{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T18:49:58Z","timestamp":1780080598811,"version":"3.54.0"},"reference-count":32,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T00:00:00Z","timestamp":1762819200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"technological innovation and application development in Chongqing","award":["CSTB2023TIAD-KPX0018"],"award-info":[{"award-number":["CSTB2023TIAD-KPX0018"]}]},{"name":"Shanghai Hansi Industrial Co.","award":["H20250293"],"award-info":[{"award-number":["H20250293"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The synthesis of high-performance adhesives imposes stringent requirements on the design of stirred reactors: simultaneous achievement of efficient mixing and minimal energy dissipation in highly viscous media remains the principal challenge. In this study, computational fluid dynamics (CFD) was employed to solve the Navier\u2013Stokes equations for the high-viscosity epoxy system and numerically simulating the flow fields of four representative reactor configurations across a prescribed range of rotational speeds. Specifically, the four representative reactor configurations were (i) single-serrated shaft, (ii) eccentric single-serrated shaft, (iii) uniaxial single-blade paddle combined with a single-serrated dual-axis assembly, and (iv) biaxial single-blade paddle coupled with a single-serrated triaxial assembly. The mixing performance was quantitatively assessed by systematically comparing the evolution of mixing speed, vorticity fields, restricted power consumption, and mixing time across a range of rotational speeds. The results demonstrated that the synergistic deployment of an eccentric impeller and a differential-speed single-propeller shaft effectively disrupted the axisymmetric flow pattern, compressed the chaotic isolation zones, and intensified both axial exchange and global chaotic mixing. Among the configurations examined, the uniaxial single-propeller\u2013single-serrated biaxial arrangement reduced the mixing time by 13.43% and cut the specific energy consumption by approximately 58.32%, thereby attaining markedly higher energy efficiency. This research will provide guidance for the study of efficient mixing of adhesives.<\/jats:p>","DOI":"10.3390\/sym17111932","type":"journal-article","created":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T10:56:27Z","timestamp":1762858587000},"page":"1932","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["CFD-Simulation-Based Multi-Axial Differential Mixing Enhancement Study for High-Viscosity Adhesives: From the Perspective of Breaking the Symmetry of the Flow Field"],"prefix":"10.3390","volume":"17","author":[{"given":"Bin","family":"He","sequence":"first","affiliation":[{"name":"College of Chemistry and Chemical Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Long","family":"Fan","sequence":"additional","affiliation":[{"name":"College of Chemistry and Chemical Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xurong","family":"Teng","sequence":"additional","affiliation":[{"name":"College of Chemistry and Chemical Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Facheng","family":"Qiu","sequence":"additional","affiliation":[{"name":"College of Chemistry and Chemical Engineering, Chongqing University of Technology, Chongqing 400054, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-3716-2123","authenticated-orcid":false,"given":"Renlong","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Chemistry and Chemical Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,11]]},"reference":[{"key":"ref_1","unstructured":"Ebnesajjad, S., and Landrock, A.H. (2015). Front-matter. Adhesives Technology Handbook, Elsevier."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Wu, H., Wen, T., Ding, Q., Zhang, J., Du, G., Charrier, B., Essawy, H., Pizzi, A., Yuan, Z., and Zhou, X. (2025). A sustainable adhesive via one-pot simple preparation derived from bio-sourced phytic acid and corn starch for green wood panels: Ideal bonding performance and ultra-high flame retardancy. Chem. Eng. J., 508.","DOI":"10.1016\/j.cej.2025.161026"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.procir.2014.06.128","article-title":"Adhesive Bonding of Attachments on Alternate Car Shell Surfaces in Automotive Final Assembly Lines","volume":"18","author":"Papadakis","year":"2014","journal-title":"Procedia CIRP"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Poddar, A.K., Patel, S.S., Kumar, A., Patel, H.D., and