# Phase Separation Study on the Storage of Technically Specification Natural Rubber Modified Bitumen
## 3 Results and Discussion
### Determination of Phase Separation Flow Velocity in TSNR-Modified Asphalt  
Asphalt modified with TSNR exhibits storage instability at high temperatures. Modified asphalt stored at high temperatures undergoes phase separation influenced by gravity in incompressible conditions. Furthermore, high temperatures will stretch the intermolecular bonds, reducing viscosity. The density and viscosity of the two components have a significant influence on phase separation rate. To simulate the phase separation that occurs in TSNR-modified bitumen at storage temperature, a fluid flow model with incompressible Navier-Stokes equations combined with a phase field model is used [6; 53]. This simulation of gravity-driven flow in TSNR-modified bitumen makes several assumptions with its incompressible Navier-Stokes equations. First, the TSNR-modified bitumen is assumed to be a Newtonian fluid with a storage temperature ranging from 130 to 180 \({}^{\circ}\)C. This assumption may be correct if the TSNR content is not too high and the temperature is high enough [6; 53]. The TSNR content used in this study ranged between 8 and 12%. Visual observations reveal that the fluid or modified asphalt exhibits the properties of a Newtonian fluid at temperatures ranging from 130 to 180 \({}^{\circ}\)C. In addition, the equation assumes that the flow of modified bitumen fluid driven by gravity at storage temperature is laminar. Modified bitumen can be assumed to be laminar flow because it has no input or output flow, is not pressurized, and has a relatively high viscosity [6; 53]. Before starting the TSNR-modified asphalt phase separation simulation, several parameters must be calculated manually, namely, the phase separation rate and Reynolds number (nRe). The phase separation rate needs to be known to determine the value of the mobility tuning parameter (\(\chi\)), and the Reynolds number (nRe) is used to determine the model used. Equation (1) can be used to calculate the phase separation rate of polymer-modified asphalt influenced by gravity during the storage period of modified asphalt. Meanwhile, the calculation for Reynolds number (nRe) to determine the type of flow that occurs in the phase separation of modified asphalt can be used in Equation (2). The assumptions used to calculate the phase separation rate and nRe are the TSNR particle size and asphalt particle diameter (D\({}_{\text{p}}\)), which are assumed to be the same at 100 \(\upmu\)m, and acceleration by gravity (g) of 9.8066 m/s\({}^{2}\). TSNR particle density TSNR (\(\rho_{p}\)), asphalt density (\(\rho\)), mixture density (\(\rho_{m}\)), TSNR particle viscosity (\(\mu_{p}\)), asphalt viscosity (\(\mu\)), and mixture viscosity (\(\mu_{m}\)) were obtained from direct measurement results which can be seen in Table 4. Meanwhile,\(\psi_{p}\) is a dimensionless number with the value \(1/10^{1.82\ (1-\epsilon)}\) as a correction factor, and \(\epsilon\) is the volume fraction of the mixture. The calculation results of the TSNR and nRe phase separation rates can be seen in Table 4.  
\[v=\frac{gD_{p}^{2}\big{(}\rho_{p}-\rho\big{)}}{18\mu}\ \Big{(}\epsilon^{2} \psi_{p}\Big{)} \tag{1}\]  
\[NRe=\frac{D_{p}v\rho_{m}}{\mu_{m}\epsilon}=\frac{gD_{p}^{3}\big{(}\rho_{p}- \rho\big{)}\rho_{m}\epsilon\psi_{p}^{2}}{18\mu^{2}} \tag{2}\]Table 4 shows that the theoretical phase separation rate of TSNR in modified bitumen decreases as the TSNR content increases. Increasing the amount of TSNR in modified bitumen also increases its viscosity, resulting in increased phase stability between components [41; 43; 62]. Theoretically, the lowest phase separation rate at 160 \({}^{\circ}\)C was obtained when 12% TSNR was added, which was 2.4693 \(\times\) 10\({}^{-6}\) m/s. However, experimental results show that phase separation increases after the addition of 12% TSNR. This is because the theoretical calculation using Stokes law does not consider the coalescence and flocculation phenomena that affect the formation time of density and viscosity differences between components.