Self-similar breakup of polymeric threads as described by the Oldroyd-B model

Abstract

When a drop of fluid containing long, flexible polymers breaks up, it forms\nthreads of almost constant thickness, whose size decreases exponentially in\ntime. Using an Oldroyd-B fluid as a model, we show that the thread profile,\nrescaled by the thread thickness, converges to a similarity solution. Using the\ncorrespondence between viscoelastic fluids and non-linear elasticity, we derive\nsimilarity equations for the full three-dimensional axisymmetric flow field in\nthe limit that the viscosity of the solvent fluid can be neglected. A\nconservation law balancing pressure and elastic energy permits to calculate the\nthread thickness exactly. The explicit form of the velocity and stress fields\ncan be deduced from a solution of the similarity equations. Results are\nvalidated by detailed comparison with numerical simulations.\n