# Rheological Performance of Bio-Char Modified Asphal with Different Particle Sizes
## 5 Results and Discussions
### Rotational Viscosity Test  
#### 5.2.1 Rotational Viscosity Analysis  
The rotational viscosities of asphalt binders before and after RTFO aging, are shown in Figure 2a,b, respectively.  
Figure 1: (**a**) Images of graphite magnified by SEM; (**b**) images of bio-char magnified by SEM.  
From Figure 2a, it is noteworthy that all the asphalt binders could satisfy the specification requirement for the rotational viscosity of no more than 3000 mPa\(\cdot\)s, at 135 \({}^{\circ}\)C. The addition of the graphite or the bio-char contributed to the increase of rotational viscosities of the asphalt binders. As the bio-char content increased, the rotational viscosities of the bio-char modified asphalts had an increasing trend. For example, the rotational viscosities of 4% GS, 2% BL, 4% BL and 8% BL increased by an average of 8.06%, 9.90%, 26.19%, and 82.81%, respectively, as compared with the control asphalt binder at 110-165 \({}^{\circ}\)C. However, the increased value was smaller when the bio-char content was lower. For example, the rotational viscosities of 2% BL and 2% BS were only higher than that of the control asphalt binder by 25 mPa\(\cdot\)s and 116.6 mPa\(\cdot\)s, respectively. These could be explained by the stiffening influence from the increasing concentration of stiff particles. The addition of bio-char or graphite increased the concentration of stiff particles in asphalt and contributed to the increase of elastic components, which accordingly increased the viscosity of the asphalt binder. The bio-char size  
Figure 2: (a) Rotational viscosities of original control, graphite modified and bio-char modified asphalts; (b) rotational viscosities of control, graphite modified and bio-char modified asphalts after RTFO aging.  
had an effect on the rotational viscosities of bio-char modified asphalt. At 135 \({}^{\circ}\)C, the viscosities of 2% BS, 4% BS, and 8% BS were higher than 2% BL, 4% BL, and 8% BL by 91.7 mPa\(\cdot\)s, 112.5 mPa\(\cdot\)s, and 25.0 mPa\(\cdot\)s, respectively (Figure 2a). This illustrated that bio-char modified asphalt binders with smaller-sized particles had higher viscosities than those with larger-sized particles. Furthermore, the bio-char modified asphalts had higher viscosities compared to the graphite modified asphalt binder. The rotational viscosities of 4% BL and 4% BS were higher than that of 4% GS, by 17.26% and 52.93%, on average, respectively. Under the same dosage, the bio-char had a higher volume and surface area than the graphite because of its lower density and porous structure. Moreover, the smaller-sized bio-char particles had a higher number of particles than the larger-sized ones, thereby, this also led to a higher surface area. The higher surface area and porous structure of bio-char led to a larger adhesion interaction in the base asphalt binder, which lowered the fluidity of asphalt binder and increased the viscosity.  
After RTFO aging (Figure 2b), all the asphalt binders had higher viscosities than the original asphalt binders, because of the oxidation of the asphalt binders [48; 49]. However, all the rotational viscosities of asphalt binders were still far less than 3 Pa\(\cdot\)s. The obvious change was that the viscosity differences of the bio-char modified asphalts, with different bio-char contents, were lower than those before the RTFO aging had. When unaged, the viscosities of 4% BS and 8% BS were higher than 2% BS by 8.44% and 29.31%, on average, respectively. But after the RTFO aging, the viscosities of 4% BS and 8% BS were higher than 2% BS by 7.03% and 20.58%, on average, respectively. This indicated that the bio-char modified asphalts had different age degrees.