ABCDEFEBAB ABCDEFAABAAEDEBDB CA DBCD BABBEBAEDCDAEBCD CCABAFEEBABBC ABB CCCEABBECBBABB EA CEACDBCACCCEA EEEACDBEAEAAB BEBDABEBACBEEEECD A BECDBEAA DCBAFEEBABECEBEECCD A BABCDA
Remerciements CABCDABBEEEBAC CA AC A B BA E B CDEBE B ECCABDABBEBEBECCA EEACABFEBBA EADEACCBFCB EAACAAECDEBA DEBBAEACECCEACDAECB CA B EA EA E B EFC BA FEE B ABECEBEECEAABCD EBECDBEAABEFCCAEA CA EC CA DE B F C B B EBE ACEFCAC CAADAEA EA C E A EA D EB A EA A EA A DB A C ABEEC DB EA C E EFC B CDA CAEBAEADECDEABB AB D C CDEA B EA BE F EA CDBBECBBABBBEACBFEA CDBCACCCEAEBBABBD CEA ECEAEACABBABEBAC BEEEECDEACDEAADCDB ABCCAEEAABEAECE BEBA DBCDFCBAAEAEACA AEAEAEACEACCE EDBCBAAE A F EA C EBAC C CCE E C C EA CA B A A EA B A E CDFEABC ABEEAEFEAEACDE BCAEACAECEACDFCBAEAE ABA FBEAECCABACC CECBECABCECCFE EC AC E EC A E BA E B FCCBAEAEACACAEAEAEEACE AEAEFCEAEAEBEFCEAEFEAA DEAFCCBAEABABAEABC AEBFEEA EADEAFCEEABABEACFBA AEEFABAFCACDEA EEEAACAEACAEAAC EECEABABEECEC
F CADEACCCCCABBACDDA CDEACC ABADBEB C D E A D ACC BC B CABE CB D E DEBEC ABCDEFFDAFDBAADFBA ABCDEFFDAFACB CFDD C D E A D ACC BC B CABE CB D E DABADACA CFDEA CFDCF CFDCB CFDFA CFDFAF CFDC CFDF AEBABCDFDA FADAACB FA A FA ABEADDCACDEADACC A EBDEDBAAACBBCEADACC CEDCABEDBECA ACBAFB ACDCAF ABCDFCDB EEEAACAEACAEAAC EECEABABEECEC
ACDFAACB DFCA FCDCABCC ACDCABCC A EBDECDFBCABECBADCAABCE ADACC FAB FBC EBDCABECCBCEADACCDFBCA CBDF CBDBBA CAAADADCABBCDADACABC CCAEBCEFABDDBDACC ACAFDFCDACFFC ACAFDADACFFC ACAFDEADDA EB CDBE ADBACACACCABCBEC ADACCADB AACBDAA FBA CABC DCAB ABDACBDB BAFACFCBBDB CFDAD CFDACABCD FDEBCACBD EEEAACAEACAEAAC EECEABABEECEC
ACEDBCEDACABCCEDFBCACB EB ACAECCE CC CABCDDA CABCDECA DCACCFFACFB CAADBAFDECFF FACBFACBADAFDCFF ECADBCEACB AEADEADACCAACBDB ACCAADEADACCADB ACAFDAADACFFCCACDFAF DACCADB BDACABCBCADCAB BDEBDACAD CAABDBCADACFFCDCABAFC EB BCDEADACCBCDCABECB FCFDCBAAAFC FCFDCBAACBAACABDAACABC FBF BCDEADACCBCDCADBDBA FCFDCBAAFABDAACA BDBFCDCABCCDECABCAD ACFFC BDFCDACBCADACFFCDEBCA ACAFDFCFADEBCA EEEAACAEACAEAAC EECEABABEECEC
B D FDBAA ACB D ECA BC A D ACFFC FBF EEEAACAEACAEAAC EECEABABEECEC
ADAB FCAFCAACBEBAEBEE FCAEBAABBAB FCAEBBCCEBFEACBCDABBAA FCAACBEEACCACBAEFBAC ACABCDCABCCCBACCACAE BCBE FCAECAEBAEBEABBFBDECDEA E FCAEEEEFEEABACB BCEABBFB BCBE CBDBDEBECBABCDEFBDEC BDBBCAEC CBACEFAEAACBFCCBCB ABBAB FCAACBCEBACEBAEAAEFCCA BE FCAEBEBDBACAABD FCAABA FCAACBBEEEBEAAAC BCD FCAACEBBAACEABCEEBDA ADBC AEEEABABEEBABBAE FEBEECCAFACCE BBBBBCEAAEBEFB ECBBCACEAAABCDBACB ECAA BEBAABB EECACEAAABECA ABDBACAB ABCEEACBEBBEAAEBA EEC ABCEEACBEBBEAAEBA C AACEAABBA AECAEBAEFBABEEBABBCAC AEBBABCEBECACBCA BAAC AEBCEACBCACCEE θ BC BECACBBEAC EEEAACAEACAEAAC EECEABABEECEC
AEBCBBEBEEEABEB CBEABACEAEC AEBEBEE EEBAEFB ABEAAEBEBAA C AEBEBEE EEBAEFB ABEAAEBEBAA C AEBEBEE EEBAEFB ABEAAEBEBAA C AEBEBEE EEBAEFB ABEAAEBEBAA C AABAEAAEFBABC EE = AEECEBBBECBA AFAEACEABACEAAFCBD ABABCEFAEBECAA AABAA ABDAEBEFCABDAEBEC BE AEECBEEBDAACBEEFCEA ECAACAEEBAEFE AEECBEEBDAEBCCBDAAC ABECAEEBAEFEABEB EBAABCECECEBA ABAACEBAABCACCC AEEBCBAEEABBABAC ECBAEEABDAAC ECEEBAEFBACE AEEBCBAABDAACECBAE CBAABDAACABBEEBA EFBACEEBCCEAABAEBA CBE AEECBEEBAACECBA AACABBACBBACBEE BCDEEBCACFE ACBAECDCEBE AEBEBABECBAEEBAEFB ACEABBECE AEECBEEBACB EEBDAACECEEBAEFBAC EABBECE EEEAACAEACAEAAC EECEABABEECEC
EEEAACAEACAEAAC EECEABABEECEC ACBBEBCBEEBACB AAA AECAEBCBEEEEBABBA AA AECAEBCBEEEEBA g g T T υ AA AECAEBCBEEAEEBCCCB AA AEBAEEBBAEAABB AE AECAEBCBAEEAEEBAEBBB ACE AEECBEEBDAACABDA ACEBD AABBCEEAAACECACCACB CCEB ACCEBAACEACABCBC EEAAACEC ACCEBAEACABCBEE ACBABCBEEBAC CCABABCCABEBCEBDEEC AEBEEAEBEEA EBCBCCAE AEAEBAFCACBE AEECACABECEBC BCCAE ABF ABCEAEBEAE ABCEACE ABBAEEEAAC AAEABAEEEAAC AABBABCABCCAAABAC BDEBCDEEC AAEABAABEBBABAABA AABCBCCAABACEA CDEEEBABFBDC ABCCAABA ABCCAAABACBDEBCDEEC AABDFCBAEEECE AEEBBDABCBFBDEECC BFBDCBC
AEEBBDABCEACCBF BDEECCBFBDCBC AEEBEABBEEBCE EEAAC AEBCEEBBAEEEA AC ACABABBAACEEBBAEE BABFBDCC ACABCBCBFECAABDEBCDEECC BFECAABDEBCDEECACEEBBA AEBCBDEEBCAC AEBAEACDABEACABABE AEBEBEEACABA AEBACCCBCBBCABEACABA AEA AEEACBACBAEFAACC BCCACCBBCC AECBBCEFACFBCDABAAAEA AEBABEBCDCBCDEEC AECBBCEFACFBCDABAAABBA AECAEBAECBCCAABCCAEBBAEA ABFBDCCCABFBDEECCC BBBCCAEB AECBABCEFACFBCDABAAA EA AECBABEBCDCBCDEECEFACF BCDABAAAEA AECBABACABCBAABCBAEBEFAC FBCDABAAABBA AECAEBAECBACCAABCCAEBBA EAABFBDCCCABFBDEECCC BFBC AECBABCECBBAEFACFBCDAB AAAEA AECBABCABAFCEEB AECBABCABAFCEAB AECBABCEBDACFABA AFCFCBAECBABCEEB CDFBCBBBCCAEB AABACAACAB AFEEEACBCCAABBAEB A AABACAACAB AFEEEACBCCAABBAEB A EEEAACAEACAEAAC EECEABABEECEC
ABBAFCBACEBABBE BCBEEBACAEA AECAEBCBFAEEFEAAEBFCCBCB CFBAA AECAEBCEEEFBFCCBCEBACDEA CEAEEBACAECA ABCFBAA AECAEBCBFAEACEAEFCBFB B BFBECBDBDEBECBABCDEFBDE CBDBBCAEC AECAEBCBFAEACEAEFBBFBE CBDBDEBECBBFBDEBBCAEBAE CAECAEBCEBAA AECAEBCEEEFBACCEAB CEEBAEABBFB BC CBECBDBDEBECBABCD EFBDECBDBBCAEC ABBABEBCBACCBEE CEA ACBCFAFBDAABAA AFAEEFBACEACDCCEBDC EBAA AEBCCECBCEECEBACBAABA A AFAEACEABBBEEFACDCB CBEECEA AECAEBA βeebabbe ABBABAECFFBFCECC AECAEBAEFBACEECDEEBA BBEFCCABCD AECAEBAEFBACEECCE CEEBABBEFCCAEECAC EFACDCBCCCEBE CCBCB ABBAECBAE AECAEBCEEBACEBAEEBC ECACAEAABFBDCBCABF BDEECBCBACBCB AEECEEBCAEACBA EEBABFBDCEABACBCBA EBABFBDEECBC AECAEBCEEBCDEECAEBAEAA ABCCAABCAABCCAEB CBACBCBB AECAEBABFBDCACBFEAAAB CCAABCAABCCAEBC BACBCBB EEEAACAEACAEAAC EECEABABEECEC
AECAEBCEEEBAEEBABFBDCA EBEBBBABEEAAABC CAABCAABCCAEBC BACBCBB AEBBFBCEEB CCEABFCCBCBABB AB ABBCABCACEBACCE EBA AAACEAEBAEAACEBDBB BEFCBABBA AAACEAEBAEAACEBDBB BEFCBABBA AEECAACEABFCCBCB EBA AECAEBCBEECECBCEEBCB ECCAEB ABEEEEBABBACEAABB ACCDABEEEA EBCEA ABEEEEBABBACEAABB ACCDABEEEA EBCEA AEECBECBCBEE CACEFACEBAEBCB α αeaabbab AEECBECBCBEE CACEFACEBAEBCB α αeaabbab AEBEEABCCACBBABC FCAEEAEBCBCCAE AEECACABABCAC EFAEEAABBAB AEECBECBCBEE EFAEABACAFCCBCCACEFAEA BBABEFAEEAABBAB AEECBECBCBEE EFAEABACAFCCBCCACEFAEA BBABEFAEEAABBAB EEBAEFBAB AECAEBAEFBABEEBABBEFCCAEA EACAABCAEBAE AECAEBAEFBABEEBBAB BEFCCABBECEAACE AECAEBCBEEBBABEFAE EEBAEFBACEECDEAABB AC EEEAACAEACAEAAC EECEABABEECEC
AEECBECBCBEE EFAEABBABEFAEEAABBAB CEBCBE AEECEBEEEFACEA CABAAEFAC EEBABBEFCCA AEECEBEEEFACEA CABAAEFAC EEBAEFBAC AECAEBCEBBEEBBDAAC EBBDAACEEBAEFBAC AEECBEEEFACEBCBCFE EABEBCEBEEBAEFB AC AEBAECECEAAC E AECAEBCEEBAEEBAEFBAC AEECEBEEEFAC CEBCBCBCECCEECCEBCBCFEEA BBEBEBAA EAC ECC AEBDAAEAEBACACABCA AEBDAAEAECCCACABCA AECAEBCEBAABACEC CEAACEEEBAEFBAC AECAEBCEBAABACEC BBEEEBAEFBAC AECAEBAEBEBAABAACEBAA BACECCEAACEEEBA EFBAC AECAEBAEBEBAABAACEBAA BACECBBEEEBAEF BAC AEECBEECBC EBCFEEABCABEBAABCD CACEEBCCEAACEBCD AEECBEECBC EBCFEEABCABEBAABCD CACEEBABBEBCD AEECBEECBC EBEABCABEBAABCD CACEEBCCEAACEBCD AEECBEECBC EBEABCABEBAABCD CACEEBABBEBCD EEEAACAEACAEAAC EECEABABEECEC
E BDA AE BCC B A CCE AC C BA A B E B B EE BDCA EA A C EBAFBECDABCDCCECCABAC EBAEACEAAECFCAFCB BEACABDACECEABCEBABCEEBEBDB EEA B E B A C E B B EEA AFCBEAACE EFA EB B CAC EBC C C B B EEC E BCEABCDEBACCCABA BCEBBCBEABACBCABCBEF FCABAEBDBCACBAEAEECE ECCD BDCB EFAABEC B CEECEBACAEAEBDFCBCC B B AC B B EFC CA B EBA BBE CAACCECAEBEBEBCBACEB BABECCBACEAEBCCEEAB EBBABABCEBCAB EACEAECCACABACA BCBCACEBBBCEBCEACEAC EEABABCBBC EEBBAC A CDCE B A CCA EE BA E B EEBCACCABEBCBB BACEABBEBACABCDEABCCFC EC ECEA EC C B BDCCE C A B B B A E B C EA C ABEBABCE ECBEAEFBDCECEE B A CCA EBCE BA B B AC B EFAE CDAB C BA EE B B B E CDCA B C EECEBACABEEA B CDAB E CDAE B E A C ABCEBEEBA BABBCEBBEEEAC ACA BA BABACBC EECE B B A A C AB A CA B EECE A CA EE EEA B BCBDABEAECAEEAAECB EEBACAEA BAEACCCACEBABEC A A EE B AC EFA EA B AC A C E CABEFCBCCABCBCBE EEC B BBEFAE B EECECBCEAACEFACACA CCCACEECEABABEECEAB CCEECEABCBEE BEBAEBCCBAAEAEA BA A EA AE A BE FFCEA BA E B EEEACACABCABCEECEAC B AC B A E B A EA C CA EA A C EEEEABACEAECBD EEEAACAEACAEAAC EECEABABEECEC
AAEAECBEBCEAAC ECEACEBEE BAABEECBDEFB AEECAECBEEBACAEAEA CEEEAACEABEACDEFBDAC B EE E BDFEB B B E FC EA E A C BCEEABCEEBBABCCB EEBACCEAEBECEAEE CDAB A AA C B BE CDA B DA B CDEEABAECBBCEBCEBAC EECBEBAFCACBDA EACACEBAEEEAACBDAEACDABBA EE EEA B AC B A B EE BA F EAEAEAEBCACBEB A B AC B A EBA B EECE C EA E C ACE BA EB CA B CB C EABABEACEEECCEACDFCBCEE B A A BE B C EB BDEFE B C B EECBCEEBAAEA BAEBABBECC AEACACAACABCB EEBACAFCCBCBDA EA EE C AC EFA B FCC B C C CBE BA E EEA AC EA C C AC E E C ECBCCAEBBEC EBACAEFABBABEFAE ACEECACFCCBCBCFABECDCAB CEECECBACBEE ACEFACECDEFBDABAEBECC AEECEABCAEEEEA CBBEAEAEFBDE BDCACACEFCEACAABACE B BDA A CDE BDA EBA A B CD BDA EACEAAECAECEACAC BBCBBCBACAEA AECEA EEEAACAEACAEAAC EECEABABEECEC
F CADEACCCCCABBACDDA CBEEACBBACACEBDACEC EABDACE CBACAEAACDEACAA C E CEA CA E E B A EEA C B B ACACEFACCACBBCB BCCAECCABEACDE B CD C AFAC BA CAB EA A C EBC B C B B EEC EAEACAFACBBAEAFACEEB AECCBACECECEAFCCE ACAEBAEAAEACE EA FE AC B CA ECCE C ECAC BA BAE FEABEEBAACABBAEEACC EEACAFAC BAEBDEACEECBEEEA AEACEBCEABCECEABE CDCAACBAEEEABACECAA CAEEAEAAEBDB BDBCACEBBEBBCE BABAEBDBEAEACAAEEEA BABEEBABBAEFEBEE CCAFACBACEBBBBBCEAA EAAEBACABBAEEBAEFBECBC ABCDECACEAAACC ACEAECAAB AEBAAB B EE CAC EA A A B E C A ABDBACAB EAF EA CDECAE B C E BE BAE FE BE E CC EE BA B B AC CACBCEBCCFCBA BAC EAFEACDECAEBCEBEEE EEBABBACCACCCEBE ( ) E + E π ρ = A C B D ECABEEA ρ CEBAAC ECAACCAACBFBA E CABCE BCCEBDBA EEBAEFBBCA EBEEACDEBCAB AAEAABBCCABCABC E B C CE C B B AC B CC A CBABEE EEEAACAEACAEAAC EECEABABEECEC
EE EBB AEFEBEE CC BAC AEEEABABEEBABBAEFE BEECCAFACCEBBBBB CEAAEBEFBECBBCACEAAABCDB ACBECAA BEBAABB EECACEAAABECAABDBACAB CA A EBC AC F A C A B E BCEEACDABBABBDEECEE BAEBEBBEBABDAECBDA CBBAEEBAEFBEECC EBCEEBEACBEE EABACBCCEBBCEC EECBBEFBECBABEB BCDEBB EBCBCEBEC BDECCAFACBBAEFEBBEBEE AECACBCACECDFCBBEE E B B A AB EEB C B B ACEBAEBACABCEAAABCEA CEAAEBAEECCEEBECBEABAC BBAABCBCCBACCDBCEE CFCBCABB EEEAACAEACAEAAC EECEABABEECEC
ABCEEACBEBBEAAEBAEEC AECACBCACEAAEBACAE ACEEBECBBACACDFCBABEAB BCDBCEEACBACFCEACAC BECCCE ABCEEACBEBBEAAEBAC EAEABCFBDAABEAACEBC BCEADAEBDEACEECB EEEBEAA BBBAE FEBEECCEABACBCCA EA CCE B C A B EA C BE BA E B EEEAACAEACAEAAC EECEABABEECEC
EEEABACABAEEEEABAC BA CDEACC EA B AC E AE B A E A B B ACEFCBDEFCAEBCECCAABCEC CAEB E EA E C ECCE C ECAC BA EA C AC A EACCB CACB B CABAFB ECCEAACACBECACCABACAB BCAEBBACFBABEABCAECAC BAAEBEEAEFCBCEBCACA ACBEECBBC ECACBCEABCECACBCEEB Plaque chaude Vecteurs vitesses des molécules Plaque froide AACEAABBA DACCEBEE CAAACBE CDEAABCABEAECACAC ECACBBDBDCCEE = B B + + B E AE E B E B E C A B ECAC CDC B ECA B CD B C A A EC C A B C AC B CDA ECEEBBFAEBBECACBACA BCACCEACECACACACECACDAC A DE CFC EA CDFC B CC B AC B C CBACBBCDEBEEBBFAEBBECAC EEEAACAEACAEAAC EECEABABEECEC
ABADBEB EABACABEBBEAECA ACBEEEACCAEACCEFBECB ABADEEBACFEAEBECACBAEABA BBCACCCE λ = B ECCFEAEBACBEAEAA ECACBAEEBECABCCBCDA EBEBBBABEAB CEEABAE BEEA BEB BEECAC C BE ECAC C E B AC E C EABECACBAEACEABACEA EBCEEBACCBEEACACBCA B B A E AF B A CAB BE E FCAEBBACBECACBBECBABCAB ACEAEBCEEBAC CBEBA EEBAEBAEABDCEEA CDECAEBAEFBABEEBABBCACCE BEB Moléculaire Intermédiaire Continu B AECAEBAEFBABEEBABBCAC EEEAACAEACAEAAC EECEABABEECEC
