{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T08:56:51Z","timestamp":1789549011892,"version":"build-2803163510"},"reference-count":29,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T00:00:00Z","timestamp":1785715200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"projects for 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":["Materials"],"abstract":"<jats:p>Polyurethane adhesives often suffer from high viscosity, poor flowability, and limited mass transfer efficiency, making it challenging for conventional single-shaft or twin-shaft mixing systems to achieve uniform mixing in large-capacity equipment. This study investigates the differential speed coupling mechanism of a 600 L eccentric four-shaft mixer for high-viscosity polyurethane adhesive systems using computational fluid dynamics (CFD). The effects of different differential speed ratios on flow field evolution and mixing performance were systematically analyzed through multiple indicators, including power consumption per unit volume, velocity variation coefficient, effective mixing region ratio, vortex core coverage, and maximum Lyapunov exponent (LLE). Among the investigated conditions, the 50:100 differential speed ratio exhibited a more favorable circulation pattern, forming a closed-loop circulating flow field in the entire reactor, with an effective mixing region accounting for 60%, a velocity variation coefficient of only 0.38, and a power consumption per unit volume as low as 21.2 W\/m3. A constant speed of 100:100 easily generates dead zones in the interaxial flow field, while a high differential speed of 100:50 leads to excessive disturbances and energy waste. Moderate differential speed can generate large-scale coupled vortices, thereby enhancing mixing through coupled axial transport, radial dispersion, and tangential shear. An eccentric four-shaft mixer combined with reasonable differential speed control can effectively improve flow field uniformity and reduce potential mixing limitations in large-scale polyurethane adhesive systems. Among the three investigated differential speed ratios, the 50:100 condition exhibited the most favorable overall mixing performance. These findings provide numerical insights into the selection of differential speed operating conditions for high-viscosity polyurethane adhesive mixing systems.<\/jats:p>","DOI":"10.3390\/ma19153285","type":"journal-article","created":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T10:24:07Z","timestamp":1785752647000},"page":"3285","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Numerical Investigation of Differential Speed Coupling Mechanisms in a 600 L Eccentric Four-Shaft Mixer for High-Viscosity Polyurethane Adhesives"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-0247-7636","authenticated-orcid":false,"given":"Yongli","family":"Luo","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":"Bin","family":"He","sequence":"additional","affiliation":[{"name":"College of Chemistry and Chemical Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8663-2599","authenticated-orcid":false,"given":"Xing","family":"Fan","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":[[2026,8,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1016\/0079-6700(91)90011-9","article-title":"Polyurethane elastomers","volume":"16","author":"Ferguson","year":"1991","journal-title":"Prog. 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