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The beads-on-string structure of viscoelastic threads

Published online by Cambridge University Press:  24 May 2006

CHRISTIAN CLASEN
Affiliation:
Hatsopoulos Microfluids Laboratory, Department of Mechanical Engineering, MIT, Cambridge, MA 02139, USA Present address: Institut für Technische und Makromolekulare Chemie, Universität Hamburg, Bundesstr. 45, 20146 Hamburg, Germany.
JENS EGGERS
Affiliation:
Universität Gesamthochschule Essen, Fachbereich Physik, 45117 Essen, Germany Present address: School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK.
MARCO A. FONTELOS
Affiliation:
Departamento de Ciencia e Ingenieria, Universidad Rey Juan Carlos, C/ Tulipán S/N, 28933 Móstoles, Madrid, Spain Present address: Department of Mathematics, Universidad Autonoma de Madrid, 28049 Madrid, Spain.
JIE LI
Affiliation:
BP Institute and Engineering Department, University of Cambridge, Madingley Road, Cambridge, CB3 0EZ, UK
GARETH H. McKINLEY
Affiliation:
Hatsopoulos Microfluids Laboratory, Department of Mechanical Engineering, MIT, Cambridge, MA 02139, USA

Abstract

By adding minute concentrations of a high-molecular-weight polymer, liquid jets or bridges collapsing under the action of surface tension develop a characteristic shape of uniform threads connecting spherical fluid drops. In this paper, high-precision measurements of this beads-on-string structure are combined with a theoretical analysis of the limiting case of large polymer relaxation times and high polymer extensibilities, for which the evolution can be divided into two distinct regimes. For times smaller than the polymer relaxation time over which the beads-on-string structure develops, we give a simplified local description, which still retains the essential physics of the problem. At times much larger than the relaxation time, we show that the solution consists of exponentially thinning threads connecting almost spherical drops. Both experiment and theoretical analysis of a one-dimensional model equation reveal a self-similar structure of the corner where a thread is attached to the neighbouring drops.

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Copyright
© 2006 Cambridge University Press

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