CDEADACCBCBCABECBDED EBEC EAEAEACBFAEBBECACC ACDCBCACBFAEB B CDAECEEFAAECAEBCDAEBEC ECBFAEB + BECACACABCAC A A EBC B CE BB C E BDA CE AC BDA CE BA EA CAC C B EE BDA AC C BE B B C BE C ECAC BA EA E C C A B C ACCECCE EACCEACCECCECABCACCECACB ECCAEACCEBACECACBE CACEACFAACCABFAEB CCBCABABCACBAB CEEAACA Réflexion spéculaire des molécules Réflexion diffuse des molécules Particule AEBBABCEBECACBCABA AC B BA B CE D CFC CDECECACBAEACACEAABE CBBEBECADAABBACEBA ACDEACDEAEADCBACECAC CCEAEBCABAEBBCEAA CCE + + + = α + α ECE αebdeebebabeace BACBAAFACEBA αaceac + C EE CC B BFAE B B ECAC BA B EA C BEBCDCBBCACDCBCEAC EEEAACAEACAEAAC EECEABABEECEC
ABCDEFFDAFDBAADFBA EBDEEBEBABEADCECCE α = E E C EE CC B C A B EA EECABCAC ABCDEFFDAFACB EA E C A BDEEBE B A B EA C A BDEEBEADCECCE α = E CCABDEBAECCEECACCABA ECB C CA BD E B A ECCE ECAC C ABAECBCDEECECABCECACC CCCBCAC CABAEBDEEBEACABA A BDEEBE C A EEBE EC A CE ACBACECACCEACFACABCAC CEADCCCAEAEBDEEBEAC ACEACAFBDACECACBCA BCACBFA CFDD CB ECEA AEBCEB EEBDAACABCBEECACEAAEEEA = E CEBCAC CEBAABA CBB A CEBDEABA EACECEACBACDEACCEBAA BA C EBA A CECC EA C ECEA B ECAC B E BA BA η E CECC B C EBAAEC DCCE η = E CEBEC EAEACACADEAADCEBDEE EEACEBEEEAEAEFCCFCBE + = EEEAACAEACAEAAC EECEABABEECEC
EAEABDCBCEDEEAEABCAC B πα = + A B E CBCACAEACAB CABA ECEBA EAEAEBBDCCECBEE BDAACAECAC η = πα ρ + E αcabdeebebabea ρcecaa BA η CEBABACAEBAAEABCAC CBBA BEEADEACE η = = ρ π + α DCDEEECBCBEE BDAACABCBEECACBBBEB CDEADACCBCBCABECBDED ABADACA CBEFAEEABCBEEBDA ACABCBEEABEEC BEBBEEACDEAEABCCA CFDEA EAEACAECBCACCBFAEB BECACB EBEEEAB BE C B EE A B CE B AE B EEFAEBEACE EBECACEACABEEBE ECACABCCBEA CBCABCACABCACEEA = F F = E CABACABCACAEBE EBEBCABCACEA = CEE CC θ ADEACE EEEAACAEACAEAAC EECEABABEECEC
F θ = ρ θ = η E CEBCAACABBC BEA Couche limite de la particule Molécules du gaz : θ z θ Saut thermique (T-Tp) Particule r y x AEBCEACBCACCEE θ BCB ECACBBEAC EBEACCDEABCEB EE η F = π ρ + E CEBAABACCBCAC CCEBCDEBCBACAAEAEAB ACAACCABCCEBEA = π η EBBACDEBCBEE Vth B η = = ρ + E AABBBAABDEEBEABEACA BECCC CEEABBBCBEEEC CCBACCECEBEACBDE EA B AC B FC EBA A E B EA BDAC B CEADECAEBACBEBAACEBAC EABEABACCEDCACFCE EEEAACAEACAEAAC EECEABABEECEC
CFDCF EAEAB EFCE BEB CEBEAC EEEBACEA F F CABCACE CCBCABCACABCAC = = = CEBEBBCEACBCACE F F η F = λ + + θ ρ θ θ θ A B = = E θ CEEBCEEBEECBACA BCAC = λ = CAABACABCACB F E EBEBBBABDEEBEAB ABEAAECB λ CCFEAE EACCEBEACECDEBCEB EEA πη + = ρ A + + + B EACBEEEDACCACCEBE ECACCDEBCEBBADEAEAB CDEABBEAEACEEAEACBE EBDCFCAEAAEFBABA F+ = πη + ACEEAEBCB EE BE η = ρ = + + + + B C CA EFA CE EA B AC B FC EBAAEEBACAEFAC EA C BE B E EE A E B C B EE F A C A B CB EB C AC E A ECACBBBEEEBEE ABBAAEABBBCAC AEBAABCACACCBA EEEAACAEACAEAAC EECEABABEECEC
CBEACDAEEAAEEBAEFBAB F F = + α + α α E CEBEEBBCBCE EEF E E C A EA B EF B AB AACEBEEBEECCEAEE BAEFBABCDAEAEACE F F + α + α α η = = ρ π + α CFDCB A CE A E BCE A EACC EBCBEECACEACCEEBEBA FCEACBEEEACEACBB AACEFCECCE η = B ρ B = + + + E CCAB CFDFA ABCCBCEBEBCBEAA EFBABBCDCFEAEACCEBE BCCEBCBAA EEBE ABEBBAACCBCEEBA CFEBEAECECBEECACCBEEA AEBCEBEECFCACDFCBABEBAEF BABECACEEA η + = π ρ A ( + )( + + ) B E EA EA CDECE B CDE B C B EE A CDFC BA BEEACCEBBCCA πη = A EACABEEBAAC A = + [ + ] EEBEC EABEBEECBABE BECDEBCBEE EEEAACAEACAEAAC EECEABABEECEC
η + A = = ρ + + + E CEBAABABCAC CFDFAF ABEAEEBDCE BEEAFAACAECDABFAAC AACEACAAEFBAB = π EBEBBABABEEAE BAEBEE EE F F F π E E + = A B F F F π + E BFCBBBAEFBABA CAEFACBCDCECBEBCD EACEBEEEEA ECEACBCCCEEEEAE BBAEBEEBEEEACCAC EECEBEEEEEECDE BCEBBCCEAAEBAEBEE EACE EECC F F F π E E + π = A A B F F F π + ECEBEEBEEEAB ACEBCBACEABEBCBDBCB CFDC EEEAEFACEBCAC EEECDABBEE EEBABCAABCEBDEEBE α αb BECEBECECACECCABCAC AC E A E BA E B EEEEBAEBCBCE EEEAACAEACAEAAC EECEABABEECEC
F π F F α + α Φ + α Φ ( ) F + α = A B + α F π F F π ( α ) + πα + ( α ) Φ + α + Φ A B A B Φ = + α + α = ϕ + αϕ π = F η λ E η ρ CEBACECAAC CEA BA EA CA B ϕ ϕ E EEBBCFCBEBCD CFDF E BCE A EACC E BA E B EE BBBCCABAEFBABBEBDEEBECE DCFCAEABEFBABA F F + A E = + + EA B AEBABCDFDA EBCCABDEEBEBCABC CEECACCABCACCEACAACECB BAAEBCACDBBABDEEBE α αacbbabace FADAACB ECAECBCBABCEACBCACA DCECCEAB F θ = ρ θ = η DEBCAEBCACBBBAECBBFAEB ACCBECCABAEBCAAC EBEEEEA EEEAACAEACAEAAC EECEABABEECEC
E CE BE A E BB BA A BDEEBEA + α = + α AEBAEAAEEBEAECCCA AECCAB ACEAC FCBEBEEBEEBCFCCA BAE AEEACBCAECEACE CEE = ± FA A EECBEABACABCACC DCCE F = λ = EACECACEEEACEACCE α = α ECCCDEAAECAC α ( ) = + α α ABEEAAEEBEAECCCA FA ECEA CE ECBEABA CABCACCEAAACACEECC θ B CCABCACD F F η F = λ + + θ ρ θ θ θ A B = = A CECBA CECBA EBCAC EABECACEEEABACCE AD CCE α = α ABEADDCACDEADACC A B EE A D EA C E B C CE A CAADCCBEEECCAEBEE η = ρ EEEAACAEACAEAAC EECEABABEECEC
E η ρ ECEBACECAACA BA CBBA CEBECBBBCCC BCACBAEBEBAABABCACAB EAC FCA FC C B E BA E B EE B FCAFCAACBEBAEBEE ABC A BABC DEDA = π + α CB >> F F E EBBBA ABEEBE ECAC = + + + A CE C C B = + = + E << BA = + F F = + + + A B CFE E < < EE EA EE < < ACCACBEBCBBBEBEE EEBAEFBABCACAEBEBBBA BEACCACCBECCBACEA ECACBECCBACEAEE AEABBAEFBABE EAAACAEBEECBACA AB EEEAACAEACAEAAC EECEABABEECEC
Agrégats D pp Talbot (eq. 1.30), Beresnev (eq. 1.33), Yamamoto (eq. 1.31 et 1.32) Bakanov (eq. 1.34) K th Brock (eq. 1.23) Derjaguin (eq. 1.26), Epstein (eq. 1.17) Brock (eq. 1.25) Waldman (eq. 1.12) 0,01 0,1 1 10 AEBCBBEBEEEABEBCBEA BACEAEC Kn EBDEDBAAACBBCEADACC EACBAAACFEAEBAEACB EEBEBECBBACDABCAC BBDACAEACACAEBA EAEACACDCABCEBAAAC EBEEEACEBCBCFEAEACDFCB EFBABEACCEABCBBDA EABAEFE DA E EF CEA C E EEEAACAEACAEAAC EECEABABEECEC A A AE BA EBEECEFBABEABEFBABAA CEBEEBBBBAEBEBAA B C CC B AC E C A E A C ACDAEBAEBEECEACE A DA EEFACA A CDECAEBAEB EEDCABACEACEFBABAEF BEEAAEBEBAA AAEACAAEBA EBEECDAEBCCCBAC
EEEAACAEACAEAAC EECEABABEECEC FCAACAEBAAEABA FCAEBAABBAB ACB DBAA ACB BBA CCC A FE C A A BBCAA A CAC EA ED A AEBEBEE EEBAEFBABEAA EBEBAA C
A CAC EA ED A AEBEBEE EEBAEFBABEAA EBEBAA C CAC EA ED A A AEBEBEE EEBAEFBABEAA EBEBAA C EEEAACAEACAEAAC EECEABABEECEC
CAC EA ED A A AEBEBEE EEBAEFBABEAA EBEBAA C AAACE EAEAAEFBAB CBCEBEEECCEBEE E EEEA CE E A B EFAAABEEEE EACACEA CAABBACDCABAEBC EBAABCACACCBA EBE CEA AEAEBCBEECEBA ABCACFCECEBEEFC BBBCCAB CEA EAEBCBEECEBAAB C AC EB E EB E C E B EE BACEA A EEEAACAEACAEAAC EECEABABEECEC
CEA EAEBCBEECEBAABC ACEB E CECE BEEB EAAEBEBBBAE EBABCEBEEBCBEE A B C E EA EA B AC B A B FC EF B AB E C EE CA A C E B EEBCBEBABBA EEEEBCCACCBA A EEA A AC EA A B B A EA B EBEBAA AACEACAEE AEFCCBEABACABCEBABABA BDAACAEFBABCACAEEFACEC BACDABCACEBBBAE EA A FCCECBACDABCACEBCABA ECACE BECACECBABCAC AEEACCBEAAEABCACCAEBDA ACACAEACAEABDCCAEACECA BCACBDAACEBABEACBACEA AEBEEEAEFEAAE CAACDEACAEABCACEEAC ABCCEAAECCEBAB CDEACB EEEAACAEACAEAAC EECEABABEECEC
AABAEAAEFBABC EE = EAEBCEABABE CEBEFCBCCAEACEBEEEAB AC A EA E E C B B EBE EA CDEBCBEECBEECACCBEEA CBEEABCECACCB EEBBBCCCBCACEACBEB EACBEBCBEEBECEB E A CE CFE A EEEAACAEACAEAAC EECEABABEECEC
BDCEEACBEEACDFCBABAB BCAACCECCAACBCCAAEACDE CECACBACABCACBCABDEEBE CDE B C B EE B EE BB CBAEBEBAABABCACECEAC CCBACA CEDCABEDBECA EEACDEABCBCEBCEE FCBCCABEABACBEBCAACCA AAAACBEABCACB BCEECEFACCEACEBDBE AEECEFCAECCBCEBCBCEAEAB EFCCEEBBACEBA B AC EEB A B BDA AC A A B ECCCBCACBEACEAABCCEFC CACBACCEACECA ACBAFB BACECAB C BB C C ECA EC A C AC EA A EE B AC E AEEAE = E CEFBAC CBBAC BACECAAACEADEFCCB CD ADCCE π = ρ E ρ CECAABAC ACDCAF BBEEAABEACEBCAEABAB BCDBEEBCEBBBBC ACCBBCD = B ABCDFCDB EA AC EA B C E BDA AC C B CDCABCEBDAACACEBACC ABEBABECECEBA CACEAEBCEBACACAB ECAACCEACBABCCCEACC DCCE χ = EEEAACAEACAEAAC EECEABABEECEC
EABACBEEACCABAAAEAB ACACCEAB ACDFAACB B B EFC CA B E C B B C E A CA B EFC CA A C AC EFC CADCCE A = = = πη E CCEA BACA EFBCECAC C AEBEEBA η EBABA BBEFCCA EFCCACCEFCBACCE = DFCA BECAEFCECBEC BDAEFBCDCCBACEBDAEFCDEF B CEAA A CDE A E E A CE B CEAA A CDEF E BBECCCE C = F C B BEBBEACCDBBBEB EAEBAFACABCBAEBCCAEABAC BCDCEBAEAECDCBCEFACDBBDAEE CEA E EA B E FC A CE C C C ADEBECEABEBECCBEC CEFBACCEBECEBAC BE C E B A A B ADA BE CEBAECAEACEECE BDBBECB EEEAACAEACAEAAC EECEABABEECEC
AEECEBBBECBA FCDCABCC EFBACEEAACAA CBEC ABBE ABBAC CCEACACCE F = ACDCABCC AC C EE C BDA A CA C EBCCACBFAEACEABAC EAABAABCEFAEBECAAACCEB BFAEBAADCCEABECCBACB EEEAACAEACAEAAC EECEABABEECEC
N p AFAEACEABACEAAFCBDABA BCEFAEBECAA A EAEABBB EACCAACBC BECBBCD BECBEA B CD C B B E C B B EFC CA C B ACECA CBEBA CBBAC CBBCDABBCEECECDAAEC EBDAAEEEEEAACBACBE AC AABAA EEEAACAEACAEAAC EECEABABEECEC
EBDECDFBCABECBADCAABCEAD ACC EECABACEAFCAECA EA B AC A EA E A B A C CC B AC E AABBACEABBEAC CEECECBCAC EACCEEBEACECAEEAEACB EE BDA E CA ECA A B BBEC E CACEBCACEAEEEBABA E A C EE EEA B AC E A E CCDAABDEEABCBBC EAEAECACACACDAABDBEFCEACB BE FAB CAAABEAACDCABCEBCACACE CBEEABEABECEBAC EBCBBEBEAEBDAEEBBA BAABCCAACECEBCAC EEA A B E A A AB EA BDA ACCBABCEAEEACBEEB ACCBAEBACABBAACB CCBDAACABBACCB EEFAECAECABCEAEACEE BEBBECBECAEECCCABBACCC EACBACBEEFCECAEBCA CACBEEFCECEBCCEBBECAEEFC EFAEEBACCAEABEBEBEAECACC ECEEBACCAEABEBBEBEAECACCE AECEBBEECACBE EBAACADEBEBACEB A AC B E EFC BE CD EB F C C B B AAACABBACDEBDEBEB BECEBAACBEECBECDC CCBBAAACABBACD EBFCAEBEEAAE CAEA CBEEBDAEBEFCACCBDAE AACBEEBECABEEAACCBDA a/2 b/2 a/2 b/2 ABDAEBEFCABDAEBECBE EEEAACAEACAEAAC EECEABABEECEC
Oblate Prolate AEECBEEBDAACBEEFCEAECA ACAEEBAEFE CCCECBEEBDAAC BEEBEFCEAECCBDAACABECAC AACAEEADAACECAB EECACADAACACEADAACEFCA CAFCCCECCDCABCEBAAB BACACBEEEAAACAEBA AEAACCBACCECEA CEBEEBDAEBEFCCAFCACC BDAACBECACCAFCCA EFAEAAEFC CEBEEBDAEBECCABACC BDAACBECACCABCA EFAEAAEFC DEFACACACACBEEBBA CEACDCEBAABCACBABAE EFFC A C A E E C E C E B EEBDAEBACCBDABECAEABEB EBAA EEEAACAEACAEAAC EECEABABEECEC
AEECBEEBDAEBCCBDAACA BECAEEBAEFEABEBEBAA BC ECECEBAABAACEBAABCAC CC CC C A A E AB C B EEBDAACBECAECCEFAEEB EAAEEBBAACABBBAC EAEACEBEEABDCABA CCBDAAABECAACBEECA BEA EECABCBCEBDAAC B EE B EE C A B B A C EBA α CECCE = α ECEBBAEFE αcabbaea EBA α C BA EEA C C EBA BA E B EE CEA υ BAEEBBE α = υ AAEABEBABEB A E C BA EEA B B AC B A B AC E B C BA EEABDAACECEEBAEFBAC AEACBAEEABDABACC A B B A AA CC BDA AC A EC E E A A C B EE BDA CCC BACABBABAEAEEAA CCBDAEC EEEAACAEACAEAAC EECEABABEECEC
ECACBEEEFCBCBAC EEFACBEECABACCBDAAC EC EEABEBABECAACAEEA ABEECAACCBDAACECAEB CEEACDBCEEBACCCBDAACA EBAEACAACA Kn << 1 Df = 1 Df = 3 AEEBCBAEEABBABAC ECBAEEABDAACECEEBAEFB ACE FBC EACDABBCDCABCEBDAACABEE BCECACBAAA DABBFE DABBE DABEABEECDCABCEBDA ADCEAEECBAACAAC BEECBBAEEBCCEB ECACCABCACEBA α AECBA t EEABBDCCBDABBACCB EF B AC EE C BD EE B C CEAABAEBACBECEEABBDBC BEEAACBAABDABAA CCBDAACABBACDBEECBA CACCBBA EEEAACAEACAEAAC EECEABABEECEC
R L AEEBCBAABDAACECBAEC BAABDAACABBEEBAEFBAC EEBCCEAABAEBACBE CBEAAABBFE AECBEEBAACECBACCBDA ACABBACBBACBDC β CDC CDCBCACCBBACDC β ACEACAC CCBBAAEBDAADAAC ECBACABBAABEEAA CCBDABDAACEEABAECBBA CEACDC β A EEEAACAEACAEAAC EECEABABEECEC
