Abstract
When a drop of fluid containing long, flexible polymers breaks up, it forms threads of almost constant thickness, whose size decreases exponentially in time. Using an OldroydB fluid as a model, we show that the thread profile, rescaled by the thread thickness, converges to a similarity solution. Using the correspondence between viscoelastic fluids and nonlinear elasticity, we derive similarity equations for the full threedimensional axisymmetric flow field in the limit that the viscosity of the solvent fluid can be neglected. A conservation law balancing pressure and elastic energy permits to calculate the thread thickness exactly. The explicit form of the velocity and stress fields can be deduced from a solution of the similarity equations. Results are validated by detailed comparison with numerical simulations.
Original language  English 

Article number  A19 
Number of pages  31 
Journal  Journal of Fluid Mechanics 
Volume  887 
Early online date  28 Jan 2020 
DOIs  
Publication status  Published  25 Mar 2020 
Keywords
 Drops and Bubbles: Drops
 Interfacial Flows (free surface): Capillary flows
 NonNewtonian Flows: Polymers
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Professor Jens G Eggers
 Cabot Institute for the Environment
 School of Mathematics  Professor of Applied Mathematics
 Fluids and materials
 Applied Mathematics
Person: Academic , Member