# Development of a Partial Clustering Model of Alloy Viscosity
## 5 Conclusions  
1. A partial clustering model was obtained that includes the contribution of alloy components to its viscosity. In this model, the impact of clusters was compared with the energy barriers that can be calculated directly in formulas. This assumption can be considered as the fundamental significance of clusters for expressing viscosity, one of the most important properties of the liquid state.
2. The new partial clustering model of viscosity was tested on the experimental data as an example of _Cu-Sn_ alloy. The liquidus temperature was applied as a thermal barrier for the alloys. The high adequacy of the obtained results indicates the correctness of the proposed equation and possibility of its use based on the state diagram.
3. The new partial clustering model of viscosity can be used for different alloys (two- and three-component) and to predict the behavior of this characteristic at the high temperatures, i.e., they face problems of difficulty in accurate measurement.
4. A probabilistic interpretation of the cluster presence in a liquid can be appreciated as a contribution to the theory of the liquid state.
5. The proposed model for the temperature dependence of dynamic viscosity is already suitable for practical application, particularly for extrapolation to temperatures above 1800 K. This temperature range is challenging to achieve experimentally, yet it is reliably represented in the model (13). Additionally, technological verification of the proposed model is feasible for viscosity-based control in the ultra-high temperature regime.
6. The relationship of the concept of viscosity in the approximation of the Arrhenius physico-chemical model is revealed when comparing the activation energy of a viscous flow with the chaotic energy according to the partial clustering model, taking into account the thermal barrier along the liquidus line. This gives the proposed model fundamental importance.  
Conceptualization, V.M., A.M. and A.I.; methodology, V.M. and A.M.; software, A.M. and A.I.; validation, V.M., A.M. and S.K.; formal analysis, A.I. and V.K.; investigation, V.M., A.M. and S.K.; resources, A.M., V.K. and L.B.; data curation, A.M., L.B. and S.A.; writing--original draft preparation, V.M., A.M., A.I. and L.B.; writing--review and editing, V.M., A.M., A.I., S.K., V.K., L.B. and S.A.; visualization, S.K., V.K., L.B. and S.A.; supervision, V.M., A.I. and S.K.; project administration, V.M., A.I., A.M. and S.K.; funding acquisition, A.I., S.K., V.K. and S.A. All authors participated in writing the paper. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Committee of Science of the Ministry of Science and Higher Education of the Republic of Kazakhstan, grant number BR24993020.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The author declares that there is no conflict of interests regarding the publication of this manuscript. In addition, the ethical issues, including plagiarism, informed consent, misconduct, data fabrication and/or falsification, double publication and/or submission, and redundancies have been completely observed by the authors.