Models for the two-phase flow of concentrated suspensions
A new two-phase model for concentrated suspensions is derived that incorporates a constitutive law combining the rheology for non-Brownian suspension and granular flow. The resulting model exhibits a yield-stress behaviour for the solid phase depending on the collision pressure. This property is inv...
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| Veröffentlicht in: | European journal of applied mathematics 2019-06, Vol.30 (3), p.585-617 |
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| container_title | European journal of applied mathematics |
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| creator | AHNERT, TOBIAS MÜNCH, ANDREAS WAGNER, BARBARA |
| description | A new two-phase model for concentrated suspensions is derived that incorporates a constitutive law combining the rheology for non-Brownian suspension and granular flow. The resulting model exhibits a yield-stress behaviour for the solid phase depending on the collision pressure. This property is investigated for the simple geometry of plane Poiseuille flow, where an unyielded or jammed zone of finite width arises in the centre of the channel. For the steady states of this problem, the governing equations are reduced to a boundary value problem for a system of ordinary differential equations and the conditions for existence of solutions with jammed regions are investigated using phase-space methods. For the general time-dependent case a new drift-flux model is derived using matched asymptotic expansions that takes into account the boundary layers at the walls and the interface between the yielded and unyielded region. The drift-flux model is used to numerically study the dynamic behaviour of the suspension flow, including the appearance and evolution of an unyielded or jammed regions. |
| doi_str_mv | 10.1017/S095679251800030X |
| format | Article |
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The resulting model exhibits a yield-stress behaviour for the solid phase depending on the collision pressure. This property is investigated for the simple geometry of plane Poiseuille flow, where an unyielded or jammed zone of finite width arises in the centre of the channel. For the steady states of this problem, the governing equations are reduced to a boundary value problem for a system of ordinary differential equations and the conditions for existence of solutions with jammed regions are investigated using phase-space methods. For the general time-dependent case a new drift-flux model is derived using matched asymptotic expansions that takes into account the boundary layers at the walls and the interface between the yielded and unyielded region. The drift-flux model is used to numerically study the dynamic behaviour of the suspension flow, including the appearance and evolution of an unyielded or jammed regions.</description><identifier>ISSN: 0956-7925</identifier><identifier>EISSN: 1469-4425</identifier><identifier>DOI: 10.1017/S095679251800030X</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Applied mathematics ; Asymptotic series ; Boundary layers ; Boundary value problems ; Differential equations ; Drift ; Laminar flow ; Mathematical models ; Ordinary differential equations ; Rheological properties ; Rheology ; Solid phases ; Time dependence ; Two phase flow</subject><ispartof>European journal of applied mathematics, 2019-06, Vol.30 (3), p.585-617</ispartof><rights>Copyright © Cambridge University Press 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c317t-7dae1d4a73d36e16d28f2dcf3cb45d306463de3c84d02e8969cbf8df60270ce63</citedby><cites>FETCH-LOGICAL-c317t-7dae1d4a73d36e16d28f2dcf3cb45d306463de3c84d02e8969cbf8df60270ce63</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S095679251800030X/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,314,777,781,27905,27906,55609</link.rule.ids></links><search><creatorcontrib>AHNERT, TOBIAS</creatorcontrib><creatorcontrib>MÜNCH, ANDREAS</creatorcontrib><creatorcontrib>WAGNER, BARBARA</creatorcontrib><title>Models for the two-phase flow of concentrated suspensions</title><title>European journal of applied mathematics</title><addtitle>Eur. J. Appl. Math</addtitle><description>A new two-phase model for concentrated suspensions is derived that incorporates a constitutive law combining the rheology for non-Brownian suspension and granular flow. The resulting model exhibits a yield-stress behaviour for the solid phase depending on the collision pressure. This property is investigated for the simple geometry of plane Poiseuille flow, where an unyielded or jammed zone of finite width arises in the centre of the channel. For the steady states of this problem, the governing equations are reduced to a boundary value problem for a system of ordinary differential equations and the conditions for existence of solutions with jammed regions are investigated using phase-space methods. For the general time-dependent case a new drift-flux model is derived using matched asymptotic expansions that takes into account the boundary layers at the walls and the interface between the yielded and unyielded region. The drift-flux model is used to numerically study the dynamic behaviour of the suspension flow, including the appearance and evolution of an unyielded or jammed regions.