Satyanarayana, B. (2025). Characterization of electrolytically developed copper filled epoxy adhesive for space applications. Hybrid Adv., 8.","DOI":"10.1016\/j.hybadv.2024.100362"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Qi, J., Luo, T., Yu, J., Wang, C., Chu, F., and Wang, J. (2024). Controllable structure, super adhesion, multifunctional, conductive pressure-sensitive adhesive for electronic skin: Enhancing cohesion by cellulose-derived covalent crosslinking. Chem. Eng. J., 499.","DOI":"10.1016\/j.cej.2024.156561"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Kumari, N., Chaturvedi, V., and Mishra, S. (2025). A comprehensive review on multifunctional adhesives\/bio adhesives and its applications. Int. J. Adhes. Adhes., 140.","DOI":"10.1016\/j.ijadhadh.2025.103987"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jiec.2015.03.026","article-title":"Synthesis and application of epoxy resins: A review","volume":"29","author":"Jin","year":"2015","journal-title":"J. Ind. Eng. Chem."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Kang, Y., Zhao, Y., Feng, X., Fang, J., Shui, L., Xin, M., and Hao, C. (2024). Adhesive and rheological properties of Polyisobutylene-based adhesives with different white carbon black fillers. Int. J. Adhes. Adhes., 133.","DOI":"10.1016\/j.ijadhadh.2024.103755"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Xiong, Y., Wu, Z., Xi, X., Li, C., Lei, H., Chen, Z., and Du, G. (2025). Modification and preparation of a bio-based Jatropha curcas L. wood adhesive with bonding strength and water-resistance by oxidation method. Int. J. Adhes. Adhes., 138.","DOI":"10.1016\/j.ijadhadh.2024.103921"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Balbinot, G.d.S., Leitune, V.C.B., Montenegro, S.D., and Collares, F.M. (2025). Silver core-shells particles as antibacterial filler for adhesive resins. Int. J. Adhes. Adhes., 138.","DOI":"10.1016\/j.ijadhadh.2024.103916"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Echarri-Giacchi, M., and Mart\u00edn-Mart\u00ednez, J.M. (2023). Structural and adhesion properties of waterborne polyurethane adhesives containing nanosilica dispersion obtained with different physical mixing procedures. Int. J. Adhes. Adhes., 123.","DOI":"10.1016\/j.ijadhadh.2023.103342"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"McGlasson, A., Rishi, K., Beaucage, G., Narayanan, V., Chauby, M., Mulderig, A., Kuppa, V.K., Ilavsky, J., and Rackaitis, M. (2019). The effects of staged mixing on the dispersion of reinforcing fillers in elastomer compounds. Polymer, 181.","DOI":"10.1016\/j.polymer.2019.121765"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Gao, Z., Wang, J., Feng, L., Gu, X., Duan, J., and Zhang, C. (2022). Flow-accelerated polycondensation reaction to prepare rigid rodlike poly(p-phenylene-cis-benzobisoxazole). Chem. Eng. Process.-Process Intensif., 176.","DOI":"10.1016\/j.cep.2022.108972"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Gu, D., Yang, H., Song, Y., Wen, L., Liu, S., and Yao, T. (2025). Design of impeller blades for fluid laminar mixing in an unbaffled stirred reactor. J. Taiwan Inst. Chem. Eng., 171.","DOI":"10.1016\/j.jtice.2025.106077"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Li, A., Yao, Y., Zhang, X., Wan, Y., Li, P., Wang, Y., Tao, C., and Liu, Z. (2024). Using CFD and machine learning to explore chaotic mixing in laminar diameter-transformed stirred tanks. Chem. Eng. J., 499.","DOI":"10.1016\/j.cej.2024.156201"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"5931","DOI":"10.1021\/acs.iecr.4c00195","article-title":"Numerical Simulation of Hydrodynamics and Mixing Characteristics of High-Viscosity Non-Newtonian Fluid in Twin-Shaft Kneaders","volume":"63","author":"Shuai","year":"2024","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Wang, S., Meng, T., Cen, S., Liu, P., Wang, Y., Qin, S., Wang, Y., and Liu, Z. (2024). Hydrodynamic intensification and interfacial regulation strategy for the mixing process of non-Newtonian fluids. Chem. Eng. J., 493.","DOI":"10.1016\/j.cej.2024.152691"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Meng, T., Yang, J., Wang, S., Wang, Y., Qin, S., Wang, Y., Tao, C., Zhang, Q., and Liu, Z. (2024). Multi-shaft stirred reactors mixing efficiency: Rapid characterization strategy based on chaotic attractors. AIChE J., 70.","DOI":"10.1002\/aic.18510"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Torotwa, I., and Ji, C. (2018). A Study of the Mixing Performance of Different Impeller Designs in Stirred Vessels Using Computational Fluid Dynamics. Designs, 2.","DOI":"10.3390\/designs2010010"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.cjche.2021.11.008","article-title":"Isolated mixing regions and mixing enhancement in a high-viscosity laminar stirred tank","volume":"41","author":"Kang","year":"2022","journal-title":"Chin. J. Chem. