Viscous fluid sheets
Name
225064871-MIT.pdf
Description
Full printable version
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11.05 MB
Format
Adobe PDF
Checksum (MD5)
a607722dd0f31c4718bdc8d548a1a765
Author(s)
Savva, Nikos
Advisor(s)
John W.M. Bush.
Date Issued
2007
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.
Includes bibliographical references (leaves 108-117).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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