# Phase Separation Study on the Storage of Technically Specification Natural Rubber Modified Bitumen
## 3 Results and Discussion
### Phase Separation Simulation of TSNR-Modified Asphalt  
COMSOL Multiphysics version 5.5.0 now includes the previously described phase separation of TSNR-modified bitumen. The phase separation of gravity-driven TSNR-modified bitumen can be simulated using a fluid flow model with incompressible Navier-Stokes equations and a phase field model. The Navier-Stokes equations for laminar flow are calculated using the fluid flow model with two-phase flow types (laminar flow) in conjunction with the phase field model in COMSOL Multiphysics version 5.5.0. Numerical simulations were carried out on a 9 \(\times\) 18 cm domain. The dimensions were chosen to correspond to the diameter and height of the storage stability testing bottle. Furthermore, the domain is divided into three sections, representing the top, middle, and bottom. Figure 11 shows that the meshing used is free triangular with an extra fine size. The boundary condition is that the velocity of the fluid or TSNR-modified asphalt is set to be zero (v = 0), and it is assumed that there is no pressure change during the storage time. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**No**} & \multirow{2}{*}{**TSNR Content (\%)**} & \multirow{2}{*}{**Temperature (\({}^{\circ}\)C)**} & \multicolumn{2}{c}{**Density, \(\rho\) (kg/m\({}^{3}\))**} & \multicolumn{2}{c}{**Viscosity, \(\mu\) (Pa.s)**} & \multirow{2}{*}{**Phase Separation**} & \multirow{2}{*}{**nRe (10\({}^{-5}\))**} \\ \cline{4-4} \cline{6-7}  & & & **Asphalt** & & & **TSNR** & & **Rate, v (10\({}^{-6}\) m/s)** & \\ \hline
1 & 8 & 160 & 1034.670 & 868.560 & 0.151 & 0.517 & 3.3206 & 1.6111 \\
2 & 10 & 130 & 1034.670 & 868.560 & 0.640 & 0.871 & 0.6756 & 0.0561 \\
3 & 10 & 160 & 1034.670 & 868.560 & 0.151 & 0.517 & 2.8639 & 1.0093 \\
4 & 12 & 160 & 1034.670 & 868.560 & 0.151 & 0.517 & 2.4693 & 0.6591 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Phase separation rate and nRe for asphalt and TSNR mixtures. In the simulation of modified asphalt phase separation influenced by gravity, it is important to ensure that the operating conditions are at a temperature of 160 \({}^{\circ}\)C and activate the gravity option in the laminar flow settings. In the phase field settings, to determine the parameter controlling interface thickness, the assumption is that the value is half the maximum mesh size (h\({}_{\text{max}}\)/2). If this value is too small, it may cause numerical instability; if it is too large, the interface motion is not captured properly [64]. In running phase separation simulations, the phase field model requires mobility parameters (mobility tuning parameters). Mobility parameters describe the rate of movement of components contained in the system. In this study, the mobility parameter describes the movement of the components in the modified asphalt. Too small a value of the mobility parameter leads to numerical instability. A good initial estimate for the mobility parameter is as follows:  
\[\text{\emph{parameter mobility tuning}}\left(\chi\right)=\left(\frac{\frac{4}{3} }{\sqrt{2}}\right)\left(v_{max}\sigma\right) \tag{3}\]  
It is known that \(v_{max}\) is the maximum speed of phase separation between the components, and \(\sigma\) is the surface tension of the modified asphalt [64]. Table 4 shows the physical properties of asphalt and TSNR components, such as viscosity and density at storage temperature, and the phase separation velocity for TSNR-modified asphalt is calculated. Equation (3) can be used to calculate the phase field model's mobility parameters based on the calculated phase separation speed. The component parameters used in this simulation are shown in Table 5.  
The parameters in Table 5 are used in the simulation with COMSOL Multiphysics.