Influence of parameters controlling the extrusion step in fused filament fabrication (FFF) process applied to polymers using numerical simulation

HAL Id: hal-01905427

https://hal.archives-ouvertes.fr/hal-01905427

Submitted on 25 Oct 2018

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

Influence of parameters controlling the extrusion step in

fused filament fabrication (FFF) process applied to

polymers using numerical simulation

Shahriar Bakrani Balani, Arthur Cantarel, France Chabert, Valérie Nassiet

To cite this version:

Shahriar Bakrani Balani, Arthur Cantarel, France Chabert, Valérie Nassiet. Influence of

parame-ters controlling the extrusion step in fused filament fabrication (FFF) process applied to polymers

using numerical simulation. ESAFORM 2018, Apr 2018, Palermo, Italy. pp.140003-1-140003-6,

�10.1063/1.5034995�. �hal-01905427�

OATAO is an open access repository that collects the work of Toulouse

researchers and makes it freely available over the web where possible

Any correspondence concerning this service should be sent

to the repository administrator:

tech-oatao@listes-diff.inp-toulouse.fr

This is an author’s version published in: http://oatao.univ-toulouse.fr/20921

To cite this version :

Bakrani Balani, Shahriar

and Cantarel, Arthur

and Chabert,

France

and Nassiet, Valérie

Influence of parameters

controlling the extrusion step in fused filament fabrication (FFF)

process applied to polymers using numerical simulation. (2018) In:

ESAFORM 2018, 23 April 2018 - 25 April 2018 (Palermo, Italy).

,QIOXHQFHRISDUDPHWHUVFRQWUROOLQJWKHH[WUXVLRQVWHSLQ

)XVHG)LODPHQW)DEULFDWLRQ)))SURFHVVDSSOLHGWR

SRO\PHUVXVLQJQXPHULFDOVLPXODWLRQ



%DNUDQL%DODQL6KDKULDU

D

_{&DQWDUHO$UWKXU}

E

_{&KDEHUW)UDQFH}

F

_1DVVLHW

9DOpULH

G

_

_{/*3(1,7,1378QLYHUVLW\RI7RXORXVH$YHQXHG¶$]HUHL[%37DUEHV&HGH[)UDQFH} :HE3DJH KWWSZZZHQLWIU

_{,QVWLWXW&OpPHQW$GHU,&$&1568058QLYHUVLW\RI7RXORXVH836)UDQFH}

Web Page: http://www.institut-clement-ader.org/

 D_{&RUUHVSRQGLQJDXWKRUVEDNUDQL#HQLWIU} E_{DUWKXUFDQWDUHO#LXWWDUEHVIU} F_{IFKDEHUW#HQLWIU} G_{YQDVVLHW#HQLWIU}   $EVWUDFW([WUXVLRQLVRQHRIWKHROGHVWPDQXIDFWXULQJSURFHVVHVLWLVZLGHO\XVHGIRUPDQXIDFWXULQJILQLVKHGDQGVHPL ILQLVKHGSURGXFWV0RUHRYHUH[WUXVLRQLVDOVRWKHPDLQSURFHVVLQDGGLWLYHPDQXIDFWXULQJWHFKQRORJLHVVXFKDV)XVHG )LODPHQW)DEULFDWLRQ))),Q)))SURFHVVWKHSDUWVDUHPDQXIDFWXUHGOD\HUE\OD\HUXVLQJWKHUPRSODVWLFPDWHULDO7KH ODWWHULQ IRUP RI ILODPHQW LV PHOWHG LQWKH OLTXHILHU DQG WKHQ LWLV H[WUXGHG DQGGHSRVLWHG RQ WKH SUHYLRXV OD\HU 7KH PHFKDQLFDOSURSHUWLHVRIWKHSULQWHGSDUWVUHO\RQWKHFRDOHVFHQFHRIHDFKH[WUXGDWHZLWKDQRWKHURQH7KHFRDOHVFHQFH SKHQRPHQRQ LV GULYHQ E\ WKH IORZ SURSHUWLHV RI WKH PHOWHG SRO\PHU ZKHQ LW FRPHV RXW WKH QR]]OH MXVW EHIRUH WKH GHSRVLWLRQVWHS

