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Dynamics and Stability of a Non-Newtonian Falling Film Symphony Chakraborty

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Dynamics and Stability of a Non-Newtonian Falling Film Symphony Chakraborty Dynamics and stability of a non-Newtonian falling film Symphony Chakraborty To cite this version: Symphony Chakraborty. Dynamics and stability of a non-Newtonian falling film. Mechanics [physics.med-ph]. Université Pierre et Marie Curie - Paris VI, 2012. English. NNT : 2012PAO66368. tel-00828305 HAL Id: tel-00828305 https://tel.archives-ouvertes.fr/tel-00828305 Submitted on 30 May 2013 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Dynamics and stability of a non-Newtonian falling film SYMPHONY CHAKRABORTY 2nd July 2012 Laboratoire FAST - UMR 7608 (UPMC-UPS-CNRS) Bat. 502 - Campus Universitaire 91405 Orsay Cedex, FRANCE. Submitted on 7th May 2012 in partial fulfillment of the requirements for the degree of Doctor of Philosophy UPMC Paris VI, FRANCE. Members of Jury: Dr. Neil RIBE Director Dr. Christian RUYER-QUIL Co-Supervisor Dr. Valéry BOTTON Reviewer Prof. Richard CRASTER Reviewer Prof. Huai-Zhi LI Examiner Dr. Maurice ROSSI Examiner Dynamique et stabilité d’un film tombant non-Newtonien SYMPHONY CHAKRABORTY soutenance prévue le 2 Juillet 2012 Laboratoire FAST - UMR 7608 (UPMC-UPS-CNRS) Bat. 502 - Campus Universitaire 91405 Orsay Cedex, FRANCE. Soumis le 7 Mai 2012 UPMC Paris VI, FRANCE. Membres du Jury: Dr. Neil RIBE directeur Dr. Christian RUYER-QUIL co-directeur Dr. Valéry BOTTON rapporteur Prof. Richard CRASTER rapporteur Prof. Huai-Zhi LI examinateur Dr. Maurice ROSSI examinateur Disclaimer This thesis includes part of the research I have published with my supervisor Dr. Chris- tian Ruyer-Quil, in the following articles: a) Ruyer-Quil, C., Chakraborty, S. and Dandapat, B.S. 2012. Wavy regime of a power-law film flow. J. Fluid Mech., 692, 220-256. b) Chakraborty, S., Ruyer-Quil, C., Nguyen, P.-K. and Bontozoglou, V. Numerical pre- diction of the properties of solitary waves in the drag-inertia regime. 4th International Symposium on Bifurcations and Instabilities in Fluid Dynamics - BIFD 2011. The research reported in this document is original and the work of any other researcher has been appropriately referenced. iii iv “karman. y evadhik¯ aras¯ te ma¯ phale.su kadachana¯ ma¯ karma phala hetur bhur¯ ¯ ˙ − − ma te sango ′stv akarman. i” - You have a right to perform your prescribed duty, but you are not entitled to the fruits of action. Never consider yourself the cause of the results of your activities, and never be attached to not doing your duty. - The Bhagavad Gita, the Science of the Supreme Spirit Chapter 2, entitled: The Philosophy of Discrimination. v I dedicate this thesis to my parents, Smt. Sukla Chakraborty and Mr. Pranesh Ranjan Chakraborty who have been my inspiration and great support throughout my life. Acknowledgements I have now come to the end of another chapter of my life. Looking back, I must admit that it was a long journey and of course very challenging too. From last three years in this project, I have received a great amount of help and support from many people and here I would like to extend my gratitude. I would like to sincerely acknowledge the support that I have received from my super- visor, Dr.Christian Ruyer-Quil, during the course of my doctoral study. He introduced me to research profession and provided me with much needed encouragement to overcome the technical challenges. I am grateful to him for devoting much of his time towards numerous discussions on the physical aspects of my research. I am indebted to him a lot and little would have been possible without him. I am also indebted to him to introduced me to the software AUTO and Gerris. Without his great guidance and support, it would have been difficult to remain focused due to many obstacles that were presented during the course of this journey. I am also greatful to him, Béatrice Guerrier and Frédéric Doumenc for making sure that all the French administrative work finished in time without any trouble which helped me in saving my valuable research time and give a comfortable working environment. I would also like to thank Prof.Bhabani Shankar Dandapat for his moral support and guidance. I am also convey my thanks to Didier who was a former intern student of Dr.Christian Ruyer-quil to help me to understand and deal with the problems in Ger- ris. My thanks also goes to Arghya Samanta, a PhD student working with Dr.Christian Ruyer-Quil, for all the helps he give me to understand the subject and his support and encouragement. I would like to convey my thanks to Prof.Vasilis Bontozoglou