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"He, B., Guo, L., Liu, R., Qiu, F., Quan, X., and Wang, J. (2022). CFD Simulation of a New Dynamic-Static Stirred Model and Its Application in the Leaching Process of Chromite. Int. J. Chem. Eng., 2022.","DOI":"10.1155\/2022\/8705274"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Kurniawan, A., Supit, S., Riyadi, F.A., Alam, M.Z., and Muharam, Y. (2024). Design of a stirred batch reactor with scale-up to ensure efficient degumming process at a larger scale. Results Eng., 23.","DOI":"10.1016\/j.rineng.2024.102588"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Thakur, H., Verma, N.K., Dhar, A., and Powar, S. (2023). Investigation of continuous stirred tank reactors for improving the mixing in anaerobic digestion: A numerical study. Results Eng., 19.","DOI":"10.1016\/j.rineng.2023.101317"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3877","DOI":"10.1016\/j.ces.2008.04.018","article-title":"CFD simulation of liquid-phase mixing in solid\u2013liquid stirred reactor","volume":"63","author":"Kasat","year":"2008","journal-title":"Chem. Eng. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Peng, Y., Zhao, T., Miao, J., Kong, L., Li, Z., Liu, M., Jiang, X., Zhang, Z., and Wang, W. (2024). Evaluation framework for bitumen-aggregate interfacial adhesion incorporating pull-off test and fluorescence tracing method. Constr. Build. Mater., 451.","DOI":"10.1016\/j.conbuildmat.2024.138773"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zheng, C., Zhang, M., Qiu, S., Li, H., Wang, T., and Wang, H. (2021). Numerical simulation and experimental investigation of gas-liquid two-phase flow in a complex microchannel. Chem. Eng. Sci., 230.","DOI":"10.1016\/j.ces.2020.116198"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Yu, S., Wang, Y., Chen, T., Li, M., Zhang, X., Huang, B., Xu, J., and Wang, G. (2025). An inclined groove and its optimization design method for improving the energy performance at the saddle zone of axial flow pumps. Energy, 328.","DOI":"10.1016\/j.energy.2025.136527"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1205\/026387600527437","article-title":"CFD Study of Homogenization with Dual Rushton Turbines\u2014Comparison with Experimental Results","volume":"78","author":"Jaworski","year":"2000","journal-title":"Chem. Eng. Res. Des."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.cjche.2024.01.016","article-title":"A strategy for strengthening chaotic mixing of dual shaft eccentric mixers by changing non-Newtonian fluids kinetic energy distribution","volume":"69","author":"Wang","year":"2024","journal-title":"Chin. J. Chem. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Qin, S., Meng, T., Wang, Y., Wang, Y., Tao, C., Zhang, Q., Li, B., and Liu, Z. Different rotation speeds: A novel approach to enhancing chaos and mixing efficiency in multi-shaft stirred reactors. Chin. J. Chem. Eng., 2025. in press.","DOI":"10.1016\/j.cjche.2025.04.024"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Jia, Z., Zhang, S., Fang, K., Kong, B., Xie, M., Zhang, Q., and Yang, C. (2024). Assessment of stress-blended eddy simulation on prediction of flow characteristics in a Rushton impeller stirred tank. Chem. Eng. Sci., 284.","DOI":"10.1016\/j.ces.2023.119442"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Li, L., Chen, N., Xiang, K., and Xiang, B. (2019). CFD study on the flow field and power characteristics in a Rushton turbine stirred tank in laminar regime. Int. J. Chem. React. Eng., 17.","DOI":"10.1515\/ijcre-2018-0215"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1932\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T11:12:59Z","timestamp":1762859579000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1932"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,11]]},"references-count":32,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["sym17111932"],"URL":"https:\/\/doi.org\/10.3390\/sym17111932","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,11]]}}}