7KLVVWXG\DLPVWRPDVWHUWKHTXDOLW\RIWKHSULQWHGSDUWVE\FRQWUROOLQJWKHHIIHFWRIWKHSDUDPHWHUVRIWKHH[WUXGHURQWKH IORZSURSHUWLHVLQWKH)))SURFHVV,QWKHFXUUHQWVWXG\QXPHULFDOVLPXODWLRQRIWKHSRO\PHUFRPLQJRXWRIWKHH[WUXGHU ZDV FDUULHG RXW XVLQJ &RPSXWDWLRQDO )OXLG '\QDPLFV &)' DQG WZR SKDVH IORZ 73) VLPXODWLRQ /HYHO 6HW /6 PHWKRGE\'D[LV\PPHWULFPRGXOHRI&2062/0XOWLSK\VLFVVRIWZDUH,QRUGHUWRSDLUWKHKHDWWUDQVIHUZLWKWKHIORZ VLPXODWLRQ DQ DGYHFWLRQGLIIXVLRQ HTXDWLRQ ZDV XVHG $GYHFWLRQGLIIXVLRQ HTXDWLRQ ZDV LPSOHPHQWHG DV D 3DUWLDO 'LIIHUHQWLDO(TXDWLRQ3'(LQWKHVRIWZDUH,QRUGHUWRGHILQHWKHYDULDWLRQRIYLVFRVLW\RIWKHSRO\PHUZLWKWHPSHUDWXUH WKH UKHRORJLFDO EHKDYLRUV RI WZR WKHUPRSODVWLFV ZHUH PHDVXUHG E\ H[WHQVLRQDO UKHRPHWHU DQG XVLQJ D SDUDOOHOSODWH FRQILJXUDWLRQRIDQRVFLOODWRU\UKHRPHWHU

7KHUHVXOWVKLJKOLJKWWKHLQIOXHQFHRIWKHHQYLURQPHQWWHPSHUDWXUHDQGWKHFRROLQJUDWHRQWKHWHPSHUDWXUHDQGYLVFRVLW\ RIWKHH[WUXGDWHH[LWLQJIURPWKHQR]]OH0RUHRYHUWKHWHPSHUDWXUHDQGLWVFRUUHVSRQGLQJYLVFRVLW\DWGLIIHUHQWWLPHV KDYH EHHQ GHWHUPLQHG XVLQJ QXPHULFDO VLPXODWLRQ $W KLJKHVW VKHDU UDWHV WKH H[WUXGDWH XQGHUJRHV GHIRUPDWLRQ IURP W\SLFDOF\OLQGULFDOVKDSH7KHVHUHVXOWVDUHUHTXLUHGWRSUHGLFWWKHFRDOHVFHQFHRIILODPHQWVDVWHSWRZDUGVXQGHUVWDQGLQJ WKHPHFKDQLFDOSURSHUWLHVRIWKHSULQWHGSDUWV

,1752'8&7,21

$GGLWLYH PDQXIDFWXULQJ UHIHUV WR D ZLGH YDULHW\ RI SURFHVVHV IRU PDQXIDFWXULQJ RI ' FRPSOH[ VKDSH SDUWV 7KHVHHPHUJLQJPDQXIDFWXULQJWHFKQRORJLHVDUHVRUWHGDFFRUGLQJWRYDULRXVFULWHULDVXFKDVWKHQDWXUHRIWKHUDZ PDWHULDO PHWDO FHUDPLF RU SRO\PHU WKH SURFHVV RI PDWHULDO GHSRVLWLRQ WKH HQHUJ\ VRXUFH HWF $PRQJ WKHVH SURFHVVHV )'0 )XVHG 'HSRVLWLRQ 0RGHOLQJ DOVR FDOOHG ))) )XVHG )LODPHQW )DEULFDWLRQ LV WKH PRVW ZLGHO\



