## 4 The Effect of Wettability on the Collapsing Bubble near the Solid Surface  
In this section, the effect of wettability on the collapsing bubble near the solid surface may be studied by comparing the shape of the bubble and collapsing time. The parameter \(\lambda_{0}\) in Figure 3 is set as 1.0, 1.1 and 1.2, respectively to study the bubble near the solid surface. The contact angle \(\theta\) of the hydrophobic and hydrophilic surfaces is set as \(26.87^{{}^{\prime\prime}}\), \(50.93^{{}^{\circ}}\), \(91.50^{{}^{\circ}}\), \(133.32^{{}^{\circ}}\) and \(158.84^{{}^{\circ}}\), respectively. The other parameters are the same as those described in Section 3.2. The discussion about the results of the simulation is divided into three parts. In the first part, we investigate the density evolution of the collapsing cavitation bubble. Secondly, the time of the collapsing cavitation bubble with different wettability is compared. Finally, the effect of wettability on the density, pressure and velocity distribution of the collapsing bubble near the solid surface is discussed. Figure 6 shows the density evolution of the collapsing cavitation bubble with the parameter \(\lambda_{0}\) set as 1.0. Each row represents the every wettability of the solid surface. The evolution of the collapsing cavitation bubble includes the density distribution when the time steps are 500 and 600. The density distribution of the collapsing bubble is also included in the evolution. In Figure 6, the cavitation bubble sticking to the surface collapses from the pie shape to the bowl shape. There was a high-density region on the bubble. We found that the profile evolutions of cavitation bubbles were almost identical under different hydrophilicities--that is, hydrophilicity almost does not affect the collapsing process of cavitation bubbles. However, there are some changes when the wettability of the surface is hydrophobic. With the increase of the hydrophobicity, the bottom of the cavitation bubble spreads at the surface in a wider range. In the same time step, the size of the cavitation bubble became smaller when the hydrophobicity was stronger. It also means the hydrophobicity accelerated the evolution of the cavitation bubble compared to hydrophilicity. The solid  
Figure 6: The density evolution of the collapsing cavitation bubble with \(\lambda_{0}=1.0\). surface had a retarded effect in the fluid system, which was similar to the Poisson flow effect. When the cavitation bubbles collapsed (volume reduction), the fluid flow and velocity in the direction of the solid surface and the fluid area above the bubbles are different, respectively. Then asymmetry occurs. The collapsing time of the cavitation bubble is shown in Figure 7. The hydrophobic solid surface obviously affected the collapsing time of the cavitation bubble. With the hydrophobicity being stronger, the collapsing time was shorter. Compared to hydrophobicity, hydrophilicity had little effect on the collapsing time. The collapsing time was shorter when the parameter \(\lambda_{0}\) was larger. Figure 8 shows the density and pressure distribution of the collapsing cavitation bubble. The left part of the small graph represents the density distribution and the right part represents the pressure distribution (Figure 8). Each column represents the different wettabilities, and each row represents the collapsing cavitation bubble near the solid surface with different \(\lambda_{0}\). Firstly, unlike the bubble adhesive on the surface, the collapsing cavitation bubble near the solid surface becomes small in size. The high-density region above the bubble becomes small, but the value  
Figure 8: The density and pressure distribution of the collapsing cavitation bubble. Figure 7: Collapsing time with a different contact angle. of the region becomes high when the hydrophobicity of the surface increases. Another phenomenon is that there are some new arch-like cavitation bubbles generated adhesively to the solid surface when the wettability of the surface is hydrophobicity.