TY - JOUR
T1 - Self-similar breakup of polymeric threads as described by the Oldroyd-B model
AU - Eggers, Jens
AU - Herrada, Miguel
AU - Snoeijer, Jacco
PY - 2020/3/25
Y1 - 2020/3/25
N2 - 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 Oldroyd-B 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 non-linear elasticity, we derive similarity equations for the full three-dimensional 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.
AB - 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 Oldroyd-B 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 non-linear elasticity, we derive similarity equations for the full three-dimensional 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.
KW - Drops and Bubbles: Drops
KW - Interfacial Flows (free surface): Capillary flows
KW - Non-Newtonian Flows: Polymers
U2 - 10.1017/jfm.2020.18
DO - 10.1017/jfm.2020.18
M3 - Article
VL - 887
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
SN - 0022-1120
M1 - A19
ER -