are evaluated. The initial experimental data are presented in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Objects** & **Initial Parameters** & **Values** & **References, Sources** \\ \hline \multirow{7}{*}{\
\begin{tabular}{} \end{tabular} } & Diameter, \(d_{i}\) & 6.2 μm & [PERSON] [35] \\  & Initial interaction distance, \(a_{F=0}\) & 20 nm & [PERSON] [31] \\  & Initial velocity, \(v_{0}\) & \(-0.010783\) cm/s & [PERSON] [31] \\  & Mass, \(m_{i}\) & 28 pg (picograms) & MedialLab, Inc. [36] \\  & Density, \(p_{i}\) & 1.12 g/cm\({}^{3}\) & [PERSON] et al. [37] \\  & [PERSON]’s modulus, \(E_{i}\) & 26 kPa & [PERSON] et al. [38] \\  & [PERSON]’s ratio, \(\
u_{i}\) & 0.5 & [PERSON] et al. [39] \\  & Surface potential, \(\psi_{i}\) & \(-24\) mV & [PERSON] et al. [40] \\  & Surface charge density \(\xi_{i}\) & \(-3\) mC/m\({}^{2}\) & [PERSON] et al. [41] \\  & The adhesion force at point A, \(F_{A,diff,h=0}\) & \(-82.25\) pN (\(79\pm 3\) pN) & [PERSON] et al. [42] \\  & (between erythrocyte and fibrin) & & \\  & The adhesion force at point L, & \(-38\) pN & - \\  & \(F_{L,adh,h=0}\) (erythrocyte–fibrir) & & \\  & Adhesive dissipative energy, \(W_{adh,diss}\) & \(76\cdot 10^{-20}\) J & - \\ \hline \multirow{2}{*}{Fibrin} & [PERSON]’s modulus, \(E_{j}\) & 4 Mpa & [PERSON] et al. [43] \\  & Density, \(p_{i}\) & 1.33 g/cm\({}^{3}\) & [PERSON] et al. [44] \\ \hline \multirow{2}{*}{\
\begin{tabular}{} \end{tabular} } & Density, \(\rho_{platelet}\) & 1.067 g/cm\({}^{3}\) & [PERSON] et al. [45] \\  & [PERSON]’s modulus, \(E_{platelet}\) & 10.0 kPa & [PERSON] et al. [46] \\  & Poisson ratio, \(\
u_{platelet}\) & 0.5 & [PERSON] et al. [46] \\  & Diameter, \(d_{platelet}\) (non activated) & 3.0 μm & [PERSON] et al. [47] \\ \hline \multirow{7}{*}{
\begin{tabular}{} \end{tabular} } & PH & 7.4 & [PERSON] [48] \\  & Temperature, \(T_{temp}\) & 36.8 \({}^{\circ}\)C & [PERSON] [31] \\  & The permittivity of the free space, \(\varepsilon_{0}\) & 8.854 \(\cdot 10^{-12}\) & [PERSON] [31] \\  & Debye length, \(\lambda\) & \(\approx\) 8.0 μm & [PERSON] [41] \\  & A dielectric constant of water, \(\varepsilon\) & 74.5 & [PERSON] et al. [49] \\  & Blood flow velocity, \(v_{max,blood}^{T}\) & \(-3.0\) cm/s & [PERSON] and Yoshida [50] \\  & Blood flow velocity at \(a_{F=0}=20\) nm distance in & \(-0.010783\) cm/s & [PERSON] [31] \\  & normal direction, \(v_{5}\) & 3 cP(0.003 Pa-s) & [PERSON] et al. [51] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Initial data. The results of the experiment in the first part are presented in Figure 2a-d. The graphs show the corresponding points of the interaction process path S-L-U-A\({}^{\prime}\)-E. The values of force, displacement, and velocity at these points are given in Table 2. In the first part of the study, contact of an erythrocyte is observed in the presence of interaction with a thrombus. This is due to the weakening of the electrostatic double layer force when the erythrocyte interacts with the forming blood clot. It is assumed that the sticking process begins when the erythrocyte reaches point A\({}^{\prime}\), when the kinetic energy is not enough to detach from the interaction surface and the reloading process begins. Oscillations are observed when the movement of the erythrocyte in the sticking process oscillates to a complete stop at point E. Moreover, at this moment, the erythrocyte stops further deformation, and the force and velocity values acting in the normal direction are equal to zero.