β AEECBEEBAACECBAAAC ABBACBBACBEEBCDEEBCAC FE CDFCBABCFCBACEBDAACEA ACAABEEEAACBE ACDEEBDAACBECAECEABDEA EAECBAECFCACBEECAC BEEBACBEECEECCEACD CCBBAAACCBDAACABBE AADEECEAEACBEEBACEA C CC B AC A A A B AC E A E C AE B CDACEBBACEACDBCAB ACCEABECDBCDEEBCDE ABBA EBDCABECCBCEADACCDFBCA CBDF CBEAEAADCAABABDACBB ACCAEACEEBDACEBECAE BEACAAAABE BEE EAEBAEEBCEAEBAA BDABCEEBDBEACACACEFCB AEEBACABBBAA ACBDECDCEBE EEEAACAEACAEAAC EECEABABEECEC
ACBAECDCEBE ECEBBCDCABDAEECECA CDBEBCBEEBBDECAC EACEEABCDECAEBABBEBAB EEBAEFBACEABBE CEBEBACEBDACEBB CDAACDEBEBABCDABEA BACEACAEAEAE EAEACEFBACBCDB CAFCBBBCBECEABCAE AEBEBABECBAEEBAEFBAC EABBECE C CE EA E A A C B EE A DEACE η = ρ E C E B EE A E C B EEBABCBEECACCBEEBDA ACECEEBAEFBACEECD AEBDAACBEEBDAEEBAC EEEAACAEACAEAAC EECEABABEECEC
ACACACABDAACECBDAA BEEACEFBEE AEECBEEBACBEEBDA ACECEEBAEFBACEABBEC E BCBEEBDACABDAEE FCBDABACAAC ECEEACEBEBACEBEEBDA FCBBBBECBEABDEAA EEBACBCDCBEEBDA CCBDAACECEACDFCBABEBAB EEB B E BEBA E DAB B E E BE A C B EE A C CC B ACDFCBABEBABAECECAA BACA CBDBBA EAEFCDBCEECEACBEEBACE AEBECAABCEEFBB EE AA CC B C E EA B AC BDEB B A B B C B E EAA CD EFCEEEEABACBABCBECAB FEAEEFABEEEABBCC EAACAEBCCBCEBCB EABCBEEBDAAACC FCACAFBDEFBBA CAEEABBAEBA BACBFECBACAAEAEF EEABBCCCCBEEBCDEB EEEAACAEACAEAAC EECEABABEECEC
ACBBEBCBEEBACBA AA AA ECCFEA AC B CCE B FE EA CA AEBCFCACAAECCC BACCECAACEFCBCDCCEABFA CECAABDAABACCECAABAACA BF FCAEBBCCEBFEACBCDABBAA ACAAECBBA BEECAACBEEA CDECAEBCBEEEEBABBAEC E C E C EEA B A C B B AACAEAEACACBECAACEFCFAC BB CCAFCECBEECCACE EEEAACAEACAEAAC EECEABABEECEC
AECAEBCBEEEEBABBA AA A CDECAE B C B EE EE BA υ T / T g g EFCB A EA CA CB EE A C B B A EA C EBE CCBEECCACEEFAEAC CECAABECCAFCEAE CCBEEEFACCCB CCEBCBACACEEACB FCECAABCCBEECCAEBCDEB CB AECAEBCBEEEEBA υ T g T g AA EEEAACAEACAEAAC EECEABABEECEC
ACDECAEBCBEEBBB CFCAEEBCACCCCBACEE BEABBCDCBBCCECD AACBEEEABACAE EACAACCEBCBAE B EE B AB A C E E A AC A C B EE B A CEACACCA DCACBEABAACB EEBDAEEBACFCBBBCCCBA EFBACACACBEEA CCCBAABBCBEBEACCAB EFA B AC EB CDAE B CB B C BE ECACDBEBCEBABEACAE EABCBEECACCBEEBDAEB CABDAACAAABCBEE EFAEABEBCCBACCEE eq. 1.11 eq. 1.26 eq. 1.25 AECAEBCBEEAEEBCCCB AA ABEBAAEACB EE B EA EA EFE B B EEEABAACCCEFAEABAC C E A C EEA BA C CC B ACBEEBDFCBEBBBCCCBAC CAABCCCBCDBABACCA BAABABCEFCBECCBCCC BACCABAACEFCBBE CDCABCCCBEEBCCBCECAABCDBA CECBEEEFACEECECBA ECACCCAEEFABCBEBEA AACFCEAEAACABCA BDCCCBACCEEECAA BEECEC EEEAACAEACAEAAC EECEABABEECEC
CAAADADCABBCDADACABC E AC A EACC EB EA C C EE EEABDAEEBBAAAEBAA BCEEAACDEEBBAB CBEEBEACBCDABBE CEB AC AEBAEEBBAEAABBA E A CDECAE B C BA EEA BDA EEBAEBBBEEEABEEAAC BEEBDAEEBBAACBBBB CEECCCCEEBACABBA FEEAABBBDAACECBA EABBACAADABEEAAE A BC E CCC A B B A C A B BA AAEFBABCAE EAEBBEABBA p k / k g CA B B CDAB B E FC AEA E C EEBBAEEBBCAFCCFCCEA CBBACEBCEEAA C E B EE A A A AC BDA EAC EEAABEEAAEEBCDEACEEAB C CD E A B B A B CC A C AC CCACEECCCAABBABBAEA ECEEEAEEEEABCBB EBBA AACEACBAEA FE DEBEEBCDEAABBAB ABABCCAAABEFCBA ABCBECCBACBCDEABB ACCEACEEAACBEE EEEAACAEACAEAAC EECEABABEECEC
AECAEBCBAEEAEEBAEBBBAC E ABFFCEABABACEACCA CAEBEBACAAABEA CBEEBECBBBACEE EAEEBDAACDEEEABBABDA ACEAACAABEEBDAE EADABDECCCBBA A A B EE C A B A EA C C EE EEA B CA EECE C C E E B ACE ECE A AE B C B EEBDACEACEFBACAAE ECCBAACBEEBDCE A CDFC B EF B AB A A C E E BECDEEABACEADCEAABB A AAACBEBAEEABCB EEBDBCBCEEB CDABCBAA EAAEB CB EEBDEEBCACCEABACAA AABBCEECECBEACB ECEBDAABBBEEBDACEB EEACCCCBBBEFCCA E B CCABAE B CB AAECA AC EBEEBBBCCCBBDAB EECEABCCAABEBDEEACEF BACBDCBBCAC EABEA ABCCBAACBD BBBA FC EF C AB EA A CDECAE B C B EEBCABACABCB E BDA EA B C C EECE B CA EE EEABDAABBCEABECAA ECAEEACDABBAEEEEABBABEFAE EEEAACAEACAEAAC EECEABABEECEC
AEECBEEBDAACABDAAC EBD CCAEBCEFABDDBDACC ABABABEEABE CABCEBEE CABCBEE CABCDBB ACAFDFCDACFFC CBAEBEABAEBEEE CDACEBDAFCBCCEBACB ACECCEBACEBCCC CEBDABBECCCCABAAABA CCABAFEBBDEABBACEAAC BEECCBCACBBBBE AAACBBAEEEAE BEBEFABECCBEFEBBC EAE EEEAACAEACAEAAC EECEABABEECEC
AABBCEEAAACECACCACBCC EB CEFCEBCACCCCACBCCA C AC D FC EEC EA EAB EFC AC AFCCEBABCAAB CEBEE EBACCACBCCCAABBECCABA CEBBCEAACECAC CBFCCACCEEC ACFCCEBAACAE EABACACBABCABECC BBAEFCBCAFACACEFC EECCDAAEEAACEACEEECD ACACCCEEAEECEBAAA CBCEBAEACBBCEEEAECEE EECBCEBEEBDAACEAEEEC EECABDEAEACABCCCBC BEEBCAC EEEAACAEACAEAAC EECEABABEECEC
ACCEBAACEACABCBC EEAAACEC EAEABEFCEBCEAEACCFC CEBAFCBEBACEAAACBC EBEEAAAACAFCBCEB EEAAACEAAACEABECE BEEBBBCDEEBCAC ACFCCEBAACEA CABCEBEEBEAFCABDCEBCAB CFBDABBFCCACAEBECC CABCCCBCACCDBBDAEEBEBEACACEA CCCACBCDECCEBCEBCACEBC ACEEEEEFACBBB AECBAB EEEAACAEACAEAAC EECEABABEECEC
ACCEBAEACABCBEE ACAFDADACFFC BEBCBEEFACABBE B E BDA AC EA A B B A B A EAC EBCAEBCEAA B BA A B BAEADA EEC ECB E B A EAC C BAC A B B AFBDABBCBEEAC ACAEBAEECCBACAEECB BCEBCAACCABECC EEABEEAEACACEBCEBAC BEEBACBCDEFEBABCBC ACBCBAEAACBEEBCB ACBAEBCEBBEEBC BCAACCBACECBABCDABACCA BCE ACBABCBEEBACCCAB ABCCABEBCEBDEEC EEEAACAEACAEAAC EECEABABEECEC
ACA B EB E EB EA E AA E EA E DACEBCEBACCBEEBBE AEACCAEACABCBEEA C AC EFA EB CE BD EA B A EEEAACEFACEBCBCFEEEEAA EBEBAAECACCCAFC BACBEEBAEBEBEECEA CE A C EF BDE EFC A AB E A C ACCFCBABAEE AEBEEAEBEEAEBCBC CAE ACAFDEADDA BDAB E B C E B EE CDAB B CDBBBDAEECABBAEBAEBBACEEB BCABCEEBCDEECEBAEBA BBBCCAAEBCBBEEAC CACBAEBEE BCBEEBBEBAFCEB EAAEACCEEA AFACEFCBCEABDABBA EBCEBABECAAEBEBACA EAACBEAEACBBA CCEACCDBBAEAEEA CCEAABCABBCBBABEEE BCEABABCACCDCE BAEBAAAEBAEBEECAC EBEBCDEECCEEBACEBABB B EEEAACAEACAEAAC EECEABABEECEC
EA C A AE B CD B B EEA C A A C CEAA B C E B B CD B ACDEECAEBBBEAEABEFCE E BCE A EAA BE B A C E B EEBACEBEACAC EAEBAEECBEAFEACDACA ACACABABBABCAFAACACABEBDEECAC BCDACBBCACABBAFCE BDEABBBAFCEABA BCAC AEAEBAFCACBE AECACABEC EBC B C CA AC E A FE EB C E B EE B E C EBC EA B EEEAACAEACAEAAC EECEABABEECEC
AEECACABECEBCB CCAE BEBBBEBAEBEECEB EEEFCCCAFCEBBCECA BDACEBCCACBCCEBFCECAAE EACDABBACEACEACEBCBBE BCBEEBBBABC C CA B AC B EA B C A CA BA EBEEEAACABEBAEFBABBCA BA B B B EEA C B BE BDA EBC C C BCEBEEEEBBCDEAC BDBBEBEEEEBBCEABE ECBDEFBAEECAECBEE BACAEAEA EB ABFFCEABDFEBBABE CEBEFCBCCAEACEBEEEAB AC A EA E E C B B EBE EA CDEBCBEECBEECACCBEEA AEACDECECACBACABCACB CABDEEBECDEBCBEEA C EF A C B EE BB E BA E B EBA A BA B C AC E CEA C CC B AC A EAEBABACEACCAC AEBEBACAAABEAC B EE BE C B B B AC EE EA E EBDAACDEEEABBABDAACE AACAABEEBDAADAB DE CCC B B A A A B EEEAACAEACAEAAC EECEABABEECEC
EEECABAEACCEE EEA B CA EECE C C E EBACEECEAAEBCBEEBDA CEACEFBACAAEECC C BAA C B EEBDC EACDFCBEFBAB FC EF C AB EA A CDECAE B C B EEBCABACABCB EABBCEABECAAECAEEACDABBA EEEEABBABEFAEAAEE ABEBCABDABEBCEEEA AC EEEAACAEACAEAAC EECEABABEECEC
EAECBCEBDABEEC AAEAEBDEACBCBABACCCEA C BA AA A C BA A EB EA C A B C B EE EACCEBACBBCEEB BEEACEBACEBCDC EA E A C EE B BA E EEA ACABDEFBAFEECAECB EEEBACCECBE EAEAEEAACEEBACABEAABEA EABAACFEAEBEBEBDEACC BABABABECFEEEBABABBAAB EB CDBE BECAEAABFAAEAE BDEACBCEECBAEBEFCCAAC BCEEAACABEFCCAAEF BACACABCECACEEBCAEFC CACEACBCBAEEBBA CA C CCA AC CCC A B B BA CAEAECCACDACA CAAE CABDEBBFC BCDCACBABAAAACBE BEAACCAAABCDCABDAEECABF EECCEBCECAEFEBBAEBDA AEBEBAACAACABDAAECABAA CA C BA CA EB A BA E E CECACEEBCAEFCCA AACACEBCBBCE EAEBABDABBECABBA EBAACCACDEECAEEB CECABEACCAAAAEAEBECE EEBCEFCCABCDEEC ACACACCBEE EACEFCBECACEBCDEEC EEEAACAEACAEAAC EECEABABEECEC
ABF ABAECBBCBCEC ACCAEFCCAAEABCBEAEC BAEABEABEBEFCCAC CEEAAABCCAAAEBDEA ACEBCDCAEBAEBEAEAEBEAB EFAACCAABAAEAEAAACAB CDCA ABCEAEBEAE BEBBEBAECA CDACBABAB CEBCBDEB CEBCBDEFFCFEAAEAC EEEAACAEACAEAAC EECEABABEECEC
ABCEACE EABCECEEEAACEAEBC E BA BC EA C A E B E EA BCEAEAABEEACDABBCBEEEA C AB B E A BA EA CDAB B C EFC CABAC CDEACCBACACDEFBEFAA CDEACBCACBCCDBDCBFEB EBCBEBCAC AECAFCBDABBAE ADCBBBEBCAC ADBACACACCABCBEC E BA E EEA AC B C EBABCEACBBAAC A EE B BA CA C CCA AC CCC ABCAAABAAAA BACCAAEBAA BBA CBACAABBA EEACABFBD ECBABEACBABA AAABFEECABFAACBE BEAACCAAABACAEACCDEEC CEBCECACEFEBBAEBDAAEB EBAACAACABDAAEBEEBAC BDABACBACABABEDEECCE CEACAACCAABA E A C BDA B B A EB C BF ECAABDBEBCDCBCDEECEAEECA ADAFEBBFBABCEBCEBAC BFCEAAFEEEBABEEACCEEAC B B C EE BA A EA E BDE B C E B CEBACBECBABEEE EEEAACAEACAEAAC EECEABABEECEC
Qa a Qm Qa Plaque chaude Plaque chaude Qc z h r Qc Plaque froide Plaque froide Qs ABBAEEEAAC ACAAAEABAECC EEBBABACCCBEBECEBAB EBBCCAABBCCAEBACEBAE BABBAEEEEAACEBCEB CECAABEBEEACAAEAFE A A EBA A A B E CDEE B A BD A E E B B A A CDABCACACFCEBBCEBCDCAA BCBBCEBAABECABACE EABA BEE CEBDEB CDEEC C BEFEBBECAEEBBC BCBCAEBAECAC EB BA BE EA E BA C E BDA A A FC EBAAAEBCDEAABFB B A A A FC EBA AAFCEBBCEBEBDA BCBEBAECBACABDABC BCBACACEBCABABE CA AB A C F B BA C B A A E B CABACBAABAA BBBAABCCAABBACAA CAEBEAEBBCEACC AEABBDABCBDEBCDEECBC BACAEACACBDE BCDEECCBACBDEACA BDECAEACAACABCCAAABA EEBCEB CEBAC BA CBA CBDEACABDECAEACAAA CAAABAEEBCEBDACFABAB EBDEAECBACCAABCCAEBFC CEACBFBDCCEBDEBCDEECDACEBBA CACCAAABDA EEEAACAEACAEAAC EECEABABEECEC
Excès d air Injection de l aérosol Résistance électrique Zone de sélection Plaque chaude Plaque froide Plaque chaude Plaque froide Isolant thermique et électrique V Circuit de refroidissement Aérosol sélectionné Mousse Air filtré AAEABAEEEAAC Résistance externe Résistance interne AABBABCABCCAAABAC BDEBCDEEC BAABDABCEBCFBDAA BAABDBAABBACBACAB EAEBBBEBCCABABA AEBACAAAEA BBAABBBEBCCEBACAB EEEAACAEACAEAAC EECEABABEECEC
Entrées du circuit de refroidissement Sorties du circuit de refroidissement AAEABAABEBBABAABA EACECBABABAAAABBABAAEBC EEEEACEBABCABCA B BA EEAC EC C A B C C A EEAC EC C A B BA AB EB EEAC EA ABABBBABACEEACEC CAAEBCDEECBCDCBA BAAEEBACABCEBCEBACBA BABDEBCDEECBEEACECCA BCBABAAB ECABECCDFCBAEAC EEAC A ACA EA BDE C A B E B BCCAABBACABEBC CAEBECEAEBDFCEEACECAEA BEACDEEBAACDFCBABA BAABBABAEB BFBDEECCABABAECAEB ECAABECAEAACBAABEA EBAEACCDEECBDACAACBA AABBCDABECADEECAA ACBBBBBCAABCBA AAEEAEBEEBEFFCACA BCCDFCBABAAA DCEBACFBAABCCDEAC EAACEBCBAAEAEAABB BDEE B C CDEAC D C B A A EACBCCBAAACBAAAAA BCBABAACEACACCCDC EEEAACAEACAEAAC EECEABABEECEC
Surface interne du disque froid Mousse Epoxy AABCBCCAABACEA CDEEEBABFBDC DEECCDCECEBCEBCECDEECEA CBABAAAACCDCCEABAEA DEACEEC B B A E C BA BA EEA C BE B ACAEBECECAAFCAABA BAEBDCAAFCAABABAAB ACAAABBABAEBA BABAABABDEBCDEECCEAEBDE ACDECEACBABAECEFFCACA ACAEBEBBAAFCDEACBCEB CEBACCEAFAECECE ABCCAABA EEEAACAEACAEAAC EECEABABEECEC
ABCCAAABACBDEBCDEEC ACAAACEFCBAFCCBAAB EBCECAECEBDECACBABA Volume tampon Disque chaud Disque froid Epoxy AABDFCBAEEECE CDEFBCBCBEEABAEEE CBBBACEAEAEEEBCA EEEACCBAABABEAEAAE CDBBDAEEBAAECBABAFC EABDECCACABDECABAFC ABECCAAECBABA ABEEEBBCEACA EEEAACAEACAEAAC EECEABABEECEC
ADACCADB EBBBEBAEEBA CEFFCADAACBCBEECECAAC EB E CE C BDE BDEECCBFBCDCACCECDEBDEBDEEC C E CA BA BE C EE B B ACCEFCCADECABCEEBB CDACEBCEBBDCBAEFFAAB FCABDEAEBCCBCAABAB EBEABECEEBBDACABEFCCA EACEF ( ) = π φ A B, (2.1) E φ CDCBDAEECACAEAEAC ACEEBBDABAAAC EFFCBDEBDAACCEFCCABCACCEA FE BA BE A EA BA CBFECAABCDCBCDEEC P 1 0 π + π Z U G AEEBBDABCBFBDEECCBFBD CBC ACEEBBDABCEAC AEBACBFBDBEBDEECEBA AABDBEBDAEABBECAC ECEBEAEBCE AFEBCDCAEEBCAEEBBA CACDBDABBAACCEBAC EEEAACAEACAEAAC EECEABABEECEC
