The beads-on-string structure of viscoelastic threads

a1 Hatsopoulos Microfluids Laboratory, Department of Mechanical Engineering, MIT, Cambridge, MA 02139, USA
a2 Universität Gesamthochschule Essen, Fachbereich Physik, 45117 Essen, Germany
a3 Departamento de Ciencia e Ingenieria, Universidad Rey Juan Carlos, C/ Tulipán S/N, 28933 Móstoles, Madrid, Spain
a4 BP Institute and Engineering Department, University of Cambridge, Madingley Road, Cambridge, CB3 0EZ, UK


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.

(Received July 21 2003)
(Revised September 25 2005)

p1 Present address: Institut für Technische und Makromolekulare Chemie, Universität Hamburg, Bundesstr. 45, 20146 Hamburg, Germany.
p2 Present address: School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK.
p3 Present address: Department of Mathematics, Universidad Autonoma de Madrid, 28049 Madrid, Spain.