{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T14:14:54Z","timestamp":1765808094198,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,30]],"date-time":"2022-10-30T00:00:00Z","timestamp":1667088000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12132015"],"award-info":[{"award-number":["12132015"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The swimming mode of two interacting squirmers under gravity in a narrow vertical channel is simulated numerically using the lattice Boltzmann method (LBM) in the range of self-propelling strength 0.1 \u2264 \u03b1 \u2264 1.1 and swimming type \u22125 \u2264 \u03b2 \u2264 5. The results showed that there exist five typical swimming patterns for individual squirmers, i.e., steady upward rising (SUR), oscillation across the channel (OAC), oscillation near the wall (ONW), steady upward rising with small-amplitude oscillation (SURO), and vertical motion along the sidewall (VMS). The parametric space (\u03b1, \u03b2) illustrated the interactions on each pattern. In particular, the range of oscillation angle for ONW is from 19.8\u00b0 to 32.4\u00b0 as \u03b1 varies from 0.3 to 0.7. Moreover, the swimming modes of two interacting squirmers combine the two squirmers\u2019 independent swimming patterns. On the other hand, the pullers (\u03b2 &lt; 0) attract with each other at the initial stage, resulting in a low-pressure region between them and making the two pullers gradually move closer and finally make contact, while the result for the pushers (\u03b2 &gt; 0) is the opposite. After the squirmers\u2019 interaction, the squirmer orientation and pressure distribution determine subsequent squirmer swimming patterns. Two pushers separate quickly, while there will be a more extended interaction period before the two pullers are entirely separated.<\/jats:p>","DOI":"10.3390\/e24111564","type":"journal-article","created":{"date-parts":[[2022,10,30]],"date-time":"2022-10-30T07:26:50Z","timestamp":1667114810000},"page":"1564","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Swimming Mode of Two Interacting Squirmers under Gravity in a Narrow Vertical Channel"],"prefix":"10.3390","volume":"24","author":[{"given":"Geng","family":"Guan","sequence":"first","affiliation":[{"name":"State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8418-1176","authenticated-orcid":false,"given":"Jianzhong","family":"Lin","sequence":"additional","affiliation":[{"name":"Zhejiang Provincial Engineering Research Center for the Safety of Pressure Vessel and Pipeline, Ningbo University, Ningbo 315211, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deming","family":"Nie","sequence":"additional","affiliation":[{"name":"Institute of Fluid Mechanics, China Jiliang University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1146\/annurev.bb.23.060194.002453","article-title":"The bacterial flagellar motor","volume":"23","author":"Schuster","year":"1994","journal-title":"Annu. 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