P 1 0 π π + π Z U G AEEBBDABCEACCBFBDEEC CBFBDCBC B B CDE CA B C EE B CA C EE EA CCE AC CE C EB BDC B AE F FACBFC E C EEBE BC C C A CBACABACABCBBEE BAC EABEEABDFEBCAAE CBBACABBEEEAE CEACECEFCB C B EEA EB C EFC B CDEAC EB E AA C BD B CEBACECEAAEEBEADCCAEAEAC CBEA EAEABCCEACBEEBDA ACDEACE η = ρ CDECBBEBCDCEEBB BCACEBACCAABCCAEBBA ABBEEBDAACBEBB BEECECCCAABCCAEBBAEAEA ECAEBCCBBCDEB ABC EACBAEAEAAE AAEBEACECCAACDEACBCCBB ACACDAEBCABACCE ρ = ( ) EEEAACAEACAEAAC EECEABABEECEC
E C B B A E BC BAC CDEACEAEBACEFAEEACCE = BBA BEBCCEA = E ACCEFBBCACECBABAB EAEAEACBAACCEB η η = = = ( ) ( ) ρ ρ ρ CBAEC ρ E AC EBEEEAEAEBEEBA = E EA EAE BE B C EE B EA AEBF EB B ψ = E C EE C BC BA B ACACEEAABEEABAC EA EAEBAEEBCABEEA ω EB B ω = E C EE BC C BA B EEA BECFACCBEEBEC BEEAEAEBBACEEBEA ψ CEEBBEE ω ψ ψ CCBABF BDEBDEEC ψ ψ CCBABFBDEECCEBFECAA BACBEA ψ ψ BECCE ψ ψ = π ψ ψ EBCACCEBE = πψ ψ CBFBDEECBC = πψ ψ CBFBDEECCEC = πψ ψ CBFBDCBC = πψ ψ CBFBDEBCD EEEAACAEACAEAAC EECEABABEECEC
A CA CA E A EB C BF BDE BDE BDEECBDACBFBDEBDEBCDCBDAA C BA C A BDE A B C CA AB C A BDE A B C CA EB E B C BF ECAAEEBEBBEBEEBCDFC BCEEB 2 Qa 1 2 Qm Plaque chaude Qc Plaque froide 4 3 Qs AEEBEABBEEBCE EEAAC EEBACBA E ADC D BDA CBACEACBEAACABCEEC BDAACBCEBCEBABEEA = + E CCECBEEBCAC CAEACEEBEACEEBCABB EEAEABAEEBEABCAC EB B ϕ = BCECCEEEF ϕ = ψ + ω ECACACCBEA ϕecdce BAEAE ϕ = ϕ = constante E EEEAACAEACAEAAC EECEABABEECEC
E ϕ B ϕe CCABCEEBEABCAC CDCEBA CCA ϕ = ϕe ϕ = ψ + ω = E ψ = ω CDCEBAEAE ψ EA = ψ ωea ω = ψ ω E ω CACDECACCDCEBCDEECBA BE r,z (( U + V ) dz r( U V ) dr) ϕ( r,z) = E r r thr z + thz CBCDEACCEBEECEAECE CACECEFFCBDEBACACECC EEBBAEFFCCEBCDCCA ψψb AA ABCEBDEB A ψ + ω ψ ω B BCDCC A ψψb ABEEACACEBAEABDE ( ( )) F ( ) = ψ ψ + ω = + + + π ω ψ ψ EACCC ( ( )) F ( ) = ψ ψ + ω = + + π ω ψ ψ EBCAACACECCCEEACFA BEBDACACECEABDEECE F = + ( + ) π ω A B Eπ ω CBFCEFCBEECCAABCCAEB CDCEBCDEECCE EA BE B C CE A B EE th V ~ B C B EE CD C E BA E EEAACEEBCBECBFCEFC BEEB EEEAACAEACAEAAC EECEABABEECEC
* 2 2 π = π a V ~ th ECEBCBDEBCDEEC EA E A C A C EE B BA E EEAACECEFFCEEBCB EEBAEBDEBCDEEC EFACCABCEEBBAAC ACEEBBABCEACACA B CA BA A B B BF ECAA C AABCEEBBADCEEBAE C BF BDEEC CE C BF BDEEC DCCA B C EE B ACACFCEAABDEFA EFFCBDEEAEAAEACAABACAB BECCACADCAEBCCEBEEF BFEEBCCEBDAACEEBBCA EEBCCEBDAACBBECCBFBCE EACBCEEBABFBDCEACCBFBCE BBBBFBDEBDEBCDC ACCBDACEEBAABCEE BCACBCBCBFECAABDEBCDEEC CBFECAABDEBCDEECBCEEEECDCA ACEBD AECEE B BFCEADCE BEFCEEBCAAACB CBBACCAABCCAEBAEAEAB B C BF BDE BDE B CDEEC B CD C B BBBFFECEEBAEA CA A C BE B C B EE B AC CE EEEAACAEACAEAAC EECEABABEECEC
F + π = β F + π ( + ) π AEBCEEBBAEEEAAC BEEABBABAABCEE BADCECCE EA ( ) + π ω = BCECCEEEFEA ACEC B EE B AC CE C BF BD C C BF BDEBCDCEBDEBCDEEC V ~ th ( Qc + Qm) = 2 2π a EACBEEBACCEC EEBAABCEEBACACA EBAECBCBAECEEBBFECAA CDCEBABE + = + CEEABDEFACEBC B EE C BF BD C C E BDE B CDEEC C BBBFECAACDECDEBCDEEC 1 F Qc V ~ th = + β 2 a π β = π EEEAACAEACAEAAC EECEABABEECEC
AEACBEEBACCE BBBCBCCAABCCAEBBCB ABCABEBEACABC BEEEBBBABBA EAFCCAEEBCFCB AACEAFCCEEBCAFE BABFBDCABFBDEECEECBB ECCABAECCABCB ABBACBACABACAACEBD EA A BE BD ACF A EA EAB EFC EA CECCEAABFBDEECABBA C CA AB C CA EB E EA FC E EE B AEAEACCBFBDEBDC EAECDCABBABBAC CAABCCAEBEAEBAACA CDCA BA B B A A C EE B BA A EEEBFCEAEBBA BBAEEBBBB ACCAABCCAEBBEAAB CCAEBCAEAEEAEEA BBFEAC EAEAEEFACAACDAEBABBA C BA CA BA A AE BA BF BD C EA CECACDCCABCEEBEAACA EBEBEEBCABAAC BAAADEABFBDEBDEECCABFBDE B B B E ACABABBAACEEBBAEEBABF BDCC CACAACCABCFBACABCEEB EBBBAEBBFBDEBDEBCDEECEB C B B E BE CEA C B B A A C B B A C CA AB C CA EB BA A C EEEAACAEACAEAAC EECEABABEECEC
EA C B C BF ECAA BDE BDE B CDEEC A EAEACACDCABCBCBFECAA BDEBCDEECCBFECAABDEBCDEECACEEB BAEAABBAECEFA CCACFCAABCEEBACEACB AECAEBBBEBACDABBCEEB ECACCAAAACFBCEEB EBABACCECAEBABDCA CECAEBACAEEABBFC BEEABBBAFC C C C E ACABCBCBFECAABDEBCDEECCBF ECAABDEBCDEECACEEBBA AACBDAA EA EE C A BF BD ADA B B AECBEE FBA BEEECEACBCBECC BEEFCBCACABFABDACEBAB EBE EAACBEACEBAECE BDAEBDEACBEEAEFBECBA CAEEBBCBDACBABACAAFAC CDEBCBBAAEDEACECCA ECCAFACCEABDEBDECACAECCA EEECACBEEACEACB CBABECEC EEEAACAEACAEAAC EECEABABEECEC
EACEABDEBDABBCBEEFCB CACCEABCDEACCCACC ACBFA EAEBCEABDE η η π B = = = ρ B ρ EBECEABCDEACCEC B BA EA BDE B CD ρ η E C ECAA C E BABCD BBBA η η ρ ρ B EA EFE B EBE A B C B B B AABFBDACEABEBEACCB EACBA BBCBBEAAEABEBC AEAEACBABCAABBCAEB CCAEEBCE BACECAABCD EAEAABCDCCEBACA ABCAEB η η ρ ρ B EACCEBEEAEFEABFCBCAF AACCAB CABCAEABCEBCECEFCBDEBBFCA ECDEACCCABEC CCEBAFAC EAEBEADABFBDACEAAEACCB EACBE CABC DABBCEECBDABBACA BAECACEBEEFCC BAECCAEBCCAABBBBCAB A AC CE B C EE BA CDCAA A B A ADCBCEAACDECEA EEEAACAEACAEAAC EECEABABEECEC
CCAABCCAEBBEECCBCBA ACDBA ACBDACEBCDEBEABE ACBEEAAACEACDBABE BABEABACEABCDEBEE CEBDE BECEABAEAEEBE AAAAA DCAB EBDEBACEECFBAB BE B AC CC B ACA B B E AAD EA C AC C CA EEC AC C B BAE B E AFCFEEEBABEEBABBCBEF BCEEACAEEBCACBAEAAC AABCEEBBAEEAFEC AA B C EE B BE A BE B BA CDCA CA E E B CD EA C EE B B CBAEBCDCAEABABAEF EEBBACBEABCBEEAAEBBFE ABAEBBE EABACEABEBA AC A A C BA CDCA E C EEABACB CBAAABABBEEABC BABBACBAEACFCEA CACEFCCBDEBCDEECAAEB EAAFACBBCABBCEAAAD BBABEACFCBCDEECEAFCEB ABEBAEBAC EA E A C A C E EE BA B B AC B C BDE B CDEEC E B AC B A EBAACBEEA CBAEFE CCEAE CC B B = EB B CBBC CEBCBE B = E CEBCDEECBCBDECEBBAE CCEAABCBDE AEACBAEECFCEABCC BACACEEFBBAEB EFBEBEEAACBCCAAB ECEBEA EACACAAEAEAACABC BABBBEEADEACEE EAAABBCEECFBACCCBAC BEBEEE EEEAACAEACAEAAC EECEABABEECEC
CAACA AC AEBCBDEEBCAC ABDACBDB B BDA C EBE BDEAC F C AECBABABDAACABABCA ABEBEAEEAECAABEACABAC FBACECF EACCEBECACEFACEBCACEB EACBABCBE BAFACFCBBDB EBECEBCEACCEBACECA CEBAEBCEABCBEEBA CEBCAACCECAAACEBC BE E B A EA BA CAB BEBEBEC CEEBCAC ABBCDCABCCCBACCACAC CEEBACBECBBABC EAEACACEBCEBABECACCEC ECBEBEEABEAFCA AFEC ABAEBEAAAABEBACEBDA EB ABAABECBACA AAECABECBAABCBAEB ACECBFAEBCDEEC ACEACDEEEBCDC EEEAACAEACAEAAC EECEABABEECEC
CCACEBAEBEEC CCEAAEEACCCAA EBABECBCCABCAC CEBCAEBA EBCEBEEBEBCEBAACAB Coquille Isolant Resistance Isolant Mousse Cloche Plaque chaude Plaque froide AEBAEACDABEACABABE EABAACCEBCACEECA CCAABEBCEACCECAA ECAA EBAA CAA CAFCB ECAA EBAA CAA CDFCDECEE ECAA EBAA CAA CCEACBE ECAA EBAA CAA CEAACAEACAA EEC EEEAACAEACAEAAC EECEABABEECEC
CCCBEC BACCBCACBECDFBEBE EEBACDEEACE BABE CACBDACABCAEEACCDABC A AEACACECEFBECBEBBC BECCE ρ = η ECEBBCEBCDCCEAAACDCE BCA CBBACACACDA ECBEAB EFBBCBCCE η = ECAABCD CEBAABCD CCACBEFBEEACACECEFBACC FBCECE A = ( ) ECEBBBCDEEBBABEEB CFCA FCAACBEEACCACBAEFBAC E C CA CF BAEFBACEACACCEBEEACC EBCDEEBBCCE A = CEEABDEFCEBEEACCEEB CDEEA C EECCF EECCA EAEACAAACBEBEBEEAC EACACCDBCACABACDF EEEAACAEACAEAAC EECEABABEECEC
AEBEBEEACABA CABCABCCAABECCABEC AAE EBBCCAEBACEEACAA BCDCBCDEECEBBABEBEACACCABE BDC ECEEA ECA BDEEC ECBFC ECA EC ECBFC EEEC ECBFC ABEB ECBFC ECA EABEB ECEEA BF BD C BDEEC E E BDAB C EE E ACABABCEBECBDACEBBBFAC ACDEACDEACFCAE CBABAACABABCAABEBEC AEBEBECCECDACEBBFBAA EBECECAEBEAB EEEAACAEACAEAAC EECEABABEECEC
CC B BA E AA CEC C CCAABBECAACCEC BBCCCECBECCCEEE BCCAAAEABACCCEACE BA AEBACCCBCBBCABEACABAA EA DCABACCACECAECAEACAACCBECCC BCCCACAABBA AECCACE CAABCDCABCCEBECCACAC EBCEBAABBCCCBACC ACABCDCABCCCBACCACAEBC BE EE DBEE ACB C AA E AB AB E EB EB EA E EEEAACAEACAEAAC EECEABABEECEC
EAEBCFCACACABCDCABCCCBA CCACAEBCBEEACDEBA CCCCDCEBCADAA C B BA A BDA A E C EBE EA EABCAA AAEEACBACBAEFA ACCBCCACCBBCCAA CACEFACBACCCEE AC CC AC CC AEEACBACBAEFAACCB CCACCBBCC EAEBECBBCDABEACABA CEBEACCDCABBCCCACAC EACCEBCABCACEEFABEC BBECBABC CFDAD EACCECECBEFACFBABAA AEAEACACACACBECB EFABC EACBCDCBCEBCDAABC EADEBCDBCCEAEAEEBBACBCD CBAEEEBCABCDEACCA CBAABCBAEBBECAFAEFA EBCBAECCBCDEAA CCBCEBCDEECBAABFBDEAAABFBDEEC EFCACCCACEEFABCDEBCDAC AABABEACEBEECAEBA EADEBACBCDEBCDEEAEB CDEACECBCDFCBA EEEAACAEACAEAAC EECEABABEECEC
AECBBCEFACFBCDABAAAEA EAACCAEFEBAECBBCEBDEBCDB CDEEC EA E A C A C A B E EA EEACEBACABCBABAABAAEA BCDEACEFECAEBCDEBCD ABCDEBCDEEC AEBABEBCDCBCDEEC EAECECBCBAABCBAEBBA A A B BA A C A A E A C A A CEBBCDCACBBCEBCE ABCCCBFAECCEEBEEA FCBCEACDBDBCECAEE BCDEBBEABABEAECEBCEEBA ACAEAAEECAFCBDACACABBA BCDEBCDC EEEAACAEACAEAAC EECEABABEECEC
AECBBCEFACFBCDABAAABBA DAEBAAEAEACACDECAEBAECB CCAABCCAEBBAEAABFBDCCC A BF BDEEC C C EE B C B B C CA EB EA BFBCBABABEFBCB EEBAECBCDEBCDEEC CBABAAECBBEBCDCBCDEEC A A C EC B C BA BA B E FECA A EEBAEACBEACCEBCEAEABAC BCAEBABABE A AECAEBAECBCCAABCCAEBBAEAABF BDCCCABFBDEECCCBBBCCAEB EEEAACAEACAEAAC EECEABABEECEC
CFDACABCD EAEACACECBABCEFAC FBCDABAAEAEFEACEBAFCAEA ABBABDFCCDEBAEBCDEECCE AAABCDEECEAADCABCEBCEC AACCAABDEFBDEEBCECB ABCD AECBABCEFACFBCDABAAAEA CAEACECBEAEEACAECECB ABCEBDEBCDCBCDEECABAECB ABEACAEBCAE EFEACDEBCDAEACDEBCDEECEAEFEACDBA ABCBABBACA AECBABEBCDCBCDEECEFACFBCDAB AAAEA EEEAACAEACAEAAC EECEABABEECEC
ACECBABACABCBAABC BAEBEFACFBCDABAAAAABBAAAC ABCDEACCBABAEECCB EAEEAEAFCBCAEACDBACE BC AECBABACABCBAABCBAEBEFACFB CDABAAABBA DAEBAAEAEACACDECAEBAECB ACCAABCCAEBBAEAABFBDCC CABFBDEECCCEEBCBBCCAEB EABFBCBABABEFBCB EEBAECBCDEBCDEEC CBABAAECBBEBCDCBCDEEC AACECBCBACBABAEBCEB CEBCDEECCCDCEBCDEACCAEAACB BACCABBBAEEACAE EF A B C EC B A EEB C E B A CEBCEACEFFCCEADEE BCCAAB EEEAACAEACAEAAC EECEABABEECEC
CABC AECAEBAECBACCAABCCAEBBAEAA BFBDCCCABFBDEECCCBFBC CDABBAECBABCDEACEACCECECB ABAEECECECBABA BBAABEBBCDEEBAEAEAC ACECBABCECBBAECBAAB EBCDECECEAECCBCCA CCDFAAFEEEBABCDFC BAABBCDFCBAEBBEEFCCDACEBCDE AEEBAEACDFCABAC FBABEEBAEFCEEBDCAA CECBABAFCEEB AECBABCECBBAEFACFBCDABAAA EA ACECBABCABABAEB EFABBACABABABECABFC EEEAACAEACAEAAC EECEABABEECEC
AAABFCBAEFEAEBC ECEEEACDFCBCABABAEBBC BDEBCDEEC AECBABCABAFCEEB ACACECBABCABABA ABECCAEBEEFBBBEAA BCBDCEEECCEBCCA DEFBDEEACBAEFBC ECBABCDEACBCEBCEBACC BCBDEBCDEEC AECBABCABAFCEAB FDEBCACBD EBDACFAEABAABCBA CBDEBCDEECBEABBABDFC CDEBCDEECBAFACEBCEB ACAECECBABEBABDA EBAACABDACBCECAEEF E CDCA B CDE B CDEEC A C EC B A A C AEBCACECBCBABAAA EEEAACAEACAEAAC EECEABABEECEC
AECBABCEBDACFABA DAEBAAEAEACACDFCBAECB AACDFCBCEBCEBACBAABC CAEBACEACDEBCDEECAEBA FCAFEBCECBAEACBBA BCCAECFCEAABA CDE B CDEEC EA EFE A AFE BA EC A CA EAACABBECEAB CDEBCDEECADEACCAEAAFBBE EAFEDABAEAEBAFC BBBACBEFCBBBAAE BE EA EFE C A C EC B A B C E B CEBCEBADEFFCACAA BCDEACBCCAABBAABCEFBCAB CCAABCEBCBDE DEEBAEFACABCCAABBAA EBCEBBAEBCACEEAEEBDEC A A BA CA E C BE ECABAAACDAEAEAB EFCCAECBEAACCBC BECCAEADCCAFECAABEAFC ACEACDEBAEEACDEABFABD CECAEAEEACEEBA EEEAACAEACAEAAC EECEABABEECEC
Qa CABC Qc Extraction Orientation de l écoulement AFCFCBAECBABCEEBCDFBC BBBCCAEB ACEDBCEDACABCCEDFBCACB EC B CDAB A EA E A C A EC BA EC B ABCABCCAAAA EECAEBDCBEEA CABCCAAB EAECBABABACFB EABABEBBEAEAC ACACBAEAAEBAA ACABCACCBBEB CDBAEAECBAFEACABABAB DBCDABCACAB ACCDCFBCEACCAB AEEAABEEACCEACCAEAC BEECCABEB AEACBACAFEEEBA BCABABAABCAFEEFBAB ACBABA DEFCBABAACACE BCCEBACACEAB DBBAACACEEACBACA BBEACAEACFEBBABAEEFBEA BACA ACAEEBCECAEBCDABA ACDACEBDABEAFCACEEAECABC BABAAB EEEAACAEACAEAAC EECEABABEECEC
