Dilute emulsions with surface tension

We consider an emulsion formed by two newtonian fluids in which one fluid is dispersed under the form of droplets of arbitrary shape in the presence of surface tension. We consider both cases of droplets with fixed centers of mass and of convected droplets. In the non-dilute case, for spherical drop...

Full description

Saved in:
Bibliographic Details
Published in:Quarterly of applied mathematics 2016-01, Vol.74 (1), p.89-111
Main Authors: Nika, Grigor, Vernescu, Bogdan
Format: Article
Language:English
Subjects:
Brinkman equations
emulsions
G-convergence
Matematik
Mathematics
Mosco-convergence
Research article
Stokes flow
surface tension
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-a314t-2fbcefd827b8893c680c64232764b56403b482c548df4761978b74393d577cef3
cites
container_end_page 111
container_issue 1
container_start_page 89
container_title Quarterly of applied mathematics
container_volume 74
creator Nika, Grigor
Vernescu, Bogdan
description We consider an emulsion formed by two newtonian fluids in which one fluid is dispersed under the form of droplets of arbitrary shape in the presence of surface tension. We consider both cases of droplets with fixed centers of mass and of convected droplets. In the non-dilute case, for spherical droplets of radius aϵa_\epsilon of the same order as the period length ϵ\epsilon, the two models were studied by Lipton-Avellaneda (1990) and Lipton-Vernescu (1994). Here we are interested in the time-dependent, dilute case when the characteristic size of the droplets aϵa_\epsilon, of arbitrary shape, is much smaller than ϵ\epsilon. We study the limit behavior when ϵ→0\epsilon \to 0 in each of these two models. We establish a Brinkman type law for the critical size aϵ=O(ϵ3)a_\epsilon = O(\epsilon ^3) in the first case, whereas in the second case there is no “strange” term, and in the limit the flow is unperturbed by the droplets.
doi_str_mv 10.1090/qam/1403
format article
fullrecord <record><control><sourceid>jstor_swepu</sourceid><recordid>TN_cdi_swepub_primary_oai_DiVA_org_kau_88399</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>26835280</jstor_id><sourcerecordid>26835280</sourcerecordid><originalsourceid>FETCH-LOGICAL-a314t-2fbcefd827b8893c680c64232764b56403b482c548df4761978b74393d577cef3</originalsourceid><addsrcrecordid>eNp1kEtLw0AUhQdRMFbBPyAERHBh7Lwfy9L6goIbFXfDJJnRqUlTZxKK_94pke5cXe493zlcDgDnCN4iqOD027RTRCE5ABliDBeUSnYIMggJKRhX78fgJMZVWpMKM3C18M3Q29y2QxN9t4751vefeRyCM5XNe7veXU_BkTNNtGd_cwJe7-9e5o_F8vnhaT5bFoYg2hfYlZV1tcSilFKRiktYcYoJFpyWjKevSipxxaisHRUcKSFLQYkiNRMiOckE3Iy5cWs3Q6k3wbcm_OjOeL3wbzPdhQ_9ZQYtJVEq4dcjXoUuxmDd3oCg3rWhUxt610ZCL0Z0Ffsu7DnMJWFYwqRfjrpp4_8pvxrZZhg</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Dilute emulsions with surface tension</title><source>JSTOR Archival Journals and Primary Sources Collection</source><source>American Mathematical Society Publications (Freely Accessible)</source><creator>Nika, Grigor ; Vernescu, Bogdan</creator><creatorcontrib>Nika, Grigor ; Vernescu, Bogdan</creatorcontrib><description>We consider an emulsion formed by two newtonian fluids in which one fluid is dispersed under the form of droplets of arbitrary shape in the presence of surface tension. We consider both cases of droplets with fixed centers of mass and of convected droplets. In the non-dilute case, for spherical droplets of radius aϵa_\epsilon of the same order as the period length ϵ\epsilon, the two models were studied by Lipton-Avellaneda (1990) and Lipton-Vernescu (1994). Here we are interested in the time-dependent, dilute case when the characteristic size of the droplets aϵa_\epsilon, of arbitrary shape, is much smaller than ϵ\epsilon. We study the limit behavior when ϵ→0\epsilon \to 0 in each of these two models. We establish a Brinkman type law for the critical size aϵ=O(ϵ3)a_\epsilon = O(\epsilon ^3) in the first case, whereas in the second case there is no “strange” term, and in the limit the flow is unperturbed by the droplets.