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HAL Id: hal-00004083 https://hal.archives-ouvertes.fr/hal-00004083 Submitted on 28 Jan 2005 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. Mathematical study of multiphase flow under shear through order parameter formulation Franck Boyer To cite this version: Franck Boyer. Mathematical study of multiphase flow under shear through order parameter formula- tion. Asymptotic Analysis, IOS Press, 1999, 20, pp 175-212. hal-00004083
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Page 1: Mathematical study of multiphase flow under shear through ...

HAL Id: hal-00004083https://hal.archives-ouvertes.fr/hal-00004083

Submitted on 28 Jan 2005

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.

Mathematical study of multiphase flow under shearthrough order parameter formulation

Franck Boyer

To cite this version:Franck Boyer. Mathematical study of multiphase flow under shear through order parameter formula-tion. Asymptotic Analysis, IOS Press, 1999, 20, pp 175-212. �hal-00004083�

Page 2: Mathematical study of multiphase flow under shear through ...

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Page 17: Mathematical study of multiphase flow under shear through ...

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. / ä * � õ ñ ê û ñ Tlj k þ ä � ü ê ø�v * j lYNb LmM>KSL)T Þ ë Q LmK �dQ * ÷ � ó � 68 j lÛë Q M>K¦k Qp��� ò K � ó �768 K 77 ü � � ? K õaä � ó �768 ê K 77 ��K - ä � ó �768 ø �&68 ø � ó �768 ê K ü .�/ K �hä ñ ê ó �hä � ê K K �%ä � ó �768 ê K�K �%ä �768 ê K

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ü K õ ñ K 7 K û ñ K 7 M � ó �&68 M ?� ¤ 6 K õ�ä � ó �&68 ê K 77 ü ¤ 6�7 K õ�ä � ó �&68 ê K 77 ü ¤ K ñ ó ñ 8 K 7 8ü p

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