XVHG WHFKQLTXH ,Q WKLV SURFHVV WKH SDUWV DUH PDQXIDFWXUHG OD\HU E\ OD\HU LQ PRVW FDVHV XVLQJ WKHUPRSODVWLF PDWHULDOV+RZHYHUWKHPDQXIDFWXUHGSDUWVE\)))ODFNIUHTXHQWO\LQPHFKDQLFDOUHVLVWDQFHZKLFKLVPDLQO\GXHWR SRRUFRDOHVFHQFHDQGLQWHUGLIIXVLRQEHWZHHQGHSRVLWHGOD\HUVDQGEHDGV8QGHUVWDQGLQJWKHSDUDPHWHUVLQIOXHQFLQJ WKHFRDOHVFHQFHDQGRSWLPL]LQJWKHVHSDUDPHWHUVDUHYHU\LPSRUWDQWLQRUGHUWRLPSURYHWKHPHFKDQLFDOSURSHUWLHVRI SULQWHGSDUWV

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

0$7(5,$/$1'0(7+2'2/2*<

,QWKHIROORZLQJVWXG\WKHQXPHULFDOVLPXODWLRQRIWKHH[WUXVLRQVWHSKDVEHHQFDUULHGRXWE\XVLQJWKH³7ZRSKDVH IORZVLPXODWLRQ´73)RI&2062/0XOWLSK\VLFVVRIWZDUH/HYHOVHW/6DQG1DYLHU6WRNHVHTXDWLRQVDUHXVHGLQ RUGHUWRPRGHOWKHIORZRIWKHSRO\PHUZKHQLWH[LWVIURPWKHQR]]OH1DYLHU6WRNHVHTXDWLRQVGHVFULEHWKHPRWLRQ RIWKHIOXLGVLQWKHFRQWLQXRXVPHGLDZKLOHWKHUHLVFRQVHUYDWLRQRIWKHPDVVLQWKHV\VWHP/HYHOVHW/6PHWKRGLV DWUDQVSRUWHTXDWLRQZKLFKLVDGGHGWR1DYLHU6WRFNHVHTXDWLRQVLQRUGHUWRWUDFNWKHLQWHUIDFHRIWZRLPPLVFLEOH IOXLGV>@(TXDWLRQ(TXDWLRQDQG(TXDWLRQVKRZWKH1DYLHU6WRFNHVFRQWLQXLW\DQGOHYHOVHWHTXDWLRQVXVHG LQ73)PRGXOHRI&2062/ ߩ߲ݑ_{߲ݐ ൌ ׏Ǥ}ሾെ݌ܫ ൅ ߤሺ׏ݑ ൅ ሺ׏ݑሻ்_{ሿ ൅ ߩ݃ ൅ ܨ} ௦௧൅ ܨ   ߩሺݑǤ ׏ሻݑ ൌ Ͳ   ߲߮ ߲ݐ ൅ ׏Ǥሺݑ߮ሻ ൌ ߛ׏Ǥ ሺߝூ௦׏߮ െ ߮ሺͳ െ ߮ሻ_ȁ׏߮ȁǡ׏߮     :KHUH ȡLVWKHGHQVLW\uLVWKHIORZYHORFLW\PLVWKHSUHVVXUHDSSOLHGWRWKHIOXLGDQGȝLVWKHG\QDPLFYLVFRVLW\RI WKHIOXLG,QWKHOHYHOVHWHTXDWLRQࢥLVWKHYROXPHIUDFWLRQȖLVDUHLQLWLDOL]DWLRQSDUDPHWHUDQGߝ௟௦LVWKHSDUDPHWHU FRQWUROOLQJWKHLQWHUIDFLDOWKLFNQHVVFstUHSUHVHQWVWKHIRUFHUHVXOWLQJIURPWKHVXUIDFHWHQVLRQDQG)LVIRUDOORWKHU H[WHUQDOIRUFHV 7KHFRORUOHJHQGRIWKHYROXPHIUDFWLRQLQ73)YDULHVIURPWREOXHWRUHGZKHQWKHYDOXHRIWKHFRORUIXQFWLRQ LVWKLVPHVKLVIXOO\ILOOHGE\WKHSRO\PHURWKHUZLVHWKHUHLVDLU7KHLQWHUIDFHRIWKHWZRIOXLGVSRO\PHUDQGDLULV FRQVLGHUHGDVYDOXH

