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The buckling and stretching of a viscida

Published online by Cambridge University Press:  29 March 2006

J. D. Buckmaster ,
A. Nachman  and
L. Ting
J. D. Buckmaster
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois, Urbana
A. Nachman
Affiliation:
Department of Mathematics, Texas A&M University
L. Ting
Affiliation:
Department of Mathematics, New York University
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Abstract

We consider the deformation of a thin thread of viscous liquid (viscida) as its ends are slowly moved together. Equations are deduced which are capable of describing the motion of the thread when the displacement of the axis from a straight line is either on the scale of the thread thickness (problem 1) or on the much larger scale of the thread length (problem 2). In the former case it is shown analytically that an arbitrary initial displacement evolves in such a way that, as the appropriately scaled time τ becomes large, the first mode of the disturbance emerges in a dominant role with an amplitude that is proportional to τ½ and independent of the initial amplitude. This provides the initial condition for problem 2, for which a numerical description is obtained.

In addition, we analyse the situation when the ends of the viscida are slowly pulled apart. In this case the high frequency end of the spectrum dominates as an arbitrary disturbance decays.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 69 , Issue 1 , 13 May 1975 , pp. 1 - 20
Copyright
© 1975 Cambridge University Press

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References

Biot, M. 1964 Phys. Fluids, 7, 855.
Buckmaster, J. 1973 J. Fluid Mech. 61, 449.
Courant, R. & Hilbert, D. 1962 Methods of Mathematical Physics, vol. 1, p. 291. Interscience.
Love, A. E. H. 1944 The Mathematical Theory of Elasticity, p. 54. Dover.
Nachman, A. 1973 Ph.D. thesis, Department of Mathematics, New York University.
Taylor, G. I. 1969 12th Int. Congr. Appl. Mech. (Stanford, 1968), p. 382. Springer.