AABACAACABAFE EEACBCCAABBAEBA AABACAACABAFE EEACBCCAABBAEBA EB EAEBCEEBDAEAABEEACA BCBEECEEEAACBE DAACEBACCACABCE EAEACAEECAEACBC BABAABAAABAEBBBEABB AFCEEBABBAAEABBFBDEEC EEEAACAEACAEAAC EECEABABEECEC
BD C A B EE FA A AC CE CE BA BE E CAA BAC E B C E B AECAEAEAAEBCBEEAAAFE EEBACEDEAABEAFCCAEAC CAABAABEBAEACCAEBCEB ADEBCDCAAEAFCBCEACDEEA AC BDEC A B A B C CA EBEABBAE EA E C BCE EA B C EE B BA B C C B EE B AC CE A EBE CEBCEEBECACEABBE CABAEBBDCAACACE ADAECBAAEACABCDEECEABCDAC BEAACEBEE EA E A C A AB A AA B BE CDABDABCDEEABCBCEBCE BACABEBECCAB BDEACBCDA EEEAACAEACAEAAC EECEABABEECEC
EAEBCBCEEBDAEAABE BBBCBEEBACEEB EACCEABEBABECACBDA EA C ACE BA E EEA AC BDA EA CDABBAEEEEABACBAEAEEABDFEB CEBEBAEBACAEACDAEAC EACACEAEACBEACEAAB CBCBDBACEECEA EA EE C A C ACE EB CA BA E EEAACBCBCEABABEEAE CEEECCBDFCBCEEBABAE E BD BBA A B EE B AC CE ACAECCE CC BDAB C EE EEA B AC A E AAFCECEEEAAC CEAFACAEEBA CCAEEAEFB BACBEECEBCCB CEACCBACEABCDEECEEB C C AC C EE B CA EE EEA BCACEEBA EABEFCFBEEEBCAABA BEEAABFCCEACEBACABDA ABDBABEFAEEEEAAC BEFCBACBEEBFCCBEA C C BE E BA EE B CA B ACEFCCABCCCBACEAEBCBE C E B BDA B E C B EEBFCCBCBEAACCACBAC BDABECCEECEBCABEE EACCECDEBACBCEECF C B A B C B EE B AC A BD EEEAACAEACAEAAC EECEABABEECEC
EEEAACAEACAEAAC EECEABABEECEC ABBAFCBACEBABBEBC BEEBACAEA Filtre Comptage (CPC) Filtre Débitmètre TSI Mesure Q TSI Q TSI Pompe Q cnc Mesures Filtre P, T, HR SMTC Générateur Haute Tension Sélection des Atomizer particules TSI 3076 (DMA) Sécheur Générateur d agrégats CAST 5201 Sélection Sélection des des Dilution particules particules VKL 10 (DMA 2) (DMA 1) Génération et sélection des particules (billes de latex ou agrégats)
CABCDDA ABACAACAEABA A ACBBFAEACEAEFAEAA ECAE B FCC B C B ECAE EFA BCA EA B EEBCBDABCCCBBECCBFCC BCEEEACDEFACA C ECAE B FCC B C AC B CDEA EE A A BDABECCCECA 1,0E+07 9,0E+06 8,0E+06 7,0E+06 dn/dlogdm p/cc 6,0E+06 5,0E+06 4,0E+06 3,0E+06 2,0E+06 1,0E+06 0,0E+00 10 100 1000 Diamètre (nm) AECAEBCBFAEEFEAAEBFCCBCBC FBAA EAEACACDECAEBCEEEFBFCCB CBEBACDEACEAEEBA EAABABAFEFCBCEBFCCBCC AACAEBCEECAC A BAC AEBECFC EECEAACABBCEBDFCAEEB BA EEEAACAEACAEAAC EECEABABEECEC
1.0E+04 9.5E+03 Concentration p/cc 9.0E+03 8.5E+03 8.0E+03 7.5E+03 7.0E+03 10 510 1010 1510 2010 2510 Temps (s) AECAEBCEEEFBFCCBCEBACDEACE AEEBACAECA CABCDECA FCBAEBAB AABDBA A EAEFAFCFCBCEE BDABCFEBDEACBBCBEBEEC ACEBAEBACEAABA ACBBAE BEAABAA EEAC A + + mix N 2 2 ABCFBAA AAFBFBFACBDAC BBAEBECEEBCFBEFAE ECDEBACBBAEEBAAEF EBACDABCEBEFAEACECBC CAFACBCEFAEAEBBA ABCDEFBCDEBEEBBBCDE BDAAAEBEAABCCBDABE CEEBAABEEEBAEECEBBEFAE EEEAACAEACAEAAC EECEABABEECEC
EEBCEBDEACAACCCBACEBA AEBDECEBCFBCCEBABACCA ADAEBDECFEABCACEEA BCAABFBD AC EA EAB BA C AABCEBDECFBEFAEAEE BCACEBACCCEBCAABCCEFA ABFBDBEBDEEBABCAEBECAC BCACBAAEBEAC BFBE CBFBEC CBFBDEBBCAEBAE C CBFBDBDEBEC CBFBDEBDEBCABCDEFC CBFBDBBCAEBEECEBAC BABCFCBBFAAF ACEBAABDCCBFABC AEABACECBFBABCDEFBDBBCAEE BEACCDCABBFBEBDBDEBEBDEBBCAE ACEACEABEECEEAB AEBECDCABBFBDBDEBEBEAC CC B AC B C BF BD B E DCA AC C CC B AC EBA E AC C E EEABACBCACEBACA CACACACEEAEEEEABEE BCCEFEEAEAEBCBAFEC EABBEECACECACBAC AC A E BA FE EA E E BA FE CBCDBEBCDEEABCDEACEECB FECEAAAEBAEBAEA CA C EE EEA B B BB B C AEABCACEBCEBAA E BA BF BDE B BCAE DCA C BA C EABFBEBDBDEBEAEABDBBAAC EEEBACBEBBBABFBDEBBCAEEA EEA EACACB ACEBAAAB C EBABFBDEEAEACACBFAEACEAEA BFBDEBBCAE BBFBEBDBDEBE CC AEBCFECBFBDEBBCAECAC BEABACABCCBEBACBEACE CACBAECCBACEBACDAEBABFBDEB BCAE EEEAACAEACAEAAC EECEABABEECEC
dn/dlogdm (particules/cm 3 ) 2,0E+07 1,8E+07 1,6E+07 1,4E+07 1,2E+07 1,0E+07 8,0E+06 6,0E+06 4,0E+06 2,0E+06 Mix N2 : 00 ml/min Mix N2 : 50 ml/min Mix N2 : 100 ml/min Mix N2 : 150 ml/min Mix N2 : 200 ml/min 0,0E+00 10 100 1000 Dm (nm) AECAEBCBFAEACEAEFCBFB BBFB ECBDBDEBECBABCDEFBDECBDBBCAE C FCA CDECAE BA EB B C BFAE ACEA EA C B BF BDE B BCAE A C A E A CDAEBABFBDEBBCAE BBCCBFAEACEA C A C AC A BAE BA B EBC CDAE BA BF BDEBBCAE FCAECAEBAEBEABBFBDECDEAE E D CAAACB ABAEBEBEEBAA BCFCAEACCDBBDACABCA ABFCAFCFCAEABACCCEBA BCBBFEEAFEEACFE C E ECC C B B C A B A EECDCCEACBCEEACEBAE CEEBFECABDAAAC EFCBBBEBCEABCACCEBEA BC BD EA CA BA B EBAE A C EECE EA A C EEEEABCDFCBCEACDAB BAEEEEABACBAECAACEB EE BA A E B EE EEB A C B BFA BFBEC BFBDEBBCAEBAE C BFBDBDEBEC EEEAACAEACAEAAC EECEABABEECEC
BFBDEBDEBCABCDEFC BFBDBBCAEBEECEBAC EBEEEABDEABFAEACEAE BAAAEBAEABAB CE B B CC B B EFC CA E BCEEEABACBABCCAA EFCECABCCACECEEBA ABBCDEECEEBFCEEBBB AAAACABCCACEABC E B BC CDAB BA EE EEA B B CCEAEABEFCAECAEBCEAEBAA B A CEE B A CA CC BF ECAABECAEBC EAEACACBFAEACEACEBA ECAEABFBECBDBDEBECBDEB BCAEBAE CAACECAEBBC CEBBCBFAEACEAEFBECAE C BDEF B EE CA C EA B B B AA 2.0E+07 1.8E+07 1.6E+07 Après volume tampon Avant volume tampon dn/dlogdm p/cc 1.4E+07 1.2E+07 1.0E+07 8.0E+06 6.0E+06 4.0E+06 2.0E+06 0.0E+00 10 100 1000 Diamètre de mobilité électrique (nm) AECAEBCBFAEACEAEFBBFBEC BDBDEBECBBFBDEBBCAEBAE CA ECAEBCEBAA EBB ACDECAEBCEEEFBACB CEACACAEABBFBDEBBCAEC CC EEEAACAEACAEAAC EECEABABEECEC
EEAC C C C AECAEBCEEEFBACCEABC EEBAEABBFB BCCBE CBDBDEBECBABCDEFBDECBDBBCAEC FCACEEEFEACD EBACBCEEABBFBDEBBCAEBC CC FCAEEEEFEEABACBBC EABBFB BCBECBDBDEBE CBABCDEFBDECBDBBCAEC E ACACABE CAACABE ADCA ADCDBCEEECEFEABCEEEFB AC BDA B CE C C E E FC C B FCBAAECEBDAEEEA DCACCFFACFB FFBAFBFCA E BA A C E C A A CC B EE CEACDBBDABEABDAEBEEBB BEACAEEBECA AAFBCEABDAAA ABEAFACDBBDAEBACC CD BAAC C AC E ECC A A CC B EE CEA AABECEEEC DEECCEBAACCEBAAFCBA ABFBCACABAAAE EAABEEBEACCBEECEA ACEBEBCCBEEBBEACCC EEEAACAEACAEAAC EECEABABEECEC
EEACCACCDBBDAEECEA EEAABEEBACC Grille MET ABBABEBCBACCBEE CEA BFCCDFCFCCBA FABCDCBCEFAEECEAE BBBEEAACEECEBBAB EBAEACEACEBDEECDEECEAAEFEB C E C C E A BC BDEC C BA EB AE B CC B B A A B EACA E CE BEFC C E EEBCDCFCCCCAACBCBD EBACA ACBCFAFBDAABAA EACCDBBDACECBCECF BB E EBABCCEECEBBAA BCDBBDACECCECCBCACCEFB AC EEBAEBABBE ACBB AC BBBACCEBAC ACEEACB BAAC BFAE B AC EFA B C A B AC EABEECCAABFAEBDBBA EEEAACAEACAEAAC EECEABABEECEC
ABBACBAEAEA EABEACABBABBACCA EAB 40 30 Nombre 20 10 0 10 20 30 40 Dpp (nm) AFAEEFBACEACDCCEBDCEBA A BE BA EF B AC C E B C EECECEFBCEAAACC EFBACEECDCECFCCE BBAACDEBAEEBECCBC B E BA BE E AC A CE A B C EE = α F E CBEEBCDBDAAC α E B E CE DA A B A A AA BEFFECAFEC A E C BE B E EA E EA CA B BA E α BEBCAEBCD DAEBCEECDCAEBDAAC CDBBABBACBACCABC AEBCDBCCABCBCDBCEB CCABACCCDBCFCABC CAFBEACDEABEABEEBCD EEBBECEBCABCEECC = EEBEBABECECACBCCEA F F = EBEBECEBBBCAC CBBCDACACCA BC BABE EEEAACAEACAEAAC EECEABABEECEC
( ) ( ) = + A B E B E B CD B C CE A A B EFAABE F + α + = BBB EAACEFBACCEBE E EAEACECEAF ACAC EFAEACACBACEBAA FEECECCECEFAAECCB B C EBA B B C EF B AC C E B E F = BEBCBECBAACEBBAC CAACCAACABCECCBEC CDEBECDECCEBAA EAACAACA EACBEC ACAB EACA AEBCCECBCEECEBACBAABAA BCAFABB BECBEECEA CDC BDA E C B EAC B BE C ABECBECAAEEBBEAAB CECEBABBABC = ( ) = EEEAACAEACAEAAC EECEABABEECEC
ECEFBBEEEC CCAABCE CEACBEBC DABACCDEBECDEAEEBC BECAAEBEBCE ABA = ( ) = ABA F = + = ( ) ABEEACBECABAEA CAABAB BB E EEACDECFCACEB ABDEAEECEEBCEBFAAA BBEFCCACEAABECCCCEECEA CBBBEFCCA EACEEEBBAEBBCCBB EFCCABCDEECECEAACAEFB AC EECBFAEACEAEFAC EACBBEFCCACDCBCEACBB E EEACCECEBFAEEEBCFC BCECEECBCE F F F B E = B π σ E σe DCBEEEB CEEEAABACA BAEACABECACA F < = B = F E E σe CEEBDAEC BBEECBBEFCCAEAEC EFBACABEAEACEEEBACA EFBACAEAC BCBBBE EEEAACAEACAEAAC EECEABABEECEC
BEFCCAB< = < CDEBACEB BBEFFCBBEBBEFCCA EABABCECEECCEEEF F F F F E E = σ E σe EECBBEBEFCCA σe σeceae A σe σe F F = E E EEEBACEEBEE βaccbbe ABCEECEBCDCBBEFCABC EFCCABCDBCDE = β ABBABCCEEE β F β = E E σ = σ E E EACACEABCBBEBCDEE BABBEFCBCA F = E E EAEACACBFAEACEABBBEEFA CDCBCBEECEAAEAEBC ABCEECAABFAEA EA EAE BBA C B B E B E C CD EAEC EEEAACAEACAEAAC EECEABABEECEC
30 25 20 Nombre 15 10 5 0 50 100 150 200 250 300 350 Dg (nm) AFAEACEABBBEEFACDCBCB EECEA BBEFCCAB E CDEAEE BCBFAEACEAEFACEBCACEBAA AEFABBEFCCAB E C AEACACCE CDECAEBA βeebabbeacaaa ACEACBBEA A A A AECAEBA βeebabbe CCEEAEAEEAABBEFCCEC BCBBEBCD EEBEFBACEECDACAC BCCECCE EEEAACAEACAEAAC EECEABABEECEC
CFABCACCDABACEFBACBB CEBBEEBBFAEACEAEAACECEBCA BEEBAFACBCCBCEEBCCEC F = AC CBEC CBBE CBB AC CFCCDABA CACC CE F F F F σ = σ + σ + σ + σ E σ σ σ σ CBAAC B CBEC BABBE BABBAC AB A E B BE C CE E C B B AC BBA B CDABCBFAEBAACCAEBC ECBCDEFEBDAABACCABA EAEEB ECACBDABACEFBAC DABACBBECACAEACCEEBDAF ACBCCBCCECD σ BE EACDABACBBEFCCA CCE F σ = σ E σ CDBABBEFCCADABACBB EFCCACECCBEEAA EAEAECCECACAABCEFCACEFB ACEFACEBBEEBBFAEACEA AB BA EB EA C C B B EFC CA A EF B ACBCDEACBCDEACEAE ACAEAABECEABAECFFBFBCEC ECC BE AC C E CEA C E A B CCACEEBCAEBAC BA CEB B AC B EEBCBBECCBACEBBCACBA CEBCACECECECACACA EEEAACAEACAEAAC EECEABABEECEC
ABBABAECFFBFCECC BEEABEBCCBBEFCCABDA EAEBCBDCEACBB EFCCABABEAEAECBBACBDA ACBCECAABAFE BA ECABDAACEACBBECBFAECCB ACACECABCACCACBA BBEBCACEBACBECCEB BEB ( ) = C σ E σ CBBBAC CDEAEEFACDCBCAB BEC ECBCDCEBACEABBA CEFBACEECDCECCE = E = π ρ A CDECAE BA EF B AC EE CD EEBABBEFCCABCDBABA AEFACDECAEBAEFBACEEB A A CE B A B EA B CAC C EF B AC EEBACEC EEEAACAEACAEAAC EECEABABEECEC
A A ABC D EEEA F AECAEBAEFBACEECDEEBABB EFCCABCD DABACEFBACEFAEBCAC AEACCEEBDAFACBCCBCCE CD σ BECCE F F F σ = σ + σ + σ ρ ρ E σ ρ σ σ CBCECAABC ACBCBCDEFACBABBAC DABACECAABEBCABC DAB A C B CD EFA C C BE EAADABACBBACE BECAC EAEAECCECACAABCEFCACEF B AC EFA C A B C B C ABACCBEB σ C E CAC BDAB EA E C CDAB A C B B AC BEAABFBEACB B AC E EF A ECAE B CDAB BA EF B AC EFA C A B C B C CDABACEFBACBACCCE EAEEACACDECAEBAEFBACEEC CECEEBABBEFCCAEFAC EE B BFAE ACEA C C E B ECCBCB CCBCBEEACECBBEFCCA C CFEAEBA λ CBBAC CEFBAC = A π λ EEEAACAEACAEAAC EECEABABEECEC
E BBBCAACEABABCCEBECACACD EEAEBCEACBCEBABB ACAB C EEEACEBCEFCCCBACB CDCBBEFCCAEEACECAC = EACEA = = EF A C A A C AC EFA C BA EB E AAAEFBACCACACEBCCBCB EEABCCBACAAACEFA CEFEEBCCEBECCBCBEAB ACBCCACACBABACBAEBAC EABCEFBACECACAEAB CEBBEEBBFAEACABEACEBC EA E EA ACE C A C AC BA EF B AC EFAC 10000 Npp (-) 1000 100 10 Lall et Friedlander (2006) Sorensen, régime moléculaire (2011) Sorensen, régime continu (2011) Distibution en taille CPMA 1 0 100 200 300 400 500 600 700 D m (nm) AECAEBAEFBACEECCEC EEBABBEFCCAEECACEFACDCBC CCEBECCBCB CAADBAFDECFF BCAA AC E BA A BD B FC C EEC EBACACEBEACEEACEEBAC BCAA C B EB CDEEC E E B C CA CEABBCAEEEBDAFABDBDAFAAC BDAFBCBBCAEACBCBBEAB FACBFACBADAFDCFF B C BFAE CC B AC E AC A EB B CECACDBBDACABEFCCAEACCECA EEEAACAEACAEAAC EECEABABEECEC
C B B EB EB A C A B C EFC CA B ACABDACA CBBBECAACEBDEF AECAEECCBACAACBFAEACEABDAEECC DBDABCBEBCECEBEECEACEB CEABEBECDEECCEEBEC ABBFEBCCCECC BACBCDEEC ABBFBCABEBCCEB AC AAACDBABECACCCA E B CC AFC BB B EAC AC C ECBDABEBEABCCE DFCBECEEC EA E B C C F C A EA B ACCEACCECACEBACE EECACBAACEECFC CEBCACE ECADBCEACB BECCFEEEBAEABEAB CEABCEABABECEE ACAEAECBAACCBCBEEACEAE CACFEBABBAEABB ECCAEAACBEEEEAEEACDEE BCCEEBBDCACFBEFA ABFBEBEEACAEAEBEE B EA CCE BE CDEB C E B CE EA CEABEECBCBCCBE EAEACACECBAE AC B C E CDEA CE C CA E B C BF BD C E C F BDA E C ECABFBABDC AEEACEBCEBECCBACE CECBEACCBCEBDABCDFB ACBCDCCEBEEBCBBEC ECEBCCAACFBDAABAE CCBCCAAAEEBBFBDEEC BDCBCBBECCBACACACECE CBCAEBABEBFBDEECE EAEACCCDFBBBACBF BDEBDEBCDCBCDEECEAEAEBE EEEAACAEACAEAAC EECEABABEECEC