)RU WKH QXPHULFDO VLPXODWLRQ LQ &2062/ 0XOWLSK\VLFV IUHH WULDQJXODU GHIDXOW SK\VLFVFRQWUROOHG PHVKHV KDYH EHHQVHOHFWHG)LJXUHVKRZVXVHGERXQGDU\FRQGLWLRQVIRUWKHQXPHULFDOVLPXODWLRQRI73)DQGKHDWWUDQVIHU  D E ),*85(%RXQGDU\FRQGLWLRQVIRUQXPHULFDOVLPXODWLRQDIORZEKHDWWUDQVIHU  ,QRUGHUWRGHWHUPLQHWKHKHDWWUDQVIHULQWKHIORZVLPXODWLRQDSDUWLDOGLIIHUHQWLDOHTXDWLRQ3'(>@KDVEHHQ DGGHGWRWKHPRGHO 3KDVH3RO\PHU 3KDVH$LU $[LV\PPHWULF 2XWOHW ,QLWLDOLQWHUIDFH RIWZRSKDVHV :DOO :DOO 1RVOLS ,QOHW _{,QLWLDO7HPSHUDWXUH7P} ,QLWLDOWHPSHUDWXUH7HQY =HURIOX[ 'LULFKOHW%RXQGDU\ FRQGLWLRQ7HQY =HURIOX[ 'LULFKOHW%RXQGDU\ FRQGLWLRQ7P D PP E PP

]

[



(TXDWLRQVKRZVWKHDGYHFWLRQGLIIXVLRQHTXDWLRQIRUGHWHUPLQLQJWKHYDULDWLRQRIWKHWHPSHUDWXUHLQRXUPRGHO WDNLQJLQWRDFFRXQWWKHPRYHPHQWRIWKHIOXLGLQWKHV\VWHP  ߲ܶௌ ߲ݐ ൅ሺݑሬԦǤ ߘሻܶௌൌ ቆ ݇ ߩܥ௣ቇ ߘ ଶ_ܶ ௌ   :KHUH7LVWKHWHPSHUDWXUHDQGݑሬԦLVWKHIOXLGYHORFLW\+HUHWKHIOXLGYHORFLW\LVWKHWHUPWKDWOLQNVWKHIORZWR3'( NLVWKHWKHUPDOFRQGXFWLYLW\ȡLVWKHGHQVLW\DQG&SLVWKHKHDWFDSDFLW\RIWKHIOXLG7KHWHUP൬_ఘ஼௞ ೛൰UHSUHVHQWVWKH WKHUPDOGLIIXVLYLW\RIWKHPDWHULDOZKLFKLVUHSUHVHQWHGLQHTXDWLRQDVĮ7DEOHVKRZVWKHSURSHUWLHVRIDLU3/$ DQG3((.XVHGLQWKHDGYHFWLRQGLIIXVLRQHTXDWLRQ 7$%/(7KHUPDOSURSHUWLHVRIDLU3/$DQG3((.IRUGHWHUPLQLQJWKHWKHUPDOGLIIXVLYLW\IURP>@>@>@>@ 3KDVH 8QLW $LU 3/$ 3((. 7KHUPDOFRQGXFWLYLW\ :P_._{   } 'HQVLW\ NJP _{  } +HDWFDSDFLW\ N-NJ_._{   } 7KHUPDOGLIIXVLYLW\ $FWLYDWLRQHQHUJ\ P _V N-PRO_   _        ,QRUGHUWRGHILQHWKHWKHUPDOGLIIXVLYLW\IRUHDFKSKDVH(TXDWLRQKDVEHHQXVHGLQDGYHFWLRQGLIIXVLRQHTXDWLRQ  ȽሺԄሻ ൌ ሺԄ כ ߙ௔௜௥ሻ ൅ ሺሺͳ െ Ԅሻ כ Ƚ௣௢௟௬௠௘௥ሻ  