</description><subject>Applied mathematics</subject><subject>Asymptotic series</subject><subject>Boundary layers</subject><subject>Boundary value problems</subject><subject>Differential equations</subject><subject>Drift</subject><subject>Laminar flow</subject><subject>Mathematical models</subject><subject>Ordinary differential equations</subject><subject>Rheological properties</subject><subject>Rheology</subject><subject>Solid phases</subject><subject>Time dependence</subject><subject>Two phase flow</subject><issn>0956-7925</issn><issn>1469-4425</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kEtLAzEUhYMoWKs_wF3A9ejNY5LJUoovqLhQwd2QJjd2SjsZkynFf-8MLbgQV3dxzncO9xByyeCaAdM3r2BKpQ0vWQUAAj6OyIRJZQopeXlMJqNcjPopOct5BcAEaDMh5jl6XGcaYqL9Emm_i0W3tBlpWMcdjYG62Dps-2R79DRvc4dtbmKbz8lJsOuMF4c7Je_3d2-zx2L-8vA0u50XTjDdF9pbZF5aLbxQyJTnVeDeBeEWsvQClFTCo3CV9MCxMsq4Rah8UMA1OFRiSq72uV2KX1vMfb2K29QOlTUffhBMVgIGF9u7XIo5Jwx1l5qNTd81g3pcqP6z0MCIA2M3i9T4T_yN_p_6AUObZ_E</recordid><startdate>201906</startdate><enddate>201906</enddate><creator>AHNERT, TOBIAS</creator><creator>MÜNCH, ANDREAS</creator><creator>WAGNER, BARBARA</creator><general>Cambridge University Press</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7XB</scope><scope>88I</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M2P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope><scope>S0W</scope></search><sort><creationdate>201906</creationdate><title>Models for the two-phase flow of concentrated suspensions</title><author>AHNERT, TOBIAS ; MÜNCH, ANDREAS ; WAGNER, BARBARA</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c317t-7dae1d4a73d36e16d28f2dcf3cb45d306463de3c84d02e8969cbf8df60270ce63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Applied mathematics</topic><topic>Asymptotic series</topic><topic>Boundary layers</topic><topic>Boundary value problems</topic><topic>Differential equations</topic><topic>Drift</topic><topic>Laminar flow</topic><topic>Mathematical models</topic><topic>Ordinary differential equations</topic><topic>Rheological properties</topic><topic>Rheology</topic><topic>Solid phases</topic><topic>Time dependence</topic><topic>Two phase flow</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>AHNERT, TOBIAS</creatorcontrib><creatorcontrib>MÜNCH, ANDREAS</creatorcontrib><creatorcontrib>WAGNER, BARBARA</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><collection>DELNET Engineering & Technology Collection</collection><jtitle>European journal of applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>AHNERT, TOBIAS</au><au>MÜNCH, ANDREAS</au><au>WAGNER, BARBARA</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Models for the two-phase flow of concentrated suspensions</atitle><jtitle>European journal of applied mathematics</jtitle><addtitle>Eur. J. Appl. Math</addtitle><date>2019-06</date><risdate>2019</risdate><volume>30</volume><issue>3</issue><spage>585</spage><epage>617</epage><pages>585-617</pages><issn>0956-7925</issn><eissn>1469-4425</eissn><abstract>A new two-phase model for concentrated suspensions is derived that incorporates a constitutive law combining the rheology for non-Brownian suspension and granular flow. The resulting model exhibits a yield-stress behaviour for the solid phase depending on the collision pressure. This property is investigated for the simple geometry of plane Poiseuille flow, where an unyielded or jammed zone of finite width arises in the centre of the channel. For the steady states of this problem, the governing equations are reduced to a boundary value problem for a system of ordinary differential equations and the conditions for existence of solutions with jammed regions are investigated using phase-space methods. For the general time-dependent case a new drift-flux model is derived using matched asymptotic expansions that takes into account the boundary layers at the walls and the interface between the yielded and unyielded region. The drift-flux model is used to numerically study the dynamic behaviour of the suspension flow, including the appearance and evolution of an unyielded or jammed regions.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/S095679251800030X</doi><tpages>33</tpages></addata></record> |
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| source | Cambridge Journals |
| subjects | Applied mathematics Asymptotic series Boundary layers Boundary value problems Differential equations Drift Laminar flow Mathematical models Ordinary differential equations Rheological properties Rheology Solid phases Time dependence Two phase flow |
| title | Models for the two-phase flow of concentrated suspensions |
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