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As the behaviour of fluids contacting on a solid surface is also governed by surface tension, the description of the wetting phenomenon is challenging. Peridynamic differential operator (PDDO) can express partial differentials of any order by integral equations. Therefore, the governing equations for multiphase fluid motion, such as the Navier\u2013Stokes equations and energy equations, can be reformulated in terms of integral equations. In this study, a novel non-local method is developed for modelling the multiphase fluid flow motion using the PDDO, and the thermal effect on surface tension force is considered. To describe the surface tension forces in the normal and tangential directions, the non-local form of the continuum surface force (CFS) model is presented. Besides, to overcome the inaccuracy of the unit normal vectors at the three-phase flow intersection region, an additional treatment for this region is presented. Finally, several benchmark multiphase fluid flow cases, such as square droplet deformation, surface wetting, and droplet migration in thermo-capillary flow are presented and validated. The results demonstrate that the developed non-local model can accurately capture the surface tension effect in multiphase fluid flow motion.<\/jats:p>","DOI":"10.1007\/s00366-023-01888-7","type":"journal-article","created":{"date-parts":[[2023,10,9]],"date-time":"2023-10-09T16:03:02Z","timestamp":1696867382000},"page":"1967-1997","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Non-local modelling of multiphase flow wetting and thermo-capillary flow using peridynamic differential operator"],"prefix":"10.1007","volume":"40","author":[{"given":"Bingquan","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Selda","family":"Oterkus","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Erkan","family":"Oterkus","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,10,9]]},"reference":[{"issue":"1","key":"1888_CR1","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/0021-9991(81)90145-5","volume":"39","author":"CW Hirt","year":"1981","unstructured":"Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. 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