:KHUHࢥLVWKHYROXPHIUDFWLRQGHWHUPLQHGE\73)PRGXOHĮDLUDQGĮSRO\PHUDUHWKHWKHUPDOGLIIXVLYLW\RIDLUDQG SRO\PHUUHVSHFWLYHO\7RWDNHLQWRDFFRXQWWKHPHWDOOLFSDUWVVXFKDVWKHQR]]OHLQWKHPRGHOWKHWHUPݑሬԦLQ(TXDWLRQ LVQHJOHFWHGVLQFHWKHUHLVQRIOXLGLQWKLVUHJLRQ7KHYLVFRVLW\YDULHVZLWKVKHDUUDWHDQGWHPSHUDWXUHIROORZLQJ WKH(TXDWLRQ7KHYLVFRVLW\RIVKHDUWKLQQLQJIOXLGVLVZHOOGHVFULEHGZLWKWKH&DUUHDXPRGHOLQ(TXDWLRQZKLFK WDNHVLQWRDFFRXQWWKH1HZWRQLDQSODWHDXDWORZVKHDUUDWH>@>@  ߟሺߛሶǡ ܶሻ ൌ ்ܽߟሺߛሶ்ܽǡ ܶ଴ሻ   ߟ ൌ ߟ௜௡௙൅ ൫ߟ଴െ ߟ௜௡௙൯ሾͳ ൅ ሺߣߛሶሻ௔ሿ ௡ିଵ ௔   

:KHUHߟ଴LVWKHYLVFRVLW\DW]HURVKHDUUDWHVDQGߟ௜௡௙LVWKHYLVFRVLW\DWLQILQLWHVKHDUUDWHȜLVWKHUHOD[DWLRQWLPH LQGH[QLVWKHSRZHULQGH[ߛሶLVWKHVKHDUUDWHDQG்ܽLVH[SUHVVHGDVWKH$UUKHQLXVODZSUHVHQWHGLQ(TXDWLRQ>@ 7KHYLVFRVLW\RI3((.3((.*E\9LFWUH[DQG3/$3UHPLXP:KLWHRIPPGLDPHWHUSURYLGHGE\H0RWLRQ 7HFKFRPSDQ\ZHUHPHDVXUHGE\UKHRPHWU\LQSDUDOOHOSODWHFRQILJXUDWLRQZLWKIUHTXHQF\VZHHSVIURPV_WR V_{ZLWKLQWKHOLQHDUYLVFRHODVWLFGRPDLQWKHUHVXOWVKDYHEHHQSXEOLVKHGHOVHZKHUH>@7KHLUVKHDUYLVFRVLW\DW} KLJKVKHDUUDWHVXSWR_V_{DQGH[WHQVLRQDOYLVFRVLW\KDYHEHHQPHDVXUHGWKDQNVWRDQH[WUXGHUHTXLSSHGZLWKDQ} H[WHQVLRQDOGLHIURP7KHUPRILVKHU&RPSDQ\7KHWHUPVRIWKH&DUUHDXPRGHOKDYHEHHQH[WUDFWHGIURPWKHILWWLQJ RIWKHYLVFRVLW\FXUYHVIRUERWKSRO\PHUV7KHWHUPVDUHSUHVHQWHGLQWDEOH 7$%/(9DOXHVRIWHUPVLQ&DUUHDXPRGHOIRU3((.DQG3/$ 3RO\PHU 3/$ 3((. 7HPSHUDWXUH . . ߟ଴   ߟ௜௡௙   ߣ   D   Q    ்ܽൌ ݁ݔ݌ ൤ܧ_{ܴ ൬}௔ _{ܶ െ}ͳ _ܶͳ ଴൰൨   



