{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T04:17:07Z","timestamp":1773375427124,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T00:00:00Z","timestamp":1630368000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004113","name":"Lebanese University","doi-asserted-by":"publisher","award":["2020"],"award-info":[{"award-number":["2020"]}],"id":[{"id":"10.13039\/501100004113","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The effect of shear flow on spherical nanoparticles (NPs) migration near a liquid\u2013liquid interface is studied by numerical simulation. We have implemented a compact model through which we use the diffuse interface method for modeling the two fluids and the molecular dynamics method for the simulation of the motion of NPs. Two different cases regarding the state of the two fluids when introducing the NPs are investigated. First, we introduce the NPs randomly into the medium of the two immiscible liquids that are already separated, and the interface is formed between them. For this case, it is shown that before applying any shear flow, 30% of NPs are driven to the interface under the effect of the drag force resulting from the composition gradient between the two fluids at the interface. However, this percentage is increased to reach 66% under the effect of shear defined by a P\u00e9clet number Pe = 0.316. In this study, different shear rates are investigated in addition to different shearing times, and we show that both factors have a crucial effect regarding the migration of the NPs toward the interfacial region. In particular, a small shear rate applied for a long time will have approximately the same effect as a greater shear rate applied for a shorter time. In the second studied case, we introduce the NPs into the mixture of two fluids that are already mixed and before phase separation so that the NPs are introduced into the homogenous medium of the two fluids. For this case, we show that in the absence of shear, almost all NPs migrate to the interface during phase separation, whereas shearing has a negative result, mainly because it affects the phase separation.<\/jats:p>","DOI":"10.3390\/e23091143","type":"journal-article","created":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T21:59:45Z","timestamp":1630447185000},"page":"1143","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Effect of Shear Flow on Nanoparticles Migration near Liquid Interfaces"],"prefix":"10.3390","volume":"23","author":[{"given":"Ali","family":"Daher","sequence":"first","affiliation":[{"name":"LAMPA, ENSAM Angers, 2 Boulevard du Ronceray, BP 93525, CEDEX 01, 49035 Angers, France"},{"name":"Faculty of Sciences1, MPLAB, Lebanese University, Beirut 6573, Lebanon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amine","family":"Ammar","sequence":"additional","affiliation":[{"name":"LAMPA, ENSAM Angers, 2 Boulevard du Ronceray, BP 93525, CEDEX 01, 49035 Angers, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abbas","family":"Hijazi","sequence":"additional","affiliation":[{"name":"Faculty of Sciences1, MPLAB, Lebanese University, Beirut 6573, Lebanon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lazhar","family":"Benyahia","sequence":"additional","affiliation":[{"name":"Institut des Mol\u00e9cules et Mat\u00e9riaux du Mans (IMMM), UMR 6283 CNRS\u2014Le Mans Universit\u00e9, Avenue Olivier Messiaen, CEDEX 09, 72085 Le Mans, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bhushan, B. 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