Capillary Thinning of Viscoelastic Threads of Unentangled Polymer Solutions

In this paper, we theoretically consider the process of the capillary thinning of a polymer fluid thread bridging two large immobile droplets in the regime of highly stretched polymer chains. We first derive a new relation between the pressure p and the flow velocity v in unentangled polymer solutions, which is called the anti-Bernoulli law: it shows that p is higher where v is faster. Using this equation, it is shown that the flow field is asymptotically irrotational, in particular, in the thread/droplet transition zones (in the case, the negligible solvent viscosity and inertial effects). On this basis, we predict the free surface profile and the thread thinning law for the FENE-P model of polymer dynamics. The predictions are compared with recent theoretical results and some experimental data on capillary thinning.

Automated summary

This paper theoretically investigates the capillary thinning process of a polymer fluid thread bridging two large immobile droplets, considering the highly stretched polymer chains. A new relation between pressure and flow velocity, called the anti-Bernoulli law, is derived for unentangled polymer solutions, showing that pressure is higher where velocity is faster. Based on this, the flow field is predicted to be irrotational in the thread/droplet transition zones. The free surface profile and thread thinning law for the FENE-P model of polymer dynamics are also predicted and compared with theoretical and experimental results.