## 4 Discussion  
In this study, hydrothermal emulsification allowed us to form an O/W emulsion made of a monomer to obtain polymer particles initiated through a polymerization reaction by AIBN. The size of O/W emulsion was comparable to the size of the polymer particles, for which the O/W emulsions acted as the template. Thereafter, the coating of WTBs was tested by using the polymer particles. The size of the polymer particles likely determined the water repellency, as well as the hydrophobicity at the surface, which is herein discussed. The size control of the polymer particles is first discussed. As mentioned in Section 3.1.1, the final size of the polymer particles was likely to be affected by the flow rate ratio of Solutions I and II. This was because of the controllable size distribution of O/W emulsions as a template for the polymer particles, as shown in Figure 2e). 2D simulations giving the velocity vector around the T-junction [41] demonstrated that the fluid was squeezed by the strong shear stress occurring at the surface of the fluid injected through the T-junction. The strength of the vortex field depended on the flow rate ratio of Solutions I and II. A large flow rate ratio such as 13 and 14 might induce weak shear stress around the T-junction, making the O/W emulsion reduce its size. The size of the polymer particles can qualitatively affect the surface roughness (Figure 4). The formation of terraces on the surface enables us to give the surface roughness. From the plots of the mean diameter of the polymer particles and their contact angles (Figure 6a-d), a coating of polymer particles of small size was subject to yield a high contact angle; i.e., the contact angle limit of WTBs coated by polymer particles was strongly correlated with the hydrophobicity of the monomer (logP value), as shown in Figure 6e. However, the correlation in Figure 6e depends on the method of surface modification. This resulted from the hydrophobicity of the polymers used as polymer particles. Alternatively, a decrease in the size of the polymer particles elevated the contact angle up to 120 deg, regardless of the type of polymer, strongly suggesting the contribution to the contact angle of the surface roughness originated from the polymer particles adsorbed on the surface of the WTBs. It is noted that the contact angle should be, ideally, negatively correlated with the surface roughness [42; 43]. Next, how the surface roughness of WTBs coated with polymer particles was generated is discussed. As seen in Figure 4, PS\({}_{30}\) gave a flattened surface as compared with the surface coated by PS\({}_{800}\). This trend was in agreement with a report that a coating of polystyrene latex particles with diameters of 309 and 2106 nm induced smooth and rough surfaces, respectively [29]. The softening temperature of polymers, \(T_{\rm s}\), is also a key factor. The \(T_{\rm s}\) value for each polymer is  
Figure 7: Long-term stability of WTBs. (**a**) WTBs modified with PS of different diameters and (**b**) four kinds of polymer particles. (**c**) Remaining ratio of WTBs. Initially, ten WTBs were prepared. Standard errors were calculated from four different experiments for each WTB. summarized in Table 1. The drying temperature for a coating of WTBs with polymer particles was set 100-120 \({}^{\circ}\)C, which was higher than that of lignin (\(T_{\rm s}\sim\) 60 \({}^{\circ}\)C) and lower than that of cellulose (\(T_{\rm s}\sim\) 240 \({}^{\circ}\)C). The \(T_{\rm s}\) values for the polymers used in this study were lower than the drying temperature, as seen in Table 1. It was considered that polymers other than cellulose became softened during the drying process. It was considered that the convective self-assembly of polymer particles occurred in the drying process. The dispersion state originating from the convective self-assembly appeared to depend on the volume fraction of the polymer particles (Figure 4f-h).