Instabilité de Faraday dans les fluides complexes

Texte intégral

(1)Instabilité de Faraday dans les fluides complexes Pierre Ballesta. To cite this version: Pierre Ballesta. Instabilité de Faraday dans les fluides complexes. Matière Molle [cond-mat.soft]. Université Sciences et Technologies - Bordeaux I, 2006. Français. �tel-00811893�. HAL Id: tel-00811893 https://tel.archives-ouvertes.fr/tel-00811893 Submitted on 11 Apr 2013. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published 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..

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(66) >+4 P 8 P E JFMNJ =G PNC GH8 P P J C LG C ½G# C E G J C ¬ 3^ P \ a z H C PCLK &. #. z y. 200 400. x. air. λc. 600 800. h. fluide. 1000. ²³¼ \ a d ¸ PCLK a P J N K G P P h C LG R JFC GHEF PJ K G P P h PJ FE O0P Gm J #G J ed. C ZG# C E G J PMNJ J \Gm J j RfH . ρ[∂t + (U · ∇)]U = −∇P + η∇2 U − ρG(t)ez , ∇·U = 0,. ρ R'E%G M GH E PMNJFO0P H m PJ U %E G J P E%G J η E%G CJ G J EFEF M EF C P P J LG J EFE%GN J C J R JFC GHEF J 'EF K G e z E%G ^G# J M : P EF GH,EF , J \Gm J I. G(t) = g − a cos(ωt),. \ \ \ \R\ #. #. &. &. J C J P I y. G(t). \ \ #. &. g = 9.81 M −1 R E%G^G# J s y a E G M E J P a CJ EFE%Gm J E G CC EFGm J _I E J #GH J E O0P Gm J \ \ G P P s µE yLGms O0PJ E J \ Kk RLGm JFO0P U0 = 0 y P0 = J PJ P C P J O0P y −ρG(t)zez _I : E%GEF P J R \3Gm O0P J u y J p EFJ EF EF y ?EF E ½ ? Gm ,E #GH ' U = U0 + u P = P0 + p u p &. #. \ \ a \ \cb. ρ∂t u = −∇p + η∇2 u, ∇ · u = 0.. #. #. &. &. _I7E JFMNJ E%G C M GH K J21 LGHEF NE%G J N P J E J GH'E Gm P ez · ∇ × ∇× Á O0P Gm J \ \ a y J GHEF'. &. #. ρ∂t − η∇2 ∇2 w = 0,. w RE%G C M GH ' R FJ C HG EF ' PsCLK G M ' J u . #. \ \Xg &.

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(99) a Á 7 PJ R P M E%GH^ s #G P d:Ê k:C E # 82d 28% & 3GH P Cyk E J 120 MNM J G MNn s ya H¬ P 29 MNM T = 23◦ ¸]Á GHG MNn 8 E z« CJ LGm J a EF^ n M P J P ac #:l M P & θ = 66.1◦ k = 4 l = 5 φ = 66◦ y f = 31 ] 1 PM GH J y k PC fH P M J GHa R¬ G CJ EF M GH3G LGH\EF ?G P O0P C GHJ P «N¬ O0P J C , z« CJ LGm J

(100) \ Á m3l , y EF \ b & y . nω y?E Gm 5# ˜ n = a [cos θ(ξn+k + ξn−k ) + sin θ(ξn+l + ξn−l )]. [f (t)ξ(t)] 2. #. \ g . &. Á \E nM P PJ %E G M M s ¬ G'0 ½¸ MNM P EF C HG P ¬ O0P C z« CJ LGm J HE G CC C GHE CP EF= PM JFO0P y P E LGmD z« FJ M LG P « R n D \q

(101) \ .

(102) . . /. . . . . '. a. . >12D

(103) / > . . !#"$=:. 6 1/ 2. n M ª GHZEF C GH P z« CJ LGm J U P a¬ O0P C DEF O0P aE G CC EFGm J a R EFP ^ C M J M P J P E G CC EFGm J C J JFO0P & ¬ GH½EF ½ I R¬ G ' R acJ # ǫ < 0.1 ]PEF J H ¬ P M J C C P Á RLGH\EF G ^ LGm 'E G EFGm GH GH G P ^ M LGm J IE G M E J P ξ ? P R¬ G C y GH E z« CJ LGm J ^ J G P 8¬ O0P C Á G P ^ M LGm J E G M E J P ' P R¬ G C GyZy P J z« JFM LGHEF M GH µ y #"$'&)(

(104) g P < E K0PJ EF J E JFC #^ C ½ P M y K : 8 #3 z« J E%GE PMNJFn 8?E%G P R¬ G C P PJ ¸ IG#HG J EG MNJ y J C O0P P d 0.02 ξ ∝ √ǫ # C ¬ 3^ P \ j sE G M E J P ǫ < 0.01 P R¬ G C R?H η &z F E D y 3 '¬ 'G 0s^GHEF 3GH,EF C GH P J RLGH\ J E J . ²³¼ \ j d M E J P M G « JFM GHEF ηmax ¬ C J E G CC EFGm J PJ ǫ P P C P CLK K0PJ EF N J E JFC # f0^ M −3 σ = 20.1 M M −1 η = 7.8 M ® G j & G J P ρ = 934 MNM J \

(105) # G & ] 1 #\ & ] 1 C & ] 1 y # & ] 1 cÁ 3k:M f = 60 f = 80 JFM

(106) # fP = 120 J fP = 160 J P C J \qEF EF D ½EF E LGm z« LG « 0Á 8E ^ 8 EF P E LGmZ E GH3GHE k a R P \3Gm J U:l E J #G J N E%Gy¬ C

(107) DÁ Z k:M \qEF C P «N8EF D P E LGm E%GI JFM P E%Gm J PM JFO0P Á J J EFEF<3GH E%G 3^ P $# G & J JFO0P E%G ^G MNM I P ? E%G CLK JFO0P z« JFM LGHEF l J ^ P , z«:G J E%G y¬ C

(108) g . Kk : E J RLGH\. k 3 G MNJFO0P ³# J GH z «] M EF

(109) J E J ? PJ P EF J P k . τ0. Á G MNJFn GHR E%G C J GH C . + \ y + g & 8 Gm C 0O P E G M E J P . dξ = ǫξ − b|ξ|2 ξ. dt. C sE O0P Gm J E O0P Gm J dξ = ǫξ τ 0 dt P µ M N:l E J #G E J RLGH\ J E J y −b|ξ| 2 R ξ. # \ 'g \ &. J J D J EFEF E J #G J J ZE JFMNJ LGH'E G M E J P .

(110)

(111) . b . RLGm J 3G J E G M E J P Gm P E%GHGHEF P '. E J RLGH\ J E J b J J ¬ z EF ^ FJ M ' &. #. ξ=. r. ǫ . b. #. \ g &. Á G CC O0P GH J LGm J ¬ C y EF J yEF 8 P E LGm8 z« JFM LG P «N RHGHE%GH\EF O0P P P ^G MNM E JFMNJ ǫ < 2% z® P G CC EFGm J ½ P J P J Eq¬ G P ' C M IEF P J P ǫ 3GHE O0P Gm J \ g'\ z ¸ GH\q 1 G #" $'&)(