Bending and buckling of a falling viscous thread
Authors
Blount, Maurice John
Date
2010-10-12Awarding Institution
University of Cambridge
Author Affiliation
Department of Applied Mathematics and Theoretical Physics
Qualification
Doctor of Philosophy (PhD)
Type
Thesis
Metadata
Show full item recordCitation
Blount, M. J. (2010). Bending and buckling of a falling viscous thread (Doctoral thesis). https://doi.org/10.17863/CAM.16144
Description
This thesis analyses the behaviour of a slender viscous thread as it falls through air from
a nozzle and lands on a solid surface, whereupon it bends and twists. If the diameter of the
nozzle is much smaller than the height of fall, then numerical solution of a slender-thread
model yields predictions in good agreement with experiment. Moreover, if the thread
falls through a height large enough that extensiona.l forces are important, then bending
forces are significant only in a small region near the point of impact and negligible in the
remainder of the thread, which forms a 'tail'. In this thesis the effects of bending forces
near the point of impact are examined by means of asymptotic analysis in the limit of a
very slender thread and the key processes that govern the behaviour of such threads is
elucidated.
The analysis focuses on three particular physical problems that have recently been studied
experimentally. The first problem concerns the steady motion of a thread as it lands on,
and is dragged sideways by, a horizontally moving belt. It is shown herein that there are
three distinct asymptotic regimes which correspond to the belt speed being faster than,
slower than or roughly equal to a 'free-fall' speed at the bottom of the tail. Solutions
are obtained for each regime, which provide good predictions of the shape and dragout
distance of the thread.
The second problem concerns the stability of such a steadily dragged thread to transverse
meandering. It is shown that meandering is caused by bending forces near the impact
point, which cause the thread to slump slowly sideways, and the restoring tension in the
tail, which is pinned at the nozzle. The competition between these effects and the structure
of the eigenmode is analysed, and quantitative asymptotic estimates are obtained for the
onset of meandering and the frequency of meandering at onset.
The third problem concerns steady coiling of a viscous thread as it lands on a stationary
surface. Provided the fall height is not too small, steady coiling is known to fall into one of
three distinct regimes, depending on the relative importance of gravity and inertia within
the thread. The asymptotic structure of the thread near the contact point is determined
in each regime, and the role of bending forces in this region is analysed. In particular,
an analysis of the interaction between the region of bending forces and the 'tail' yields
quantitative estimates for the coiling frequency and radius.