Channel flow of electrorheological fluidsunder an inhomogeneous electric fieldVom Fachbereich Mechanikder Technischen Universit¨at Darmstadtzur Erlangung des akademischen Grades einesDoktors der Naturwissenschaften (Dr. rer. nat.)genehmigte Dissertationvorgelgt vonAna Ursescu, M. Sc.aus Cˆampina, RomaniaReferent: Prof. K. Hutter, Ph.D.Korreferent: Prof. Dr. M. R˚uˇziˇckaTag der Einreichung: 16. September 2004Tag der mundlic¨ hen Prufung:¨ 21. Januar 2005D 17AknowledgmentsThis work was done during my stay at the Institute of Mechanics of the DarmstadtUniversity of Technology within the framework of the Graduiertenkolleg “Modelling andNumerical Description of Technical Flows” with the financial support of DFG.I express my sincere gratitude to my supervisor, Professor Kolumban Hutter, for hisinstructive guidance, for his generous advice, for his constant encouragement and hiscontinuous care to provide me everything I need for my research work, especially for thefinancial support for conferences and graduate schools and also for his prompt effort andhis precious time spent to correct my manuscripts. Thank you for the fresh spirit whichmade the work at the University to be sunny.I would like to thank my co-referee, Professor Michael R˚uˇziˇcka for his interest in mywork, for his kind invitation at his department for discussing the modeling of the ER-fluids under inhomogeneous electric fields. I gained a lot of insight from these meetings.