ZKHUH(DLVWKHDFWLYDWLRQHQHUJ\>@>@DQG5LVWKHJDVFRQVWDQW>@

5(68/76$1'',6&866,21

7KHQXPHULFDOVLPXODWLRQRIWKHSRO\PHUIORZKDVEHHQGHWHUPLQHGIRU3/$DQG3((.ZKHQLWH[LWVIURPWKH QR]]OHDWW XSWRW VHFRQGV7KHLQLWLDOWHPSHUDWXUHVDUHFKRVHQDW7P .IRU3/$DQG7P .IRU 3((.$WWKHVHWHPSHUDWXUHVWKHSRO\PHULVIXOO\PHOWHG>@7ZRWHPSHUDWXUHVRIHQYLURQPHQWIRUHDFKSRO\PHU UHSUHVHQWLQJ WKH WHPSHUDWXUH RI WKH SULQWHU¶V RYHQ DUH VHOHFWHG DV IROORZLQJ IRU 3/$ 7HQY   . URRP WHPSHUDWXUHDQG7HQY .JODVVWUDQVLWLRQ7JRI3/$)RU3((.7HQY .URRPWHPSHUDWXUHDQG7HQY  .7JRI3((.7KHLQOHWYHORFLW\IRUDOOWKHVLPXODWLRQVZDVVHOHFWHGDWPPV_

)LJXUHVKRZVWKHHYROXWLRQRIWKHYROXPHIUDFWLRQDQGWHPSHUDWXUHVIRU3/$DW7HQY .DWGLIIHUHQWWLPHV IURPW WRW V7KHEODFNOLQHUHSUHVHQWVWKHYROXPHIUDFWLRQRILQWKHPRGHOZKLFKLVFRQVLGHUHGDVWKH LQWHUIDFHRIWZRIOXLGVDLUDQGSRO\PHU)LJXUHSUHVHQWVWKHYROXPHIUDFWLRQWKHWHPSHUDWXUHDQGWKHYLVFRVLW\IRU 3/$DW7HQY .DWW V7KHEOXHDUHDLVWKHHQYLURQPHQWRUSULQWHU¶VRYHQ

$V LW LV VHHQ LQ )LJ E WKH WHPSHUDWXUH RI WKH ILODPHQW GHFUHDVHV ZKLOH LW H[LWV IURP WKH QR]]OH DQG LW LV H[SRVHGWRWKHHQYLURQPHQWURRPWHPSHUDWXUH)XUWKHUPRUHWKHQXPHULFDOVLPXODWLRQVKRZVWKHJUDGLHQWRIWKH WHPSHUDWXUHEHWZHHQWKHFHQWHUWRWKHVLGHRIWKHH[WUXGDWHWKHWHPSHUDWXUHGLIIHUHQFHLVXSWR.&RQVHTXHQWO\ ZKLOHWKHFHQWHURIWKHH[WUXGDWHLVVWLOOLQWKHPHOWHGVWDWHWKHH[WHUQDOZDOORIWKHH[WUXGDWHKDVDOUHDG\WXUQHGLQWR VROLGVWDWH6LPXOWDQHRXVO\WKHYLVFRVLW\LQ)LJFFKDQJHVIURP3DVLQWKHFHQWHUWR3DVRQWKHVLGHV  7LPH

