Analytical solutions and dynamic behaviors to synchronous oscillation of same bubbles at vertices of cuboid and rectangle
The present work focuses on the nonlinear dynamics of the synchronous oscillating multiple bubbles in two typical spatial locations, namely, cuboid and rectangle arrangements. The governing equation for such synchronous oscillating multiple bubbles is derived from a modified Rayleigh–Plesset equatio...
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Veröffentlicht in: | Physics of fluids (1994) 2023-08, Vol.35 (8) |
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description | The present work focuses on the nonlinear dynamics of the synchronous oscillating multiple bubbles in two typical spatial locations, namely, cuboid and rectangle arrangements. The governing equation for such synchronous oscillating multiple bubbles is derived from a modified Rayleigh–Plesset equation. Theoretical results including the collapse time and analytical solution (in three forms) for multiple vapor bubbles, as well as the maximum/minimum radii, oscillation period, and analytical solution in the form of Weierstrass elliptic function for multiple gas-filled ones, are provided. On the basis of these results, we not only study the dynamic characteristics of multi-bubbles straightforwardly but also carefully observe a series of evolution behaviors of bubbles when the number of bubbles decreases gradually on the order of
8
→
4
→
2
→
1. It should be pointed out that we also compare the multi-bubble behaviors between the general cuboid/rectangle arrangements and the corresponding cube/square arrangements under two reasonable restrictions, respectively. Furthermore, the limiting behaviors of the synchronous oscillating multiple gas-filled bubbles are discussed as the initial pressure of the gas in bubble approaches to zero. |
doi_str_mv | 10.1063/5.0151939 |
format | Article |
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8
→
4
→
2
→
1. It should be pointed out that we also compare the multi-bubble behaviors between the general cuboid/rectangle arrangements and the corresponding cube/square arrangements under two reasonable restrictions, respectively. Furthermore, the limiting behaviors of the synchronous oscillating multiple gas-filled bubbles are discussed as the initial pressure of the gas in bubble approaches to zero.</description><identifier>ISSN: 1070-6631</identifier><identifier>EISSN: 1089-7666</identifier><identifier>DOI: 10.1063/5.0151939</identifier><identifier>CODEN: PHFLE6</identifier><language>eng</language><publisher>Melville: American Institute of Physics</publisher><subject>Apexes ; Bubbles ; Dynamic characteristics ; Elliptic functions ; Exact solutions ; Fluid dynamics ; Initial pressure ; Mathematical analysis ; Nonlinear dynamics ; Physics ; Rectangles</subject><ispartof>Physics of fluids (1994), 2023-08, Vol.35 (8)</ispartof><rights>Author(s)</rights><rights>2023 Author(s). Published under an exclusive license by AIP Publishing.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c327t-595c59e08dd73a6d2cde457bc9227e951dd81743deb5bc7ab0df34eb45e22d863</citedby><cites>FETCH-LOGICAL-c327t-595c59e08dd73a6d2cde457bc9227e951dd81743deb5bc7ab0df34eb45e22d863</cites><orcidid>0000-0003-4874-7579 ; 0000-0003-1669-3844 ; 0000-0001-7487-3187</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,794,4512,27924,27925</link.rule.ids></links><search><creatorcontrib>Qin, Yupeng</creatorcontrib><creatorcontrib>Wang, Zhen</creatorcontrib><creatorcontrib>Zou, Li</creatorcontrib><title>Analytical solutions and dynamic behaviors to synchronous oscillation of same bubbles at vertices of cuboid and rectangle</title><title>Physics of fluids (1994)</title><description>The present work focuses on the nonlinear dynamics of the synchronous oscillating multiple bubbles in two typical spatial locations, namely, cuboid and rectangle arrangements. The governing equation for such synchronous oscillating multiple bubbles is derived from a modified Rayleigh–Plesset equation. Theoretical results including the collapse time and analytical solution (in three forms) for multiple vapor bubbles, as well as the maximum/minimum radii, oscillation period, and analytical solution in the form of Weierstrass elliptic function for multiple gas-filled ones, are provided. On the basis of these results, we not only study the dynamic characteristics of multi-bubbles straightforwardly but also carefully observe a series of evolution behaviors of bubbles when the number of bubbles decreases gradually on the order of
8
→
4
→
2
→