Génération des aérosols Qa Qm Qa Contrôle du débit d air Qc z h Qc r Variation de la tension : 0 à 10 000 Volts Qs Détection des aérosols ABBAECBAE BCFEBCDFBABCBE EACEAEABEBDEECCDEABDAC ACDBDEECEBBA AAABCBDEAACDCA EFCBAECAEAEABBFCCBCB BBEAFCEEEBCBFACEBC ECCBFEACDCBCEACBFBDEEC ECEAECDEECB CEE ACEAABEEACECEEBACEA EFECEAFBCAEAEEAEBDACAB EFC CA EA EAE F A EAF C EEB A ACBBBEACBEBCE EAEACACEEBECBBCEB CECEACACEECCEAFBBAC E BB BA EEB A AC E A DEBBABEEABECEBCECEEB AABACDCACAEAEAEACABC ECECAEEBAACBEAEAEBE EBACEEEECAAADCD BEFCBAAEAEAAEBEACABABE 200 nm, 1 charge EE 200 nm, 2 charges E AECAEBCEEBACEBAEEBCE CACAEAABFBDCBCABFBDEECBCB ACBCB EEEAACAEACAEAAC EECEABABEECEC
CBAEACEBDABBA FCAECACEBDAECCACDABA BEEAEACEBDEABCDACFAA EEAEFCEAEEACAE ABBAEEBABFBDC EACBEEAEACBBAEAC EBCEEEAACEEAEAABFBDEECCC BACBCBAEEBECEAEA CBFBDCACEECEEACEA EEACACEEBCACEFAEAB ACBECEEBEAFCC CEEAAEACDCCABEAFECAEABABF BCE BACCC EAEAEAEAFB BABFCCCABEACB AC E A C BE EE F E CA A B CA C EEEAAEEBABFAEBCE CCF E E AEECEEBCAEACBA EEBABFBDCEABACBCBAEBABF BDEECBC AEADEADACCAACBDB ECBCECAEACCEBEEB CACEBABEEAACECAAEFA CDBCEEBACEADCEAAEB A B C B AC E A EA CCE E EFCCEEBABABECEEECC FCECCFECA EEBACEADCEAAEBA EABCDFBCBACC CEADCEAAEA BDEFACABEACACEFAAEAE EB C EEEC C BDFC B C EE B CEBACAEEBABEECAA B AC A FCC B C EA B A AC E A CEABEBAAEECEEBEECC ABCABFECAABABEABF EEEAACAEACAEAAC EECEABABEECEC
ECAABBACCAABCCAEBE EACFCCBFECAABDCEEB CDFCBCACBDABBEECEC EAFCCEEBBAEAEBECBFBDC ACAECEEBACEBAC CBBBCFECACCCEE BECCBFBDCACBFEA AEBBEEAEBABF EAEAABEBABFBDCEABEB AAEEECEABDEFEAAEBABFBD CACBEEFC EAEACACECAEBCEEBCDEEC EBAACBABFBDC ACBFA EBEBBBABEEE AABCCAABCAABCCAEBC BACBCBBEAAEAFEAC EEAEACBFBDCCCEEBABEBA BF C EA B C AB C A CAAE B C EEACBABFACBF 5.0E+03 4.5E+03 4.0E+03 3.5E+03 Concentration p/cc 3.0E+03 2.5E+03 2.0E+03 1.5E+03 1.0E+03 5.0E+02 0.0E+00 0 1000 2000 3000 4000 5000 6000 Temps (s) AECAEBCEEBCDEECAEBAEAAAB CCAABCAABCCAEBCBACB CBB EEEAACAEACAEAAC EECEABABEECEC
E AECAEBABFBDCACBFEAAABCCA ABCAABCCAEBCBACBCB B EA CACE A EA A C BF EE C E EEBBEAECDECAEBCEEEBAEE BABFBDCEAEACACEEBFAEFA EAAABCCAABCAABCCAEB CBACBCBBEAAEACDCCAB CEEBBBCCEFAEBCAACA EACCEBCAAEFE ACACABE AECAEBCEEEBAEEBABFBDCAEBE BBBABEEAAABCCAABCA ABCCAEBCBACBCBB EEEAACAEACAEAAC EECEABABEECEC
ACCAADEADACCADB ACAFDAADACFFCCACDFAFD ACCADB EAEABCACBEECAC CCE 1 F Qc V ~ th = + β 2 a π β = π EA EF C B EE C EA E BE FE B ECBFBDCBCEBCEBACBACBF BDEEC CE C BE BF E B AFCBCBECACBFCEBECBFA CEBACBFBCFEACBACEBCDC CCDEBCDCDEBFEABEABFAEBE BBBABEEAFCCEEB CFACBFECAAACBFEAEBE CAEBCEBCEBACBAC CE + A + B = E ECACEBCEBCE BACBAABEFCBDAB EEAEBACEBABCCAABBC CAEBACEEACBBCBFECAA EACADEEABBACC CAABCCAEB BFECAAACACBCBEEE ABCEEBCAEACEEB FAEFAEACACEECCEAFBBAC EBBBCEEBDEBBABE C CA C B C EAF C BE A CA A EEB C B B BF ECAA B BA C B B ACEBDEBCDEECCAABCEBDEB CDEECCAEBEAEACAACBBEB BFBCEEBCEABFCCBCB ABBABACACCAEEB FFCCBAAEBBACCAAB CCAEB CDE C BA BE EA BE C BF ECAA BD C EEBABFECBCEBAC EEEAACAEACAEAAC EECEABABEECEC
ACACABE AEBBFBCEEBC CEABFCCBCBABBAB ECBBFCEBDEBCDEECC EA EAE A CAC C B EE EEB EA EBCFCAACBACEFAEAAC BFCCBCBABBABEFBDA AFEFCBABDAACDABACCACBC B EE C B C BE B C B C BF ECAA CBACEFAEAACBFCCBCBA BBAB Qs - Qa (L/min) Qc (L/min) V ~ th (cm/s) Exp. 1 0,195 2,843 0,156 Exp. 2 0,208 2,888 0,159 Exp. 3 0,194 2,871 0,157 Moyenne 0,199 2,867 0,157 Ecart-type 0,008 0,023 0,001 CV (%) 3,9 0,8 0,9 BDACABCBCADCAB EEACDEBEACCEBABAA BFCCBCBCACECECAEA ACAABABEEABAEAB BDABCCBBCBEEAEABAC EAEABAACEAEBAEAEA CACBBAEEACAACEAEBA ACEBACAECEABC BEAECECACCBFCBBA EBECBAECBCC EEBA B C EEEAACAEACAEAAC EECEABABEECEC
EE B E A E A ACEA B AC CEACCFBDA Générateur de suies CAST Filtre Pompe + filtre + débitmètre Volume 4 l SMTC Sélection des particules (DMA) VKL SMPS ABBCABCACEBACCEEBA C EA E A A A ACEA B CDEECEBACABDECAEECABCE BAAEAAACEECEABBEFCCA EEBAEBEEACACEECAEEA CCECA CBACCEBABBEBABBC EBCDBACCEBEEAEAC A A EA A EFC CA CE C EEB CAA BBEFCCABBBAEFBAECDDAE BACAEEAECACEACEBACEBA CEA ADE CE A EFC CA EE B CD B B ACBCBFAEACEABBEBAA ACBCACBCFCA FCAACBCEBACEBAEAAEFCCABE EAEABEA C EFB BEFC CA EEB EBCC BAC CEC EAEABEA C EFB BEFC CA EEB EBCC BAC CEC EAEACACACBCAACEA AEBAEAAEFCCEEEBBACB AAAAC FABAACEAEEFAFEEB CACACEACCACEABCFCA EFCEEBABCECEAC EEEAACAEACAEAAC EECEABABEECEC
EEBBACBEAE ACAACA ACAEAACBBBEFCCA CEEC CECEEFFCACA E A ECA B A A C A B EEBAEBCCCBAEBEEF ACEBACEEAEBADCFC CA AC E CEFC C A BE EB C EE B C B C BACC CDFCB CCBCAACEB ACCFBBAAEAECACEAC EBACEBACEAADECEAEFCCAEE BCDBBACECBFAEACEA EBAACECACEADEBACD BACCACDEECEBAEBCEBACE BEBAEBAEBEAACEBA BBBEAACEBABB EBBEBBACEFBACECAA BCBACDEECBEAEEBEBAEB AAACEAEBAEAACEBDBBBEFC BABBA EEEAACAEACAEAAC EECEABABEECEC
AAACEAEBAEAACEBDBBBEFC BABBA AAEECAACEABFCCBC BEBACABBAB AACFCCBCAFBEBECCCEADCCC EEACEEFACACEEBAFCCB C B A C EEB B FCC B C B E EEEAACAEACAEAAC EECEABABEECEC
1.4E+06 1.2E+06 1.0E+06 Granulométrie en sortie du SMTC Granulométrie en entrée du SMTC dn/dlogdm p/cc 8.0E+05 6.0E+05 4.0E+05 2.0E+05 0.0E+00 10 100 1000 Diamètre de mobilité électrique (nm) AEECAACEABFCCBCBEBA BDEBDACAD CEBDCDBCDABCBCB DCAABEBEAEAAFCACAAB EBEAEBACDEBABFBDCCAC ABABEEBCCAEBDCBCBE CAFACEBDABC ABCFEACBACEBCDCEAC CFCCBCEACC ABCACCABEACEACCCA AEACFCCBCABABFBDCABC A B E C EA C C CA A EA C ABABFBDCABC ABEEAADCDBABEBEEA CAABCCAEBCAAAC ABEEEACCAABCCA EBCCEAAABEBEBCAB CDE B C E BDE B CD C AA CC B C CA EB AAAEEACAAACEAAB EBE EEEAACAEACAEAAC EECEABABEECEC
CAABD BC A D ACFFC D CAB AF C CFABCACCDABACABCBEE EAACECEBCABEEBAFACBCCBC CEBFACEBDEBCDEECC FCCDABA CACCCE F F F σ = σ + σ + σ ( ) E σ σ σ CBCDFBCBDE BCDEECBABFBDCBCBBBFECAA EBBCEABCDCAACEAC BCEABCDFBCBDEBCDEECC EAAACBCCAABBAEBAAABB DABABECFCBABCFCA C DABACBFBDCCACAEACCEEBDAFA CBCCBCCECD σbecce F F F σ = σ + σ + σ E σ σ σ CBABFBDCA CBFCAECAABEBCACBCE A DABBABFBBCAABEEAACE ACDABACACEEC BEEAAABEACCEBCACA ABACBFBDCC EA EAE C CE CAC CDAB CEFC A C BEE ACCBEB σ C ACECBABABEE AAECAE EB ECBEBABECACBDAEA CACEBAEEEAACBDAEACDABBA EE EEA B AC B A EA E C E B EBAEB ACA EA A CBE B CECACBEFCCA EBACABAEAC BDBACEECEACEABDEF CEECEABBECACBB ACEAEEBAEBBECEFB ACBEACAAABA A EEEAACACBA EBCABCBCEABABEEEECC EEEAACAEACAEAAC EECEABABEECEC
CDFCBCEEBABAEABE CACACEEBCBACABB AABFBDEECEEBABFBDCBC BEBABCEEBEABBCBF ECAABDCCBCBFECAABDEBDEB CDEECDECBABCEEBEABEC BFBACDECCCACBCEEB EABEACAEEBBEEEEBC EE B C CAC B C B B BF ECAA BABFBDCCACCAEBCCAAB BCCAEB BABCEBEAECDFBEBE BCBEAEAAFCABBEECACB A B E E E A C A B C CA EB AA C ABEEACBABBA EECAACEAEBAB FCCBCBDEAFCBABBACBC BACFCCBCEABCDCABECA CCAACEAECABACCB ACCEAEBAEAEAEEBDAC BABDEFAEECEEBBBAB ACC EAACACBEEBDABCACCDABCC BEEBACEFAAABCEC BABABEEAAECAE EEEAACAEACAEAAC EECEABABEECEC
CACAACABBEE BACAEAE AEAEECACEFABFCCBC CCBEBAEEEAACEACCACE ECECBCCA EB B E C E B AC AEFABBABEFAEACEE CACFCCBCBCFABECDCABCEECECB ACBEE EA CE EA E B C B A EF BDEBDCACACEFC BCDEADACCBCDCABECB FCFDCBAAAFC BCBCDACEBDAAEEACACCEA BEEEAECACCDECAEBCBEECECBC CCAEBCCAABAECBACC BACAEAEAECACCDECAEBCECAABCEBA BAEBEECBACAACBCACEAA BBAECBACAB EAEACACDECAEBCBEECECBC C CA EB C CA AB EA A B B A C EAAFCCBCBBCB ECCAEBBEECACBCCEB CFE CE EF A C B EE BB E B C ACECEAECACACEB CECBEECACEAACCACC BEEBCAEBCCAABBCCA EBEEFACACAACDCBA ACFCAEABCBCBBEEB ACAABEEEACACCA EBCCAABBCCAEBBACCBEAA ECBA CAC BCAAB ACBCDAB AA EEEAACAEACAEAAC EECEABABEECEC
A E AECAEBCBEECECBCEEBCB ECCAEB B C A C AC B A B C B EEEABFCCBCEEBABBACEACA CACEEFAEACCBACBB EA A B B A C A EEB A ABCAABCAABCAEBC EABBABBEEFBEFBAB EEACACACEEFAEACCCB AC EA A B B A C A EEB A ABCAABCAABCAEBC EABBABBEEFBEFBAB EEAABEAABBAE AABBEEEA DFCBACBCAEAEB CFEEEAECFCEACDFCBAEFBAB CB A C C B E B C BEECACEAABAACBCCACB EEBAECAACFEAEEBAA ECACCAEEBCCAEBABCCA ABBCCAEBEBAABFCCBCBE C EAEEA CA ACACEFA CEBA EBCBCFEEBEBEACAEACBABB AEBCEBCBCFEEE CAAFEBCEAEAEABCACA CBCBEEEACDFCBBABEFE EEAECAEBEBAEAEFAAAE ACCEBCBCFEEEECAAEBEBE BCDEEEAAEFBABBC EBCBEEBEBCAEFAB ABBEBEFCEEACEECBAEBCEE EEEACEEBABEAEBB CC EABFCCCBAC CAC BABCECAE EA B CB B C E B CB AA E CA CACAACAECABAEFBABE EEEAACAEACAEAAC EECEABABEECEC
AACAADAABBACABEABC ECACEACCCBACEBABEEAE CABCECAEEABDECABAEFBABE AAAACBABEABCEA ACAEADECEBD ACDFCBCCBACABCEBCBC ACAEAAFEEBEAACAECAC EFACDACEBAEBCBBCBDAEEBEEC α α EA BAE B CDCA B A BDEEBE A C B EEBCEEACBABBACA EAFEEBCEBCBEEFEAABB ACACBCECACBD ACBEAABBAC A EEDEA A EA A CAC AEE ED AC ABEEEEBABBACEAABBA CCDABEEEAEBCEA AECCAAFCBEBEAC A A B E A C BE CA FC EA C AC AEFAABBABAEACBB EEFAEBEAEACC EA A B B A B A EA A B B A B B B BE A A CDABACBFBDCBCEEEAAC CCEAABBABCDACEB FCBFACAABCCAEAEAC CEAABBAB EEEAACAEACAEAAC EECEABABEECEC
A EEDEA A EA A CAC AEE ED AC ABEEEEBABBACEAABBA CCDABEEEAEBCEA EA EE B C A C EE E BE CBCBEEEABACBCCACEFA ACCEBCB α αeaec ACACEAFAEBCAEAEACEBC BEBCBEACBABBA ECEBCBECCCAEBAAEA CBEACCECAEAEACCBBFEEB EACACEBCBBABDEEBE A ACAE EEDEA CAC A C AEECBECBCBEEC ACEFACEBAEBCB α αeaab BAB EEEAACAEACAEAAC EECEABABEECEC
ACAE EEDEA CAC A C AEECBECBCBEEC ACEFACEBAEBCB α αeaab BAB FCFDCBAACBAACABDAACABC BCBCACEFACFCCBCEACCEB EEACCACABCCABC FCAAAABABCCCEBEBDA BAAEACCABBCEEEADFC BEBFCAECCDBBDACCACBCC EBBBC FCAEBEBDBACAABD Légende Particule Référence SR Huile de lin 0,110 Saxton et Ranz, 1952 SC-2 Tricrésyl phosphate 0,101 Schadt et Cadle, 1961 RL Tricrésyl phosphate 0,123 Rosenblatt et Lamer, 1946 LD-3 polystyrène 0,164 Li et Davis, 1995 LD-4 polystyrène 0,164 Li et Davis, 1995 EAEACACACBABCFCA B E B EE AC E EE A EBC B C CACAAEBEBAAACCAC AACBCABAEFBABEEACBEB ABCACCCAEFAEFEEB CEBCBAEFBEBAC E ABEAECACB CEBCBEACEFBABAA FA C AFE B CDFC BA B B A B CDCEBCAEABEFBABAA EEEAACAEACAEAAC EECEABABEECEC
AEBEEABCCACBBABCFCA EEAEBCBCCAE AC EFA CDAB BA B EE E EBACECAEAEAFEEBCEBCB CAACAABEABDACEB ECBABBEEEBEBEB A EA CDEEC AC A A B EAE B E B ACCEEACEBCECEBCBBBCC B αadccfeebcebbccbc α EACEABDACACABAE α EACD CAACBDCEBCBEBECA BDACACABAEBDEEBEAACB CAB αeabcdcab αeabcdeeaca ABEACBCDEAAAACA ECEBBEBBACABAE BDEEBEACAAEBCDEF CAACACEBCB EAEEBCACEECACAB ABEABACBCCACAEFAE ABEABDACEAABBABABACA ECCACCACCEBCB BABDEEBEAA α αbdaba BDEEBE A A α α BDA E AC AEFACFCCBCEFEEBAEFAB EABDACEEABBAAEAEFE EBCAAEABBAEEAEACE BEACEEBAEBCBCACBA BDEEBEABEEFAEACDBAEBCB CEADE BA C A BDEEBE A E E EF CCACBEADABAEBAEA CCAEBAABDEEBEACEA A C A C B E E C EA C EBC B EABACBBAACEBCAC EEEAACAEACAEAAC EECEABABEECEC
BEEEABACBBAAEA CDACEB α = BCDCEFCCEBCCACB EEAABCCBACEABA α = BA ACDACEB α = AABBEBEBAEEA BACBBAA A CACAE CABEDEA AAE CACAE AC AEECACABABCACEFAE EAABBAB ABEBEEEA C EBC B BDEF A E B C B EEBACAEEBEACAAC BEEBFCCBCCABEB ECBEACBDCBAE EEAACBBBEE FBF CDEFBCBCEEAECBBAC AFCCBCBECEEEEAEACAB EFAEEAEEEACACBEBC B B EE BEFC B C CA A C AC EA CDCAEBBEEACEBCBCFEEAEAEABCAB CACACCBEABCBBBAB CCAEEACEBCBEEEA CCABCBEECEADEEBAEEBB EBCEACEBBCC EAEFEAFEEBCBEEBC CC EFA CE BA EBC B AC E C ECAE B EB E B C D A EA EF A FE EB E A C E B EADEFEBEAEBDEEBEAA EBBECDEECCECCC ECACBACACEAEFAFEEBCAACA EEEAACAEACAEAAC EECEABABEECEC