VHFRQGV 9ROXPHIUDFWLRQ /HJHQG&RORU 7HPSHUDWXUH &RORUOHJHQG.         _{ }             D E ),*85((YROXWLRQRIWKHVWDWHRIYROXPHIUDFWLRQDQGWHPSHUDWXUHIRU3/$ZLWKWLPHIRU7P .DQG7HQY . DYROXPHIUDFWLRQEWHPSHUDWXUH.    7KHVROLGVWDWHIRUZKLFKWKHYLVFRVLW\LVKLJKHUWKDQ3DVLVUHSUHVHQWHGLQKDWFKHGDUHDRIWKHH[WUXGDWHLQ )LJF7KLVUHJLRQLVQRWZHOOGHILQHGEHFDXVHWKHSRO\PHUKDVFKDQJHGIURPOLTXLGVWDWHLQWRVROLGVWDWHVRWKH HTXDWLRQVRIIORZDUHQRWYDOLGDQ\PRUH 6LPLODUUHVXOWVZHUHREWDLQHGZLWK3((.QRWVKRZQ)URPWKHQXPHULFDOVLPXODWLRQRIWKHIORZRIERWK3/$ DQG3((.WKHYDULDWLRQRIWHPSHUDWXUHDQGYLVFRVLW\RIWKHH[WUXGDWHVDFFRUGLQJWRWZRHQYLURQPHQWWHPSHUDWXUHV DUHSORWWHGLQ)LJ)RUERWKSRO\PHUVWKHWHPSHUDWXUHDQGYLVFRVLW\DUHQRWLFHGLQWKHFHQWHURIWKHH[WUXGDWHIURP WKHGLVWDQFHG PPSRLQW,MXVWDIWHUH[LWLQJWKHQR]]OHXSWRG PPSRLQW,,DWW VIRUZKLFKWKHYROXPH IUDFWLRQLV





 _{  }  _

D E F

),*85(1XPHULFDOVLPXODWLRQIRUH[WUXVLRQRI3/$DW7HQY .IRUW V

DYROXPHIUDFWLRQEWHPSHUDWXUH.FYLVFRVLW\3DV 

7KHYDULDWLRQV RIWHPSHUDWXUHDQGYLVFRVLW\IRU3/$DUHSORWWHG LQ)LJD:KHQH[SRVHG WR . URRP WHPSHUDWXUHWKHH[WUXGDWHWXUQVIURPOLTXLGWRVROLGDIWHUDGLVWDQFHRIPPZKHUHDVWKHGLVWDQFHRIPPLV UHTXLUHGZKHQWKHH[WUXGDWHIORZVLQWRWKHDLUUHJXODWHGDW.

7KHYDULDWLRQVRIWHPSHUDWXUHDQGYLVFRVLW\IRU3((.DUHSUHVHQWHGLQ)LJE:KHQH[SRVHGWR.URRP WHPSHUDWXUH WKHFRROLQJ RIWKHH[WUXGDWHLVYHU\IDVWLWWXUQV WRVROLG DIWHU PP RIH[WUXVLRQ7KLVGLVWDQFHLV KLJKHUDERXWPPZKHQWKHH[WUXGDWHH[LWVLQDQHQYLURQPHQWUHJXODWHGDW.

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

7KHFRPSDULVRQEHWZHHQWKHREWDLQHGUHVXOWVIRUWKHYROXPHIUDFWLRQVKRZWKDWWKHOHQJWKWKHGLVWDQFHIURP SRLQWV,WR,,RI3/$H[WUXGDWHLVKLJKHUWKDQIRU3((.)RUWKHVDPHHODSVHGWLPHWKHOHQJWKRIWKH3/$H[WUXGDWH LV DERXW  PP ZKHUHDV IRU WKH 3((. WKH PD[LPXP OHQJWK LV DERXW  PP 7KHVH GLIIHUHQFHV DUH GXH WR WKH YLVFRVLW\WKHYLVFRVLW\RI3/$EHLQJORZHUWKDQWKRVHRI3((.DWWKHVDPHVKHDUUDWH 



D E ),*85('HWHUPLQHGWHPSHUDWXUHDQGWHPSHUDWXUHUHODWHGYLVFRVLW\DWVIRU3/$DQGVIRU3((. ,QWKHFHQWHURIWKHH[WUXGDWHD3/$ZLWK7P .E3((.ZLWK7P .          \





