# Adhesion Performance between Solid Waste and Bitumen Based on Surface Energy Theory
## 4 Experimental Program  
### Scheme  
The measurement method of the surface energy parameters of solid materials aims to use liquid reagents with known surface energy parameters to wet the solid to be tested and calculate the contact angle between the gas-liquid and solid-liquid interfaces. Equation (19) is obtained in accordance with the Young-Dupre Equation, which is expressed by Equation (18). The contact angle measured in the experiment is substituted into Equation (19), and the obtained equation sets will be solved to identify the surface energy parameters of solid materials.  
\[\gamma_{l}\cdot\cos\theta_{1}=\gamma_{s}-\gamma_{ls} \tag{18}\]  
Figure 8: Schematic of bitumen–aggregate spalling.  
\[\begin{array}{l}\gamma_{l}\cdot\cos\theta_{1}=\left(\gamma_{s}^{LW}+2\sqrt{\gamma_{s }^{+}\gamma_{s}^{-}}\right)-\left(\begin{array}{c}\gamma_{l}^{LW}+\gamma_{s} ^{LW}-2\sqrt{\gamma_{l}^{LW}\gamma_{s}^{LW}}+2\sqrt{\gamma_{l}^{+}\gamma_{l}^{ -}}-2\sqrt{\gamma_{l}^{+}\gamma_{s}^{-}}\\ -2\sqrt{\gamma_{l}^{-}\gamma_{s}^{+}}+2\sqrt{\gamma_{s}^{+}\gamma_{s}^{-}}\\ \end{array}\right)\\ \Rightarrow\frac{(1+\cos\theta_{1})}{2}\gamma_{l}=\sqrt{\gamma_{l}^{LW}\gamma_ {s}^{LW}}+\sqrt{\gamma_{l}^{+}\gamma_{s}^{-}}+\sqrt{\gamma_{l}^{-}\gamma_{s}^ {+}}\end{array} \tag{19}\]  
where: \(\theta_{1}\): Number of degrees of contact angles between the gas-liquid and solid-liquid interfaces, \({}^{\circ}\)_;_ \(l\)_: Liquids with known surface energy parameters; \(s\): Solid to be measured.  
The 70% bitumen and the SBS-modified bitumen were selected in this article as the bitumen research objects to obtain the surface energy parameters of bitumen and aggregates, and the hanging plate method was used to measure the contact angles. Limestone, glass, and ceramics were selected as the aggregate research objects, and the contact angles were measured by the sessile drop method [26]. The two measurement methods should be both tested 5 times when measuring the contact angle of each solid and each liquid, and the final result is equal to the average value of the sum of the data of five tests, and the D-values of the data of five measurements must not exceed 30%.  
The hanging plate method, which is suitable for measuring flake-shaped solids, is based on the principle that the resultant force of the substance is zero when balanced. The substance force is then analyzed, and the value of the contact angle is obtained through equation sets.  
The sessile drop method is a measurement method, based on optical image analysis, which can directly measure the contact angle of solids that cannot be made into flake, as is shown in Figure 9. The machine used for this test in this manuscript is the SL200B contact angle measuring instrument invented by the American Kono Group. The image analysis method used in the test is the tangent line method, as is shown in Figure 10. The test step is to drop the liquid, meeting the specified volume, onto the solid surface, and the software system will automatically generate a virtual circle. By adjusting the radius, horizontal line and position of the virtual circle, the virtual circle and the liquid drop will be overlapped to the maximum extent, and then the software will automatically calculate the contact angle.  
Figure 10: Tangent line method.  
Figure 9: Schematic diagram of contact angle measurement by sessile drop method.  
Ethylene glycol, formamide, and distilled water were selected as the liquid reagents, and their surface energy parameters are shown in Table 4. Each test must be performed five times to obtain the average value.