</description><identifier>ISSN: 0033-569X</identifier><identifier>ISSN: 1552-4485</identifier><identifier>EISSN: 1552-4485</identifier><identifier>DOI: 10.1090/qam/1403</identifier><language>eng</language><publisher>Providence, Rhode Island: American Mathematical Society</publisher><subject>Brinkman equations ; emulsions ; G-convergence ; Matematik ; Mathematics ; Mosco-convergence ; Research article ; Stokes flow ; surface tension</subject><ispartof>Quarterly of applied mathematics, 2016-01, Vol.74 (1), p.89-111</ispartof><rights>Copyright 2015 Brown University</rights><rights>2015 Brown University</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a314t-2fbcefd827b8893c680c64232764b56403b482c548df4761978b74393d577cef3</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.ams.org/qam/2016-74-01/S0033-569X-2015-01403-4/S0033-569X-2015-01403-4.pdf$$EPDF$$P50$$Gams$$H</linktopdf><linktohtml>$$Uhttps://www.ams.org/qam/2016-74-01/S0033-569X-2015-01403-4/$$EHTML$$P50$$Gams$$H</linktohtml><link.rule.ids>69,230,314,776,780,881,23303,27901,27902,58213,58446,77581,77591</link.rule.ids><backlink>$$Uhttps://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-88399$$DView record from Swedish Publication Index$$Hfree_for_read</backlink></links><search><creatorcontrib>Nika, Grigor</creatorcontrib><creatorcontrib>Vernescu, Bogdan</creatorcontrib><title>Dilute emulsions with surface tension</title><title>Quarterly of applied mathematics</title><addtitle>Quart. Appl. Math</addtitle><description>We consider an emulsion formed by two newtonian fluids in which one fluid is dispersed under the form of droplets of arbitrary shape in the presence of surface tension. We consider both cases of droplets with fixed centers of mass and of convected droplets. In the non-dilute case, for spherical droplets of radius aϵa_\epsilon of the same order as the period length ϵ\epsilon, the two models were studied by Lipton-Avellaneda (1990) and Lipton-Vernescu (1994). Here we are interested in the time-dependent, dilute case when the characteristic size of the droplets aϵa_\epsilon, of arbitrary shape, is much smaller than ϵ\epsilon. We study the limit behavior when ϵ→0\epsilon \to 0 in each of these two models. We establish a Brinkman type law for the critical size aϵ=O(ϵ3)a_\epsilon = O(\epsilon ^3) in the first case, whereas in the second case there is no “strange” term, and in the limit the flow is unperturbed by the droplets.</description><subject>Brinkman equations</subject><subject>emulsions</subject><subject>G-convergence</subject><subject>Matematik</subject><subject>Mathematics</subject><subject>Mosco-convergence</subject><subject>Research article</subject><subject>Stokes flow</subject><subject>surface tension</subject><issn>0033-569X</issn><issn>1552-4485</issn><issn>1552-4485</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp1kEtLw0AUhQdRMFbBPyAERHBh7Lwfy9L6goIbFXfDJJnRqUlTZxKK_94pke5cXe493zlcDgDnCN4iqOD027RTRCE5ABliDBeUSnYIMggJKRhX78fgJMZVWpMKM3C18M3Q29y2QxN9t4751vefeRyCM5XNe7veXU_BkTNNtGd_cwJe7-9e5o_F8vnhaT5bFoYg2hfYlZV1tcSilFKRiktYcYoJFpyWjKevSipxxaisHRUcKSFLQYkiNRMiOckE3Iy5cWs3Q6k3wbcm_OjOeL3wbzPdhQ_9ZQYtJVEq4dcjXoUuxmDd3oCg3rWhUxt610ZCL0Z0Ffsu7DnMJWFYwqRfjrpp4_8pvxrZZhg</recordid><startdate>20160101</startdate><enddate>20160101</enddate><creator>Nika, Grigor</creator><creator>Vernescu, Bogdan</creator><general>American Mathematical Society</general><general>Brown