2026-09-19T12:04:06Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/417252022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
John W.M. Bush.
Savva, Nikos
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2008-05-19T16:12:25Z
2008-05-19T16:12:25Z
2007
2007
http://hdl.handle.net/1721.1/41725
225064871
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.
Includes bibliographical references (leaves 108-117).
We present a general theory for the dynamics of thin viscous sheets. Employing concepts from differential geometry and tensor calculus we derive the governing equations in terms of a coordinate system that moves with the film. Special attention is given to incorporating inertia and the curvature forces that arise from the thickness variations along the film. Exploiting the slenderness of the film, we assume that the transverse fluid velocity is small compared to the longitudinal one and perform a perturbation expansion to obtain the leading order equations when the center-surface that defines the coordinate system is parametrized by lines of curvature. We then focus on the dynamics of flat film rupture, in an attempt to gain some insights into the sheet breakup and its fragmentation into droplets. By combining analytical and numerical methods, we extend the prior work on the subject and compare our numerical simulations with experimental work reported in the literature.
by Nikos Savva.
Ph.D.
117 leaves
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Viscous fluid sheets
Thesis
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