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

&21&/86,21

,QWKHFXUUHQWVWXG\WKHH[WUXVLRQRIWZRVHPLFU\VWDOOLQHSRO\PHUV3/$DQG3((.DUHPRGHOHGLQRUGHUWR RSWLPL]H WKH ))) SURFHVV SDUDPHWHUV 7KH WKHUPDO ILHOG DQG WKH HYROXWLRQ RI WKH YLVFRVLW\ RI SRO\PHUV ZHUH FDOFXODWHG7KHFRPSDULVRQRIWKHUHVXOWVIRU3/$DQG3((.VKRZWKDWWKHFRROLQJUDWHRI3((.LVIDVWHUWKDQ3/$ ZKLFK PHDQV WKH 3/$ VWD\V ORQJHU DERYH LWV PHOWLQJ WHPSHUDWXUH WKDQ 3((. GXULQJ WKH H[WUXVLRQ VWHS $V D FRQVHTXHQFHWKHFRDOHVFHQFHRI3/$GXULQJ)))SURFHVVLVPRUHIDYRUDEOHWKDQIRU3((.

:KLOH WKH WHPSHUDWXUH LQ WKH FHQWHU RI WKH H[WUXGDWH UHPDLQV DW PHOWLQJ WHPSHUDWXUH WKH FRROLQJ UDWH DW WKH ERUGHURIWKHH[WUXGDWHFORVHWRDLULVPXFKIDVWHUWKDQLQWKHFHQWHUZKLFKLVXQIDYRUDEOHWRWKHFRDOHVFHQFHRIWZR DGMDFHQWILODPHQWVGXULQJWKHSURFHVV

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

5()(5(1&(6

 2OVVRQ(.UHLVV* =DKHGL6$FRQVHUYDWLYHOHYHOVHWPHWKRGIRUWZRSKDVHIORZ,,J. Comput. Phys.

±

 /DQGDX/' /LIVKLW](0Fluid Mechanics3HUJDPRQ3UHVV  9LFWUH[9LFWUH[Š3((.*

 *DUORWWD'$/LWHUDWXUHUHYLHZRI3RO\/DFWLF$FLGJ. Polym. Environ.±

 .DVHHP0 *XQ<0HOW)ORZ%HKDYLRUDQG3URFHVVDELOLW\RI3RO\ODFWLF$FLG3RO\VW\UHQH3/$36 3RO\PHU%OHQGVJ. Polym. Environ.GRLV

 6KLEX\D1 3RUWHU56$NLQHWLFVWXG\RI3((.VXOIRQDWLRQLQFRQFHQWUDWHGVXOIXULFDFLGE\XOWUDYLROHW YLVLEOHVSHFWURVFRS\Polymer,±  'HDO\-0 :DQJ-0HOW5KHRORJ\DQGLWV$SSOLFDWLRQVLQWKH3ODVWLFV,QGXVWU\0HOW5KHRORJ\DQGLWV $SSOLFDWLRQVLQWKH3ODVWLFV,QGXVWU\6SULQJHU6FLHQFHGRL  6FKUDPP*$3UDFWLFDO$SSURDFKWR5KHRORJ\DQG5KHRPHWU\5KHRORJ\  /DIOHXU3*([WUXVLRQGHVSRO\PqUHV/DYRLVLHU

 %DNUDQL %DODQL 6 &KDEHUW ) 1DVVLHW 9 &DQWDUHO $  *DUQLHU & %HKDYLRXU RQ WKH FRDOHVFHQFH SKHQRPHQRQ 7RZDUG LPSURYHPHQW RI WKH SURSHUWLHV RI SDUWV PDQXIDFWXUHG E\ ))) )XVHG )LODPHQW )DEULFDWLRQ WKURXJK XQGHUVWDQGLQJ WKH LQIOXHQFH RI WHPSHUDWXUH DQG UKHRORJLFDO EHKDYLRXU RQ WKH FRDOHVFHQFHSKHQRPHQRQLQAIP Conference Proceedings 1896