University</general><scope>AAYXX</scope><scope>CITATION</scope><scope>ADTPV</scope><scope>AOWAS</scope><scope>DG3</scope></search><sort><creationdate>20160101</creationdate><title>Dilute emulsions with surface tension</title><author>Nika, Grigor ; Vernescu, Bogdan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a314t-2fbcefd827b8893c680c64232764b56403b482c548df4761978b74393d577cef3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Brinkman equations</topic><topic>emulsions</topic><topic>G-convergence</topic><topic>Matematik</topic><topic>Mathematics</topic><topic>Mosco-convergence</topic><topic>Research article</topic><topic>Stokes flow</topic><topic>surface tension</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nika, Grigor</creatorcontrib><creatorcontrib>Vernescu, Bogdan</creatorcontrib><collection>CrossRef</collection><collection>SwePub</collection><collection>SwePub Articles</collection><collection>SWEPUB Karlstads universitet</collection><jtitle>Quarterly of applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nika, Grigor</au><au>Vernescu, Bogdan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dilute emulsions with surface tension</atitle><jtitle>Quarterly of applied mathematics</jtitle><stitle>Quart. Appl. Math</stitle><date>2016-01-01</date><risdate>2016</risdate><volume>74</volume><issue>1</issue><spage>89</spage><epage>111</epage><pages>89-111</pages><issn>0033-569X</issn><issn>1552-4485</issn><eissn>1552-4485</eissn><abstract>We consider an emulsion formed by two newtonian fluids in which one fluid is dispersed under the form of droplets of arbitrary shape in the presence of surface tension. We consider both cases of droplets with fixed centers of mass and of convected droplets. In the non-dilute case, for spherical droplets of radius aϵa_\epsilon of the same order as the period length ϵ\epsilon, the two models were studied by Lipton-Avellaneda (1990) and Lipton-Vernescu (1994). Here we are interested in the time-dependent, dilute case when the characteristic size of the droplets aϵa_\epsilon, of arbitrary shape, is much smaller than ϵ\epsilon. We study the limit behavior when ϵ→0\epsilon \to 0 in each of these two models. We establish a Brinkman type law for the critical size aϵ=O(ϵ3)a_\epsilon = O(\epsilon ^3) in the first case, whereas in the second case there is no “strange” term, and in the limit the flow is unperturbed by the droplets.</abstract><cop>Providence, Rhode Island</cop><pub>American Mathematical Society</pub><doi>10.1090/qam/1403</doi><tpages>23</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0033-569X
ispartof Quarterly of applied mathematics, 2016-01, Vol.74 (1), p.89-111
issn 0033-569X
1552-4485
1552-4485
language eng
recordid cdi_swepub_primary_oai_DiVA_org_kau_88399
source JSTOR Archival Journals and Primary Sources Collection; American Mathematical Society Publications (Freely Accessible)
subjects Brinkman equations
emulsions
G-convergence
Matematik
Mathematics
Mosco-convergence
Research article
Stokes flow
surface tension
title Dilute emulsions with surface tension
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-29T01%3A02%3A29IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_swepu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Dilute%20emulsions%20with%20surface%20tension&rft.jtitle=Quarterly%20of%20applied%20mathematics&rft.au=Nika,%20Grigor&rft.date=2016-01-01&rft.volume=74&rft.issue=1&rft.spage=89&rft.epage=111&rft.pages=89-111&rft.issn=0033-569X&rft.eissn=1552-4485&rft_id=info:doi/10.1090/qam/1403&rft_dat=%3Cjstor_swepu%3E26835280%3C/jstor_swepu%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-a314t-2fbcefd827b8893c680c64232764b56403b482c548df4761978b74393d577cef3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_jstor_id=26835280&rfr_iscdi=true