## 4 Wettability
### The Effect of Surface Roughness on Wettability
Some scholars studied the relationship between wettability and polymers with a different surface roughness, but some results were also contradictory. Figure 8: Relationship between contact angle and different surface roughness values of ((**a**,**b**) [60]) ultra-low-ash coal. Figure 9: Effect of surface roughness value on wettability of apatite and dolomite in presence of NaOL (\(3\times 10^{-4}\) mol/L) [24]. [PERSON] et al. [28] investigated the effect of surface roughness (created by polishing and abrasion and measured using profilometry) on the wetting behavior of at least 12 different commercial polymers. They concluded that roughness levels below 100 nm had no effect on the surface wettability. However, they found that an average roughness above 100 nm increased the contact angle for surfaces with contact angles greater than 86\({}^{\circ}\) (relatively hydrophobic surface) and decreased the contact angle for surfaces with contact angles below 60\({}^{\circ}\) (relatively hydrophilic surface). They asserted that roughness had no effect on surfaces with contact angles in the range of 60-86\({}^{\circ}\). This finding is supported by other researchers [123,124], who explained that for surfaces with a roughness of less than 100 nm, the chemical heterogeneity and composition were the dominant factors influencing surface behavior. [PERSON] et al. [125] also reported that a surface roughness in the range of 5 to 15 \(\upmu\)m did not affect the contact angle of glass beads (as determined by the Washburn method). This method is based on the principle of capillary action, and the wettability of porous materials or powders can be determined by measuring the penetration rate of liquid in capillary tubes or porous media. Conversely, [PERSON] et al. [57] stated that any nanoscopic roughness on hydrophobic particle surfaces should enhance flotation. A similar result was reported by [PERSON] et al. [126], who found that an increase in surface roughness from 6 to 13 nm increased the contact angles of hydrophobic PTFE (poly-tetrafluoroethylene) surfaces. [PERSON] and [PERSON] [127,128] observed that the static contact angle increased from 99.6\({}^{\circ}\) to 128.8\({}^{\circ}\) as the surface roughness of Teflon plates increased from below 1 \(\upmu\)m to 100 \(\upmu\)m (modified by abrasive papers). Additionally, [PERSON] et al. [108] investigated the roughness of vacuum-coated PTFE by an AFM and concluded that even a nanometer-level surface roughness (\(\sim\)80 nm) significantly affected the wettability of the surface. Numerous researchers have also explained the mechanisms and analyzed the reasons why surface roughness improves the hydrophobicity of the hydrophobic surfaces and hydrophilicity of the hydrophilic surfaces, which can be mainly divided into several points as follows. (1) A rough surface increases the effective contact area of the solid-liquid interface, which is conducive to the wetting of water on the hydrophilic surface; the valleys and gutters cause the edges of water droplets to get stuck, and water on the hydrophobic surface cannot penetrate through valleys and scratches, increasing the contact angle [129]. (2) A certain amount of air may be entrained in the tiny grooves and pits on the hydrophobic rough surface before the contact of solid particles with water, and an increasing surface roughness leads to higher air surface percentages [130,131,132]. The air that remains on the particle surface is difficult for the liquid to remove, which results in a bridging effect during particle-bubble interactions in flotation, particularly with hydrophobic particles [133]. (3) A higher surface roughness exposes a larger effective area and more active sites on particle surfaces due to an increased specific surface area. This results in a greater adsorption density of collectors and activators on the surface, ultimately enhancing hydrophobicity and increasing the contact angle [3,38,41,134,135]. Numerous studies have explored the relationship and mechanism between surface roughness and wettability.