C EBC B EB E E BA C A BDEEBEA αeaebeea ECEBDEEBEA αc EEBEACACEBCBA BABBAEACAFCBEBE ACEA C CABBA C A EBEABAAABC ACBFBDCCAEACCCBBAC CAFC EEBEACACBEBCBDCAEB CBEEBEFCBCCABDACAA BEBEBDAEAB BCBACBBEEEFAC EABACAFCCBC BCDEADACCBCDCADBDBA FCFDCBAAFABDAACA EAEEBCACEECACEFAEABFCC BCAEFACEEBABBEFCCAEA E C A C A C AB A C B EE A B AC E EFA EA CC BDBBEFCCAA C B B B C EE CEA E E EAEEACAACAFCBE BACAEACCABBAC EA C E B C C C B C EAEBABBACCACCAEEBA ABCAABCAABCAEBC EAEEAABBACEAABBAA ABBEE AEAAEAFEFCBACEFA CEACEAEFEACAAFCBEBAC AEBEAEACDFCBBABB EEAEAABAEACCAECAEBA CEBEACEAEBBA A EB EA EE A C A A E C AC BD C C FCC B C C CE A C B EEEACFCCBCBACEACBBACAC BEEBACBBEFCCAE EF A B C FCC B C B A A C CC AAADEFEAABBEFCCACABB CBEEBDACBEEBDAFCCB C EAECACACCAEFACEBCB EAEABACBEE EFABFCCBCEEBAEBCBEAEBEEA ACACACEFACEBAEBCBEABB FEBCEBCBCAAFCCBCAFCCB FE AC B C EBA A EA E EA C FE A EBA A C A EEB C EBA A BA FE E B C A B AB EA B AC B B AEAEAEEAFCCABCBBEBA AACEBCBAEABCCCBACAC EEEAACAEACAEAAC EECEABABEECEC
BEECACEACFCCBCBBCACAAACC EFABAFEEAEECBEEEFA EACCEBCBCABBFEEA BFCAEEACAAACCAE CCFCCBCABCEBA CEBCBBFE A EEDEA CA CACEA CACC ACDEAEACB AEECBECBCBEEEFAEA BACAFCCBCCACEFAEABBABEFAE EAABBAB EAEACACEECACEFAEABFCC BCAEFACEEBAEFBABEAE BCACEFBABBBCEABACAA BCCEBCEFBABBBBBACF EAEBCBEABCDACACACEF BABCACEEBABBEFCCACCFEAE CACCAEBCCAABBCCAEB EEEAACAEACAEAAC EECEABABEECEC
A EEDEA CA AEECBECBCBEEEFAEA BACAFCCBCCACEFAEABBABEFAE EAABBABEEBAEFBAB EAEAC A CDECAEBAEF BAB EEBA BBEFCCAEFBABCACEA ABCCAAB ABCCAEB AEBBACA A A C A A BB BA EF B AB C ACACACBBBCBEAE EAEACACCACCBABEBEFB ABCACCAEBCAEAEBEAB CD CBBEFCCA CBBE CCEAACEBCD CEAACEBCCE 1/ + + F = = EEEAACAEACAEAAC EECEABABEECEC
ACABCEBCD ACABC ACABCEBBD CACAB AECAEBAEFBABEEBABBEFCCAEAE ACAABCAEBAE A E A C E B C BE A B AABCAACEFBABBBC EABACABEAAECACAAC EFBABAACAEEFABBBCBE A B C A E EA EFE EAEA B EF B AB AAACDFCBABBCBBE ABEABCB D m 0,31 8,47 0,21 7,62 D g L 0,14 5,16 0 5 Kn (-) 10 AECAEBAEFBABEEBBABBEFC CABBECEAACE ACEAEAEECAACEBCBEE CACACEBDABACBCEEEEA BAEAACCEBCCAEBABAC ACBBEFCCABCBCACACBCA CDFC B EBC E A BAE B C B EE CDAE BA B C AC E C A E EEEAACAEACAEAAC EECEABABEECEC
CACBDAACEAEBAB AC FC A EA B E CDCA B C EECE B CD A CA B EE A CA CD EFCECACAEACCEBCAB BEAACEECEABCDAADABAC AACDAEBCBEECDEFCAC BFCCBC B DB FC D CAB CC D ECA BC A D ACFFC C EA E C AC B CDC EECEA B CDBBABCEECEAEEEAE BDEFCBECCACCBCEFBAC BCCEACBCEECEA EABDCBEEBEEECABCA B B EFC CA EE B CA EF B AC EEB EAEB CAC BEEEFAEA C EEBAEFBACEEBABBB EFC CA BA EF E B AC EE CD DBBCBBCDABBACEAABBEFCCA BACEAABBEFCCAC EFBACEFAABCEF EB BACEAABBEFCCAB ACEAABBEFCCACCEB BDCBEAEEAAEBCBEE EEBAEFBACAECEA BEABACEBECEFCBAA BEEEABBCCABEBBEAA EF E B AC A B B C B EE BDA AC EC EA E A C A A ABECABDCBEEB EEBAEFBACABCE = CDAEEAEFCBDECCBEEBDA ACEC ABEACCE BBE = E CBEEBDAAC EEEAACAEACAEAAC EECEABABEECEC
A EBA A AECAEBCBEEBBABEFAEEEBA EFBACEECDEAABBAC EAEACAAEECBEC BCBEEEFAEABBABEFAECEBCB EACACEBCBCCACBEE BDEEBAEFBACECEC E B C B EE BDA A C B EE BDA ACECEEBAEFBACBCDADC B BEECAAEBCBEEAEACAC E B C C B EE B A C B EEBDAACBCD EAEEBCB ECEAFCBEEBCEECE CCCAEBBCBBEABA EECEABACAEACBCFCA FCAABA Légende Dpp (nm) D f K f Agrégats (CAST) 19,7 1,69 2,8 Mackowski (2006) 10-30 1,8 2,2 EACACCBEEBDAACEACCE E AEBECBEEB ACACCEBCBCBACEBCECACB CCAEACBACABCECACEA CCEBCBCBDCCE EEEAACAEACAEAAC EECEABABEECEC
η = ρ = π + CEAECACEAEEBECCB EEBCACCCEBCBCACCE BA C ECAA C A BA C A E CA ABCAEBBAEAEFEA CE EFAAAACABAEBCBEBEA EEBECEEFEAABBACCA EFBABCEFBABACECACD EACEFCACDEACB EEBCACACCEBCBCB EAECBCACE CFBEACA ABBABCCEA CDECAEBCBEEAEACBCBB EABEEBAEFBACC ACBBEEBEAAAC BDBCFCA FCAACBBEEEBEAAACB CD V th (Dpp) en cm/s Ajustement (Cf. 4.12) 0,1621 Walmann 0,1767 CACE CCDACEBDAB EEBDAACECCACCDECEAAA AC A B C ACE ECE B E EF A B EEAABEAAEEBACA B C EBC B E EA E A CDAEBCBEECEFBACA AEBAEFBCEECACACDCABCDA CEA ACBBBAEECEA C ABEACACABAEBCBE CAEBDCABACBEEB EABFC BCDEFECACEBCBEA A C E CA B C BCE B E EBC EEAEECEBEEABBA EE B B C EB A CD B A EE CC A EA B E EEA E E A CEADAEEBBAEAABBACDB DECCCABBAFEE E E A C E BDA AC E EE B C B B A A CA A B EE E EADAEAEBABEEAACC BDA AC EC CEA CD E CCC A B B AAEABEEACCBDAAC ECCEACDEBACABBA BEACACEBCBEBEAE DE F CCC A B B A CE B CA E EEAABEEAACCB CEBCBE EEEAACAEACAEAAC EECEABABEECEC
ACECAEBAEACBAC BEACBEEEEECEBCB EAEBCCECACEAEBE ADCEABABABEFAE AA E CACECE CACCB AEECBECBCBEEEFAEA BBABEFAEEAABBABCEBCB E EAEEACAEACAAB EFACAEB CAACEECECBCACEBA EEBABBEFCCABCA EAEACACDECAEBAEBEEB ACABCBEECBDECB CEBEBAAECDACEBAE B DBBBCEBEEEEBEE CAC B C CE A ECAA A E BA A EBEECA CACCAEBCCA ABBCCAEB CACEEBAEBEE E EAAEACDECAEBAEBEE BC EAAEBACEACBEEEA CBBEFCCAAEAACE ACEEAEEAABAAEBC ACEACAEAEFEBABEAC ABEABBA BACACBEAEBCEFB ACEEBABBEFCCA EFBACEFAACBACEBABC EBECEEBCDABBAA BCEFBACBBAB BCCEAECAABABAA C CABBEB ACCACBCCEC EEEAACAEACAEAAC EECEABABEECEC
EEEACABACAEA EFEAFEEBCEBEEEFAEACABA AABACBBEABCEBAC EABBACBEFCCEAAEBA CEABBACBEFC BBCCBACAABACAC AFCEACAACBEEB A B B AEECEBEEEFACEAC ABAAEFACEEBAB BEFCCA A B B AEECEBEEEFACEAC ABAAEFACEEBAEFB AC EEEAACAEACAEAAC EECEABABEECEC
BDFCDACBCADACFFCDEBCA EAEABCACBEEBDAAC AEAEAACBCDACFCEBEEDAC ACCEBDEEEEAEACCEBEEA CDCAACEBAEACBEEBDA E B EA A AC A F EA D A CDFCBCABAEFBABBCEACACEACAC EBEECCE πη = A ( ) E CBBCAC CBEE C B CDAB B C E B BB BA BDEAC ECAC CDE C CA C E AE A AACEACDECDEACBBBABCB CAEAEACECACEABAE CFEFBECACBAAAEEBBBC CCEABCEBCDCEBBDAB EEB CE πη BCB = A ( ) E CBBCAC EAEABCECACEECFBDA ACE ECE A C E B BDA E B B D η = E CEBBEBBBBBCCE BECACCABCACCEACDECE CEABCEBACEABCEAC EEBCACCEBBDAEBACCEB ECACCABCACACBAAEBAACA B B E CDB B ACE ECE A B AA EEEAEBABBEBA BDAEEBCCCBAEFBACEAB AEFBACEBBEBAB E CBBDA CE B A CD B BEBA CECCE = CDBCCABDEEACEBB CBEBABBCCEEAEACAC ACEBEEBDAACDFCBEFB ABFACACABACBBEFCCAEA BBEBABEC EEEAACAEACAEAAC EECEABABEECEC
CEBBE πηac = A ( AC ) EACEABAEBCEB BDA BB B C E B BDA EE BA EF B AC B = EBCDEAEAFEE ACECAEACEBBDAAAACBC BEEADCECCE ( ) A F + δ = A( ) A + δ B E C FC B CD D BD F C CE = << ( ε)( ) E εceecceaacebcdba ε EBBCBBF CCE ( ) δ + A B EAEACACDECAEBCEBBEE BBDAACEBBDAACEEBAEFB ACEACBEBCEBBEBA AEAEEACEBBACEF BACBEFCBCECDEFEBC CEEEBAECACCEBECEB BCCACAECCEBBCFCEAC EABECEBCCAFCAAFCACACCA BEBBECCEEEEAB EEBEBACAEBEAACE BDABBEFCCAEACEBBDAE BCCACCBBEBABEAACEBCCE BEBBBEBAEBBBEFCCA EEEAACAEACAEAAC EECEABABEECEC
CA BCEA ACABBEFCCA BCBECAC FC EBBEBA AECAEBCEBBEEBBDAACEB BDAACEEBAEFBAC EAEEBCACCBEEEFA EACCEBCBCFEEABEBCEB EE BA EF B AC E A EBC B E A EBEBCEBACCEBCBCFEEAC BDCA A E B EB EA EFE A C A A C EBCEBABCEBCAC ECBEEBADEEFAAEBC B EE B EE BA EF B AC E EBCEACCCEBBCDEFE EEEAACAEACAEAAC EECEABABEECEC
A CA CABECBDACDEA EACB DCAECAB CDEDCCEBEC CCCAE AEECBEEEFACEBCBCFEEA BEBCEBEEBAEFBAC EAEABBECDCABCEBACB EEBEEACAAEBCBCFE CACBEBCEBBEFCBCCAEA E A C AC EBE B C E B B CDE B C B EEBACDEFCCFCCBC EEABEECAEBECEBCEECE BBCEBEEAA ACAFDFCFADEBCA EAEABCACEACBEFCBCCAEA C EA C E B EE E EAEA BB BDA B EAEABACBCACBBCEAE EAAEBCBEEEEBAEFBAC EECDEAEACCEBBA ECEECECBCBACEAC BACBEFCEEEEA BACACBDAEECAEBEE A CA C CE B C EE FC CB EA B A B EBECEACA EACCEBEEAECAEBCEEBBEACA EE EEA E B EBA A CAACECBEEB DFBEAA EACCEBEBCEEBEEEAACEB BEEAEEEEBAEFBACBCD EEEAACAEACAEAAC EECEABABEECEC
BBECBCDEBDAEAABA BAADCAAAEABEFAABACEE BAEAEACFCBDAAEBB CDCABCAEECECACEBABEAC A B A E BE EEAEAABCAAEB CDEAAEEEE DACCEEBCCE = 1 particule carbone ECECAABCACBEABDCC CE AC C = C E AC AC CCECABCAC EB CD E A C EA A BE FC A B ACBCDEABCECABCACEACEACCEEBA BACBBCEECCCEAAC EBBDCCECCCE + + F 1/ = = ECEBE ABEABCBFAEBCAB CDEABDAECECEAA CEACACBACBEB B C B C AC EB A AC AC B C ECBBCDBEBAFECBCDEBC CEEEBBECEBBACEAE BE 3 mparticule = N pp..d pp. 6 FE B C ECA B C AC EE B C CEAA C E C CE AC = ECDEABCECAABCAC Df 3 3 2 F D g F D f particule = k f... Dpp Df + 2 FE EEEAACAEACAEAAC EECEABABEECEC
D pp Cercle circonscrit L AEBAECECEAACE CCECDEBCEEBCDD BECCE Df 3 3 2 F D F D 1 k.. g f = f D pp Df + 2 EEEEBAEFBAC 3 D 3 2 ( ) f 3 D F D f D f f L = f pp Df + 2 1 k. N. DCCEEAEEABCEEBCDC BBACCEBBBAABCEECE CBAEFBAC DFAEB A E A C EA B C EE B CD E EBCBBE BCD CAEACDEBCCEAACEEAEAE BAECABCACEEBABBE AC = E C E B C CE C ECAA B CD DEEBABBECCE Df 3 F D g particule = k f.. Dpp FE CEEABDCEEBDAEE BEBBE F D g D = 1 k g f. D pp Df 3 EEEBAEFBACBCD 3 D ( ) f 3 Df Df Dg f pp = 1 k. N EEEAACAEACAEAAC EECEABABEECEC
DFCBBAACEACBEBCEEBDA EEBCEAACEEABEBBEBC FCAEFBACEEBAABBCBB EACBFCA FCAACEBBAACEABCEEBDA D m (nm) D g (nm) L (nm) N ppmin < < N ppmax (déterminé avec le CPMA) 30 33 49 1,6 < 1,9 < 2,2 64 77 114 10 < 12 < 13 100 126 186 29 < 34 < 39 200 271 400 149 < 175 < 201 350 504 743 564 < 662 < 759 430 632 932 920 < 1079 < 1238 600 913 1348 2029 < 2380 < 2731 EAEACACDECAEBCEEBDAEEBA EFBACCBDCCEEAE EA C BE C A AC B C CE A EEBAABCEBEAEEBCFCAE C CEAEAEAAEAEBCEEB CDCEFBACEACEEBE EABEEBCABACCEECAC AAACDCACCEAEACEE BBBBCBECECABBCBB EAEABECCABC EEAACAFEBEABABECEB EEACEACEEBEEDCA BEABAEFBABAC ACACDCABAEBABCDA CEEBCAEEFABACACBCEEEEBA EAEABAEFBACA CAACEABEEBEBACABCB ACCEEBCDCACEEB EABE E EEEAACAEACAEAAC EECEABABEECEC
CAEBEAD CAEBEAD AECAEBCEEBAEEBAEFBAC BDFDBAAACBDECABCADACFFC BBABCBACDACAABEE CEAEEACEEACBEE EAAACAEBBBAECEBAABA BCAC EBCBEEAEAECEA C A A B AC E A B EBAABBEEAABBEFCCA C CEA BDA E A EAD C A E C EBA AECCEEBBAEBAA BCDEBAEBECABBFEEBCEB EBCDEABABECCCEAA EBEBAA E CEBAABCD EBEEAAECCCABBA E CBDEFAFEEBAEEEEAB A A B A C A E E A C A C E B EEEFACAEBBBABABA A A A FC AE BA E B EECDAEBCCCBACBAEBAEFBAB EACCEBCBCBBCFEEACEBCB CFECCEBAABCDABCCAB ACACAEACFEBE ACA ECCAAEAB CABEBAABCAC AACCBACDEB CFEBEACCABAEBEEEFAEACA EECAACCACBAEBEEE EBACBAEBCBCFECEADEBCDEBDAEBEBA A C E F CDE A C EBA A BDA BEEBCBDBCAC EEEAACAEACAEAAC EECEABABEECEC
AEECEBEEEFACCEBC BCBCECCEECCEBCBCFEEABBEB EBAA EACECC ABECCEEAD AEBAABCDCCCBACEBEEBDA BCEBCBCFEEABFCEFBABEE BDEEBEACCEEBBCEEA AEBAABAB E CDE A CD A A EA C CA EE BCEEACEBAABAEA ABCEEACEBA AB AACAEAEABEBCB B E ABCCACCBEBAABA ACAEABE CACBEBAABEEAAAEA BECEACABECBEEBACACABCAAC AACA DCCE FE = ε + ε FE ( ) E εceebaa EEEAACAEACAEAAC EECEABABEECEC
Flux de chaleur k g Phase gaz k p Phase solide AEBDAAEAEBACACABCA CA C B EBA A BE EA A A EABECEACABECBEECCCACABCAAC AACA DCCE ( ) ( ) = ε + ε FE CABEBAACCBE EECCABEAAEBAEA EABAEBAABBBCEE BCDDCECCE F FE CEε CE F FE = A Flux de chaleur k g k p Phase gaz Phase solide AEBDAAEAECCCACABCA EAEACACEBAABDAA C A C E EE BA EF B AC EE ACBCCEECACCFBCCEAB CECABCACCCEAACEABECC ACACEEACAECAB ACBEBBE EACEAEAAFCEFBAC CEEB EEDBEABCAEAEFBAC AEAAEAECABCEEACEBAA BDA CAC EE BA B B E B C CEAA C E A EBA A B CD BA E AC A CA E B CC BA EABEEBCABAC EEEAACAEACAEAAC EECEABABEECEC
EBAACBCCEBCC BCCEBAEEBCCBAEAB BFCEFBAC CBA AECAEBCEBAABACECCEAA CEEEBAEFBAC CBA AECAEBCEBAABACECBB EEEBAEFBAC EAAEACAEECE ACE EFA EBEABEFBACAA ACACCABECCEBAFC ECCABE EEEAACAEACAEAAC EECEABABEECEC
CBA AECAEBAEBEBAABAACEBAABA CECCEAACEEEBAEFBAC CBA AECAEBAEBEBAABAACEBAABA CECBBEEEBAEFBAC EAECDEBCEBAEA EAEAEEACEBDABACBBEEA CEAACEEACACCEEBDAFCBEC AEAACAEABEEBEBAC EABEEBCABACEEFBEE CACEEBABBEEABCCEAACEE EEEAACAEACAEAAC EECEABABEECEC