in Volos (Greece) to give me his FORTRAN Code to perform numerical simulations; and Khanh, Zhehui, Judith and Anna to make my life comfortable during my staying in Volos for two months and collaboration with UTh group. I would also like to thank Dr.Sandeep Saha for correcting me on every occasion when my usage of the English language was incorrect. Also, I would like to mention his frequent jokes which kept the atmosphere of my office lively. I have always found in him the person whom I could approach for any help at any hour and he has never disappointed me. My gratitude is also reserved for Ching Hsueh, a fellow student one of my closest friends. She has been a great moral support and has kept me company every time I was lonely. vi vii Neil Ribe, Ching, Sandeep, Anna, Floriane, Jesica, Francesco and Chia-ling also deserve a special mention in this section as they are responsible to keep my social life in Paris active by always inviting me to various events. I would like to thank all my fellow students and friends for all the good times within the laboratory FAST as well as number of outingd to different places. I am also very greatful to the EU/FP7 PEOPLE under Marie Curie Actions - Network for Initial Training - “MULTIFLOW" for organizing sightseeing trip, banquet in many conferences and workshop to give the opportunity to visit different places in different countries. During these trips I met many people who belongs to the network became very good friends. The fun times with them will definitely be missed, but one aspect of this chapter in life I can never forget. Finally, I would like to acknowledge the love and affection of my parents. No words can express my appreciation and gratitude for all the love and blessings showered by my parents on me and the support from my brother during all these years. They have always encouraged me to pursue the noblest of dreams and advised me appropriately in all my endeavours. I would not have reached this milestone, had it not been for their support. viii Abstract A thin film of a non-Newtonian flowing down an inclined plane under the action of gravity is studied focusing on the effects of the fluid rheology on the complex wave dy- namics that develops at the free surface. In chapter 3, the properties of the solitary waves, which organize the disordered dynamics of the Newtonian film, are considered. Direct numerical simulations (DNSs) of purely solitary waves have been performed and compared to the results from the four-equation model derived in [112]. The evolution of a power-law laminar film flow is considered in chapter 5 and modeled within the frame of the lubrication approximation by means of the weighted residual approach. Comparisons to Orr-Sommerfeld stability analysis and to DNS show convincing agreement in both lin- ear and nonlinear regimes. A viscoplasctic film is modeled by the Herschel and Bulkley law and is presented in chapter 6. The elasticity of the pseudo-plug region close to the interface is taken into account by an elasto-visco-plastic constitutive relation derived by Saramito [121]. A model is derived in terms of four-equations for the film thickness, local flow rate and amplitudes of the normal and tangential stresses. A linear stability analysis gives values of the critical Reynolds number in remarkable agreement with the Orr-Sommerfeld analysis. Key words : Non-Newtonian Fluid, Falling Film, Elasto-visco-plastic, Power laws, Weighted Residuals. Résumé On étudie la dynamique d’un film mince d’un fluide non-newtonien s’écoulant sur un plan incliné sous l’action de la gravité en tenant compte des effets d’une rhéologie complexe sur la dynamique des ondes de surface. Au chapitre 3, les propriétés des ondes solitaires, qui organisent la dynamique désordonnée d’un film Newtonien, sont considérées. Des sim- ulations numériques directes (DNSs) d’ondes solitaires ont été effectués et comparés aux résultats d’un modèle à quatre équations formulé dans [112]. Au chapitre 5, l’évolution d’un film de fluide en loi de puissance film est modélisée au moyen de l’approche aux résidus pondérés. Les comparaisons avec l’analyse de stabilité d’Orr-Sommerfeld et de la DNS est en bon accord dans les régimes linéaires et non linéaires. Un film de fluide vis- coplastique est modélisé par la loi Herschel et Bulkley est étudié au chapitre 6. L’élasticité du pseudo-bouchon à l’interface est pris en compte par une relation constitutive élasto- visco-plastique proposée par Saramito [121]. Un modèle est formulé en termes de quatre équations pour l’épaisseur du film, le débit local et les amplitudes des contraintes nor- males et tangentielles.
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