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.

中文翻译：

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Oldroyd-B 模型描述的聚合物线自相似断裂

当一滴含有长而柔韧的聚合物的流体破裂时，它会形成几乎恒定厚度的线，其尺寸随时间呈指数减小。使用 Oldroyd-B 流体作为模型，我们展示了通过螺纹厚度重新缩放的螺纹轮廓收敛到相似解。利用粘弹性流体与非线性弹性之间的对应关系，在溶剂流体的粘度可以忽略的限度内，推导出全三维轴对称流场的相似方程。平衡压力和弹性能量的守恒定律允许精确计算螺纹厚度。速度场和应力场的显式形式可以从相似方程的解中推导出来。结果通过与数值模拟的详细比较得到验证。