## 2 Materials and Methods  
### Theoretical Analysis on the Anti-Soil-Adhesion Mechanism of the Unsmooth Surface  
Studies [5] have shown that the nonsmooth surfaces of soil animals, whether convex domes or scaly, have a corrugated cross section (Figure 1), which is the common feature. Here, \(\phi\) is the apparent contact angle; \(\theta\) is the intrinsic contact angle; and \(\alpha\) is the slope angle of the unsmooth wave curve at the rim of the drop (the rim is the profile of wave in the cross section); \(S_{0}\) and \(h_{0}\) are the period and the amplitude of the wave, respectively; \(S\), \(h\), and \(o\) are the axes and the origin of the cylindrical coordinates, respectively; \(p_{1}\) and \(p_{2}\) are the points of intersection between each ringlike strip of the gas-liquid interface and its two adjacent waves; \(p_{0}\) is the ridge of the wave near the origin in the above two adjacent waves; \(d_{1}\) and \(d_{2}\) are the distances from \(p_{1}\) to \(p_{0}\) and from \(p_{2}\) to \(p_{0}\), respectively; \(S_{0}\) is the period of the wave; \(R\) is the radius of the interface between the liquid drop and the unsmooth surface; and \(S\), \(h\), and \(o\) are the axes and the origin of the cylindrical coordinates, respectively. As [PERSON] [30] described, the equation for the cross section of the unsmooth surface through the origin is  
\[h=h_{0}\cos\frac{2\pi S}{S_{0}} \tag{1}\]  
Figure 1 indicates that  
\[\tan\alpha=\frac{dh}{dS} \tag{2}\]  
The conditions for forming a composite interface between a liquid and a nonsmooth surface (Figure 1) are [31] as follows:  
\[\theta=\phi-|\alpha| \tag{3}\]  
where \(\alpha\) is the slope angle of the unsmooth wave curve at the rim of the drop. Hence  
\[\alpha=\arctan(-\frac{2\pi h_{0}}{S_{0}}\sin\frac{2\pi S}{S_{0}}) \tag{4}\]  
Equation (4) suggests that the larger the value of \(h_{0}\)/\(S_{0}\) is, the larger the value of \(|\alpha|\); therefore, given the relationship between \(\theta\) and \(|\alpha|\), the larger the value of \(|\alpha|\) is, the smaller the value of \(\theta\). Hence, for the unsmooth surface, the larger the value of \(h_{0}\)/\(S_{0}\) is, the larger the apparent contact angle of liquid drop \(\theta\), the stronger their hydrophobicity, the easier the formation of composite interface between the soil and the unsmooth surfaces, and the better the ability to reduce soil adhesion. These properties indicate that the larger the value of \(h_{0}\)/\(S_{0}\) is, the easier the formation of the composite interface. Figure 1 indicates that, after the composite interface forms, the real contact area between the soil and the unsmooth cuticles will decrease, and some of the contact area is replaced by the interface between the soil and the gas. Clearly, soil adhesion will decrease greatly [30]. Figure 1: Interfaces between an unsmooth surface and drops of liquid (and soil): a formed composite interface [30]. According to the water film tension theory of soil adhesion [32], the formation of the composite interface can significantly reduce the contact area between the soil's water and the nonsmooth surface on the contact surface, which is beneficial to the antiadhesion and drag reduction of soil animals. When the composite interface forms, the apparent contact angle \(\theta\) and the intrinsic contact angle \(\theta\) can be expressed as [33]:  
\[\cos\phi=r^{\prime}\cos\theta-\eta \tag{5}\]  
where \(r^{\prime}\) is the ratio of the real contact interface area between the soil and the rough surface to the projected area of the rough surface and \(\eta\) is the ratio of the contact interface area between the liquid and the gas under the liquid drop to the projected area of the rough surface. Figure 1 shows that the shape of the gas-liquid interface is a ringlike strip. Each ringlike strip interface and its two adjacent waves intersect at \(p_{1}\) and \(p_{2}\), and the ridge of the adjacent wave near the origin is denoted by \(p_{0}\).