1. It should be pointed out that we also compare the multi-bubble behaviors between the general cuboid/rectangle arrangements and the corresponding cube/square arrangements under two reasonable restrictions, respectively. Furthermore, the limiting behaviors of the synchronous oscillating multiple gas-filled bubbles are discussed as the initial pressure of the gas in bubble approaches to zero.</description><subject>Apexes</subject><subject>Bubbles</subject><subject>Dynamic characteristics</subject><subject>Elliptic functions</subject><subject>Exact solutions</subject><subject>Fluid dynamics</subject><subject>Initial pressure</subject><subject>Mathematical analysis</subject><subject>Nonlinear dynamics</subject><subject>Physics</subject><subject>Rectangles</subject><issn>1070-6631</issn><issn>1089-7666</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKAzEUhoMoWKsL3yDgSmFqLpNksizFGxTc6HrIrXZKOqlJpjBvb3pZuzo_nO98cH4A7jGaYcTpM5shzLCk8gJMMGpkJTjnl4csUMU5xdfgJqUNQohKwidgnPfKj7kzysMU_JC70Ceoegvt2KttZ6B2a7XvQkwwB5jG3qxj6MOQYEim814dLmBYwaS2DupBa--KIMO9i0VbctmZQYfOHrXRmaz6H-9uwdVK-eTuznMKvl9fvhbv1fLz7WMxX1aGEpErJplh0qHGWkEVt8RYVzOhjSREOMmwtQ0WNbVOM22E0siuaO10zRwhtuF0Ch5O3l0Mv4NLud2EIZavU0uaWmCECGWFejxRJoaUolu1u9htVRxbjNpDsy1rz80W9unElgLy8f9_4D9GoXrG</recordid><startdate>202308</startdate><enddate>202308</enddate><creator>Qin, Yupeng</creator><creator>Wang, Zhen</creator><creator>Zou, Li</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0003-4874-7579</orcidid><orcidid>https://orcid.org/0000-0003-1669-3844</orcidid><orcidid>https://orcid.org/0000-0001-7487-3187</orcidid></search><sort><creationdate>202308</creationdate><title>Analytical solutions and dynamic behaviors to synchronous oscillation of same bubbles at vertices of cuboid and rectangle</title><author>Qin, Yupeng ; Wang, Zhen ; Zou, Li</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c327t-595c59e08dd73a6d2cde457bc9227e951dd81743deb5bc7ab0df34eb45e22d863</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Apexes</topic><topic>Bubbles</topic><topic>Dynamic characteristics</topic><topic>Elliptic functions</topic><topic>Exact solutions</topic><topic>Fluid dynamics</topic><topic>Initial pressure</topic><topic>Mathematical analysis</topic><topic>Nonlinear dynamics</topic><topic>Physics</topic><topic>Rectangles</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Qin, Yupeng</creatorcontrib><creatorcontrib>Wang, Zhen</creatorcontrib><creatorcontrib>Zou, Li</creatorcontrib><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Physics of fluids (1994)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Qin, Yupeng</au><au>Wang, Zhen</au><au>Zou, Li</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analytical solutions and dynamic behaviors to synchronous oscillation of same bubbles at vertices of cuboid and rectangle</atitle><jtitle>Physics of fluids (1994)</jtitle><date>2023-08</date><risdate>2023</risdate><volume>35</volume><issue>8</issue><issn>1070-6631</issn><eissn>1089-7666</eissn><coden>PHFLE6</coden><abstract>The present work focuses on the nonlinear dynamics of the synchronous oscillating multiple bubbles in two typical spatial locations, namely, cuboid and rectangle arrangements. The governing equation for such synchronous oscillating multiple bubbles is derived from a modified Rayleigh–Plesset equation. Theoretical results including the collapse time and analytical solution (in three forms) for multiple vapor bubbles, as well as the maximum/minimum radii, oscillation period, and analytical solution in the form of Weierstrass elliptic function for multiple gas-filled ones, are provided. On the basis of these results, we not only study the dynamic characteristics of multi-bubbles straightforwardly but also carefully observe a series of evolution behaviors of bubbles when the number of bubbles decreases gradually on the order of
8
→
4
→
2
→
1. It should be pointed out that we also compare the multi-bubble behaviors between the general cuboid/rectangle arrangements and the corresponding cube/square arrangements under two reasonable restrictions, respectively. Furthermore, the limiting behaviors of the synchronous oscillating multiple gas-filled bubbles are discussed as the initial pressure of the gas in bubble approaches to zero.</abstract><cop>Melville</cop><pub>American Institute of Physics</pub><doi>10.1063/5.0151939</doi><tpages>12</tpages><orcidid>https://orcid.org/0000-0003-4874-7579</orcidid><orcidid>https://orcid.org/0000-0003-1669-3844</orcidid><orcidid>https://orcid.org/0000-0001-7487-3187</orcidid><oa>free_for_read</oa></addata></record> |
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subjects | Apexes Bubbles Dynamic characteristics Elliptic functions Exact solutions Fluid dynamics Initial pressure Mathematical analysis Nonlinear dynamics Physics Rectangles |
title | Analytical solutions and dynamic behaviors to synchronous oscillation of same bubbles at vertices of cuboid and rectangle |
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