CEBABBEEABCEAACEEACACC EBAABCDFCCEAEABEE BEBAC FBBCDF EACCEBEEEACACEB CFEBCABCCCEEBEBAAB CDEABEEACEBCBBABDEEBE α α A EAEEACACACACEB CFEEABEBAABCDCAEAEA CACEBCBCFECACAE CAE C AEEBAEBAABCDCCCBAFE EEBAABCD EBCDFCB CECAAEAEAECAC EFACEBCBCFEEBDAEBAAEA AEEBEEBCCEAACEBA EAAEEBEEBABBEBA EAAEACAACEBCBCFEBEAFE E B C B EE B CDACE B C EBA AC EE BEEEFA EBCBEEEFAAE CA DCABEBAACEBCCBAA A CA B B EE E E B AC AECABEABEFABEAFC BCACBBABAEBCBCFEEABEEB ACEEFAFCBEBCBEE BEEBAEFBACEDEAB EEBCABACBCEFFC ACABACBACEACAACAE CEA CEBCBCFE A CA EA EACBA EA EA EA ED AEECBEECBCEB CFEEABCABEBAABCDCACEEBCCEAA CEBCD EEEAACAEACAEAAC EECEABABEECEC
A CA EA EACBA EA EA EA ED AEECBEECBCEB CFEEABCABEBAABCDCACEEBABB EBCD EAEEACACACAEFAEAC C E B EA B EBA A B CD E B EA E A C A C EBC B CACAE CAE C ACAEAEAECACEFACEBCB EBDAEBAAEAAEEB EE B C CEAA C E B A EA A EE BEEBABBEBA EA EE A C A A C EBC B AC C EBAACEEBEAFEEB CBEEBDACEBA BCEBCB CDEBABBEAACCAEBC BEEBACDEBCCEAACEA DACEBAEBCBEAFCEBAA BDEFAFEEBCBEEBAFC BE C AC E CDE EA B A CA A A B EE B CDE B C B EE EA C BCEEBAEAEABABE C A A E AFC C CAC B EBA AEEEEACFCAB BDECACEEACAAAC EBA A BA FE B C B FC CFC B C EBCEBAEEEEAB EEEAACAEACAEAAC EECEABABEECEC
A CA C C C CCBA C ED AEECBEECBCEB EABCABEBAABCDCACEEBCCEAA CEBCD A CA C C C CCBA C ED AEECBEECBCEB EABCABEBAABCDCACEEBAB BEBCD EEEAACAEACAEAAC EECEABABEECEC
FBF EA E C AC A A C A B BEEBACAEA AEAECBBACAFCC B C BE C EE EEA EA CA B EFA EEAEEEACACBEBCBB EE BEFC B C CA A C AC EA CDCAE B BEEACEBCBCFEEAEAEABCAB CACA CCBEABCBBBAB CCAEEACEBCBEEEACCABC BEECEADEEBAEEBBEBC EACEBBCC EAEFEAFEEBCBEEBB EACAAEFACEBAEBCB ACECECAEBEBE BCDAEAEFAFEEBEACE BEADEAEAEBDEEBEAA EABBECDEECCECCCECACBA CAC EEBEACACBEBCBCB EEBEFCBCCABDACAAB EBEBDAEABCBC ABBEEEFACEABACAFCC BC AEBEAECBCABAA CEBABBAEABDEF B B EE EA B AEEB EA B CC B B B EFC CA CC B E C B EE B CC EFA C FCC B C E A A EABAFCCBCABCAEA EFEAEEEEABCABEA AE A AE B C B EE B CEA CA CC A EAEBCDCABCEECECBACAEE EEAEAECDECAEBBEEB EEBAEFBACEAAEACBEEA ACEBAEBBBAEFBACBCD EAEEACCACEECEBEAE A F ADBB B C BE C B CD C B EE ACEFBACAAAAAE BA EF B CE ECAC A CD CEA C A EA EFE B A E AC C EBC B E EA B BBAACEEBC BCEBEEBCAEAEECEBEEA BBAEEBBEBACDB AEECCAEABEEEABE ACACEBCBEBEAEEA DECCCABBACEBCAEEEA A B EE AA CC B C EBC B EACECAEBAEABACB EACBEEEEECEBCB EAEBCCECACEAEBE ADCEABABABEFAE EECEBEEEFAC ABABAAEC AAEBCBEEBEAEBCEBA EEEAACAEACAEAAC EECEABABEECEC
CACCEAEFEAFEEBEACABCC BBCCCBACCEBACA EBA C B EA BE A C CC B AC EABB ADAACBEEB EAEABCAECAACB EEBDAACECDEECACACCEBCEBA ABAACCBCACCEBBCACBCB BDACDEECACACABAAAEBBAEF B CE ECAC A CD CEA C A E E A DEACBCEBAABDABEB EABCDCABABEE EEACAAEBCBCFECACB EBCEBBEFCBCCAEAEAC EBCEECEBEBCAACDEF CFCCBCC EBCDEAEAEAEABAEE B CD EE B CEAA C E EA B E E B E EE EA AC C CE BEFC B C CA ABDFCAEBAABCDBBB CEAACEEABEEBEEBAA BCEBCBBCFEEAEAEAACDACEBA EBC B E A FC EBA A BDEF A FE E B C B EE BD B FC BE C ACEBDCCACDEEABACAAA BEEBCDEBCBEEB EEEAACAEACAEAAC EECEABABEECEC
DEF BC BBDCE CEE BABB ACBEFAECDABCBAEEBBB ECDCABCEECEBACABEEA ACEFAAEABABAACEACDCEEBEBC BBACCACCD EAABFFCEACCBDFEBB ABECEBEFCBCCAEAC EBEEEABACAEAEECB B EBE EA CDE B C B EE C BE ECACCBEEAAEACDECECACBA CABCACBCABDEEBECDEB CBEECEFACBEEBB EBAEBEBAABABCACECEAC CCBACA ABFFCEAAEABABACEA CCACAEBEBACAAA B EA C B EE BE C B B B AC EE EA E E BDA A CDEE E A B B ABDAACEAACAABEE BDAADABDECCCBBA AABEEECABAEA C C EE EEA B CA EECE C CEEBACEECEAAEBC BEEBDACEACEFBACAAE E CC C BA A C B EE BDCEACDFCBEFBAB FC EF C AB EA A CDECAE B C B EEBCABACABCB EABBCEABECAAECAEEACDABBA EEEEABBABEFAE C B EB EA CDAB C B C EE EBBDABBCEBEECECACDACEBCCAC B CC EB FC ECA A E EA CDAB B AC E A EB C B BE B C B EEEEEBBAB CCCABACEBBBCEEA BACABAEBEEBBEBDAEBCCC BCEBEEEEBBCDEAC AEEEBBCEABEECBDEF BAEECAECBEEBACAEA EACEEEAACBEDAAC EBACCACABCEEA BEAEECAEACBCBABABDCAA ABAAABAEBBBEABBAFC EEBABBAAEABBFBDEECBDCA BEEFAAACCE CEACCEBABEEBCEB AECAEAEAAEBCBEEAAAFE EEBACEDEAABEAFCCAEAC CAABAABEBAEACCAEBCEB ADEBCDCAAEAFCBCEACDEEA AC BDEC A B A B C CA EBEABBAE EEEAACAEACAEAAC EECEABABEECEC
EA E C BCE EA B C EE B BA B C C B EE B AC CE A EBE CEBCEEBECACEABBE CABAEBBDCAACACE ADAECBAAEACABCDEECEABCDAC BEBEAACEBEEEAECAAB A AA B BE CDA B DA BDA EE ABBCEBCEBACABE BECCABBDEACBCDA EECBEBABECACBDA EA C ACE BA E EEA AC BDA EA CDABBAEEEEABACBAEAECE BEBAEBACAEAACBEB CECACBEFCCABDEFAEEC EEBEBACABAEA CBDBACEECEACEA BDEF C EECEA B BE C A C BBACEAEEBAEBBEC EFBACBACCFACEECCA FCABA EEEAACACBA EBCABCBCEABABEEEECC CDFCBCEEBABAEABE CACACEEBCBACABB AABFBDEECECACEBABFBDC BABCEEBEABBCBFECAABD CCBCBFECAABDEBDEBCDEEC DECBABCEEBEABECBFB ACDECCCACBCEEBEABEC CAEEBBEEEEBCEEB CCACBCBBBFECAABA BFBDCCACCAEBCCAABBCCAEB EECAACEAEBABFCCBC BDEAFCBABBACBC BACFCCB CEABCDCABE CACC AACEAECABACCBAC CEAEBAEAEAEEBDACBA BDEFAEECEEBBBAB ACCCACBEEBDABCACCDABCAC BEEBACEFAAABC ECBABABEEAA ECAE BBABECCEBDEACA BBEEBACABDAEA ECBBACA FCCBCBECEE EEA EA CAB EFAEEA EEE ACACBEBCBBEEBEFCB CCAACACEACDCAEBBEEACEBC BCFEEAEAEABCAB CACACCBEA BCBBBABCCAEEACEBC BEEEACCABCBEE CEADEEBAEEBBEBCEACEBB CC E EA EFE A FE EB C B EE BBEACACEBCB ACECECAEBEBE BCDAEAEFAFEEBEACEB EADEAEAEBDEEBEAA EABBECDEECCECCCECACBA EEEAACAEACAEAAC EECEABABEECEC
CACACEAEBCBCABBEE EFACEABACAFCCBC AEBEAECBABBEEEA BABAAEABBBEFCCACCB ECBEEBCCEFACFCC BCEAAEABAFCCBCA B CA EA EFE A EE EEA B CA B EA AE A AE B C B EEBCEACACCACDECAEB B EE B EE BA EF B AC EA E AACBEEAACEBAEBBBA EFBACBCDACEFEEBCACE ECEBEAEAFADBBBCBEC BCDCBEEACEFBAC ACAACDAEBAEFBCEECACACD CEAC AEAEFEBAEACCEBCB E EA B B B A A C EEBCBCEBEEBCAEAEE CEBEEABBAEEBBEB ACDBAEECCAEABE EEABEACACEBCBEB EAEEADECCCABBACEB CAEEEAABEEAA CCBCEBCBEACECAEBAEA BACBEACBEEEE ECEBCBEAEBCCECACE AEBEADCEABABABEFAE BBB CEFBACCEFE EACCACBABABAA EAEFEAFEEBEACABCC BBCCCBACCEBACA EBA C B EA BE A C CC B AC EABB ADAACBEEB EA EB C EE EEA B EA EA E EACBCEBAABDACEB EABCDCABABEE EEACAAEBCBCFECACBE BCEBBEFCBCCAEAEACEB CEECEBEBCBEBAACD EF C FCC B C C EB CD E A EAEAEABAEEBCDEEBCEAAC EEABEEBEEEEAACCCEBEFC B C CA A BDFC A EBA A BCDBBBCEAACEEABEEBE EBAABCEBCBBCFEEA EAACDACEBAEBCBEAFCEBAA BDEFAFEEBCBEEBDB FCBECBACAACEBAABAFE B C B FC CFC B C EBCE BA EE EEAB B CEEFAA CEA EBDEEBEEBEBAABDD ABECAACEAAABEA CAEEBBCEBAABACECEC BAACDEBCBBEAB EEEAACAEACAEAAC EECEABABEECEC
CCA E A C E C AE B C E B A BDEEBEACBCCEEABACAABACCC EBCACABBABEECB FECCCEBDBEEBFEEA EEACEAAEBDBEBEEEC ACDBCABACBEE EAEEFABBBCBEEBC EFBACEABEEBEBAC EAEAEAEBDBBCAEAC ABBABCEAEBDCDECAEBB EE EA B B B B EFC AA A EEEAEFBACFCAE CDABEABBBCBEECCCB AC EA B A EAA B AB B A B EE B AC B CC AA EEFECFCEAB CAE EEEAACAEACAEAAC EECEABABEECEC
EEECCABAFFCCDB EEEEECBABDCFB CDBCF ECCECBEE CEBAEEEBEFCBCBCDBE EEECCB ACCFBEEBCAEDFCFAF BBABACEE BEBBECBBCC CCEEEEC CFC EEECEEEECCAB CBC EBEECEEE BCC AEEEEBEECEEEE BBFCBCEEECAEC ECACBEEAE DF EBEBECCAABBB DCDFCF EAEEEF CCD EE E E EEC F CBC CC FF BB AEECEFECEEE EEEEEECCBCC A CE A E E EE E C EEC C ABCBC AFEEECEFAE EECCEBEECEECEEC CBCC AEBBEDF EC E EF B B BE E C CC B E FE E EECCFECCCEECECEBBC CDB A A C EEEEABCEFCCEEEECAF CCDB EEEAACAEACAEAAC EECEABABEECEC
BCBEABABCEEECEBBE EB AEEECEBFFBB FEEEEEECCB CECACBFDBE FCCEEECC CCAAECFC CEACBECABECBEE BAEEEBAFACACCEBBBABADF BEBEEECCBCEEBE BEECECEEFEABAEFE C BEC ECEABEBCEBEEE CEEEBCEECCCAFFBABDFCDF EFECEECEBACEBEEC C CAEEEECECEBAEC D BBC BBCFABACD ACCEEBCECB CFCEBAEFEFC BDBBCDFDAB ACECCBAAACEEA E B EC A E BC EFC C E E ABAFEEABFCDDBBFABFB CDBE ABEBEBCABCC FCBCC CCECBEBAA EEEEAFBB CEFCEECECEEFAEB AACCBCEEEBEA AEFEECCEFCEFCAE BCEFC ACECEBAACCBDBEBE CCFAEBCBCAEAC ABECABFAEFCCEFCCEEE ABEFCBC EEAEACABEAEBC EFCCEBEBBBEEECCF C E EE B BAEE E C EEC C E B FC EEEAACAEACAEAAC EECEABABEECEC
A E EE E F CEB CEEFC ACCEFEEEECBEEAFAC CEFC EEFEECCEACFA EBCC E E CE ACE E BEB B B EE E CEECACCEFC BEFFEECECBEECBC AFBCBCBCDBE F EACAB EA EA AC CC EFC EEEAEEEECEFC CEEBEEEEEEECC ABCEBECEEBBCAAB FCBC E AB BA B B EEC EE B A EAC CE AEAEEABEEEEEECC AFCEACECCABABF CBC E EBCE BA B EEC B A CEC C B CDABEACEAE EEEBEEEEECC BBEBEDCFFFF CECCEBECCEEA ACCCFC ECAEEEAB EBEBCAEFC E EF A EE CE A E EE CABEEBECBEDAFBBFA AEBEECCEBDABBCDB EAE CEAAE CEECCEBCF FCCEEEEAEECCAB CBAEEECECFAF EAACEABACBDEEC EACCEFCCEEBC EB EB A E EE CE E EECCEEFC EBEBE A E EE CE E EEC C E EBE BABFCBC BEAACCECEBBEE EEEAACAEACAEAAC EECEABABEECEC
ECCEF EAAEEBEEE EECCAFACCEFC EEFBAAE EEEEBEEDCBAFCCDB E BE BE B ECE E FC D E C ACCDAB E CC C EECE B AB E E EECC BEB EC BEE E EACEB EEC EACEABFCBC E E AE AC CE EAE BEE ECBEEEEBAEEAB FCBC EEFAECDABBAEEACACDE BEABEACEACBBCDA BECEBE EBECAEEE EEABFCBC BBCCEEEECCDFD ECEBABFCBDDFCFAF EEECEEEEEEFCBCD E EFC E C F FCBC B CDBE EEECBBAECCE EECBCAFCEABFCBC AAAEFECEECEEEE CEEBEECBFFBF CFECCEEEC BFEABCACD CEBAEACEEACB FFBF EBEFEAAEEE EDDF CE E C FC DC BEBBE CBC BEBECBCC FCBCC CBEEBBAEEEEECF CBCBBEBE CCFCEECCCECAFD ABDFCF EEEAACAEACAEAAC EECEABABEECEC
CEAEFAE CEEECBEECBCEEEEEECABF CBC CCEEEEEBDFDF CCEEEEFCDF DF EEEEECCBE EDFAF EE E A E E E FC EEECBECCEEB BCFBBBCCBC EEEAACAEACAEAAC EECEABABEECEC
ABCBBCEFBAEADBDEDA AFCBCABFC EEBAEFBAB BCFC EEEAACAEACAEAAC EECEABABEECEC
ABCBBCEFBAEADBDEDC AFCBCAB EEBA AFCBCAB ϕ ϕ EEBA EEEAACAEACAEAAC EECEABABEECEC
CABCDEEDEA BABACECBCEBCABBCDABCC ACCDBBDACEEABDBACA CCBDBACABEAEECAECF EAC CC E EAC C C E EE CA E D EACCAB AACCCEBDBCABCA EACACEAABCDEACCABDBAAE AEEC BDFEFCDABEECEACBABAACBC ABBAABDEECEBCB EEEAACAEACAEAAC EECEABABEECEC
DEBBC BFBDE BAEBDEAFA ACAEACFABDBCDEECBECEA CDEBDABFBDEEC EECCECECCD EBCFBCCBFBDEAAEBC EBDCECBFBDEECBCFAACAAB EECABBCAEAB = + ABEAEABABCAA ABD ABE AAC FBC AF B E BCD ABABCAA ACBBABCAA E ABD ABE BDE B AAA BDBDE BACEBE ABBABCAA EEEAACAEACAEAAC EECEABABEECEC
FACAC BDFCBCBAACA ABBAACE ACDEFBABDEABAAC ABBCAEFCCAEACACEA BDACAFECAEACCBEEACEB BEEEEEAEBAABE BCDECCEECECAECACFEACEB ECABACCDFCBDABABCDEEC EEBCDACFBEC AAACCAEAEFCCAAA CDCEBDACACEACAEEBBA CBEAAAECACCBAAA ECCCBACCCACE CBACBAACEBECCA CDCEBC CEBBAEACAECEACBC BBEABACEAABBBCDCEBC CABCDCEBB EEEAACAEACAEAAC EECEABABEECEC
ABCECEBA EACBACACACBAFAECCA = BABEEFCCAD A = πη CACC EFBCECAC η EBABA AEBA EFCCACEBCD = C π F EEEAACAEACAEAAC EECEABABEECEC
ECCAEACCB BFBDBDBCCA CEAABACA EABCDAC EABCDAC EFBABAEEEFCBACEFC CA = A F η C BECEBDACEBCCAECBB EFCCABCACCECECACACAEA EFCCACECABACBCCCA EFCCACAFCEECCACFBACBCE F B CDCEB C B A CE C E CA C ACBDABBEFCCA EBACEBACAEACABACEEA EBAEACDFCBCEEBAAEA EABEBE BDAEAEABEBEFACEBEBA ACACBCDEECCCEACBBB E BFCBEBEACAEAEECCCB ACEABBBEEAAABEEA ACDBBDAACACBEEBA ACBDFEBBCFBAEEBECACBFAECE EAEAECACBFAECEABADBEFC ABACDEEC ABAAFBEBEECAC B B EBE A A B FAEC A B C EE B EEACEEACEABABAEABD E ABDAEABACBEBE EACBACEBBEBCACCA CE CA EE C B B C A B AC ABEAB AC CBEDEEBBEF B A A AC E BBACC EE EAE E ABA B AC EA E B C EB B CAA EEEAACAEACAEAAC EECEABABEECEC
AC B C EEBA ABC B AC CDA B C EEACBDAEAFBDCEDCEBEEA AEBBEBA CFBBEBAAACEABEACEBC CECBDABEBEABCCE EABACAACDBEBA CABEAB CDBEA CEAB ACB A CD BA E C AC C CA E EA E CAA CA B C ECE B CE BA EA EACAAAEABABDBCE A ABBDAEBDACABDE ACCBDEAFAAFAAB BEACCAEBBCBEA DACCAEBABDEACBECDCA FCACCBEAEBEEAFCABB EAAEEBABEACACBACEBEC BBEAAEEBABBABDEBABFBCDAB EBA = πη ρ A BBEAA EEEAACAEACAEAAC EECEABABEECEC