Scaling of singular structures in extensional flow of dilute polymer solutions

TL;DR

This paper investigates the mathematical nature of singular structures in elongational flows of dilute polymer solutions, deriving asymptotic results for their scaling to aid experimental understanding.

Contribution

It introduces new asymptotic analyses of singular structures in the FENE-P model, linking mathematical solutions to observed birefringent strands in experiments.

Findings

Derived asymptotic scaling laws for the width of singular structures

Linked mathematical singularities to birefringent strands observed experimentally

Provided analytical tools for future experimental validation

Abstract

Recently singular solutions have been discovered in purely elongational flows of visco-elastic fluids. We surmise that these solutions are the mathematical structures underlying the so-called birefringent strands seen experimentally. In order to facilitate future experimental studies of these we derive a number of asymptotic results for the scaling of the width and extension of the near-singular structures in the FENE-P model for polymers of finite extensibility.