## 4 Conclusions  
In this study, the impact of different types of dispersants (Na(PO\({}_{3}\))\({}_{6}\), PEG, and phosphoric ester compounds), dispersant concentrations, and abrasive concentrations on the dispersion stability of a polishing solution and the dispersibility of abrasive particles were investigated through sedimentation experiments, zeta potential measurements, and particle size analysis. Additionally, the influence of phosphoric ester compounds as dispersants on jet polishing performance was explored through micro-abrasive water jet polishing experiments. The following conclusions were drawn:  
1. The dispersion stability of the polishing solution is negatively correlated with the abrasive concentration, showing an initial increase and subsequent decrease with an increasing dispersant concentration. The impact of different dispersants on the dispersion stability of the polishing solution and dispersibility of abrasive particles is ranked as follows: phosphoric ester compounds > Na(PO\({}_{3}\))\({}_{6}\) > PEG. Particularly, at a phosphoric ester compounds concentration of 1.0 wt% and an abrasive concentration of 20 g/L, the polishing solution exhibits the most stable dispersion effect. Na(PO\({}_{3}\))\({}_{6}\), at a concentration of 0.5 wt% and abrasive concentration of 20 g/dm\({}^{3}\), performs great as well;
2. For point polishing, the optimal concentration ratio of the polishing solution is a phosphoric ester compounds concentration of 1.0 wt% and an abrasive concentration  
Figure 12: Comparison of polished surface morphology of local area before and after the addition of dispersant: (**a**) without dispersant; (**b**) 1.0 wt% phosphoric ester compounds.  
of 20 g/dm\({}^{3}\). At this concentration ratio, a smooth, regular, and symmetrical material removal profile is achieved;
3. The polishing solution with the optimal concentration ratio significantly enhances the polishing quality, leading to a substantial reduction in RMS and PV. In local polishing experiments, compared to the polishing solution without a dispersant, the reduction rate of RMS increased from 54.33% to 82.24%, and the reduction rate of PV increased from 38.84% to 68.97%.  
In summary, this study concentrated on the impact of dispersants on polishing quality but did not examine nozzle wear, which will be explored in future research.  
Conceptualization, L.L. and Y.Z.; methodology, D.J.; software, D.J.; validation, D.J., Y.Z. and L.L.; formal analysis, D.J.; investigation, Y.Z.; resources, H.Y.; data curation, Y.Z.; writing--original draft preparation, Y.Z.; writing--review and editing, D.J.; visualization, L.L.; supervision, L.L.; project administration, L.L.; funding acquisition, H.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Guangxi Bagui Scholars Project (NO. 2019A02) and Guangxi Key Laboratory of Manufacturing System and Advanced Manufacturing Technology (Grant No. 15-140-305005).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author/s.  
Thanks to all who contributed to this study.  
The authors declare no conflicts of interest.