Orientation dependent elastic stress concentration at tips of slender objects translating in viscoelastic fluids

TL;DR

This paper analyzes how elastic stress concentrates at the tips of slender objects moving in viscoelastic fluids, revealing orientation-dependent thresholds for stress buildup using theoretical calculations in the weak-coupling limit.

Contribution

It provides a theoretical framework for understanding elastic stress accumulation at object tips in viscoelastic fluids, focusing on the influence of orientation and flow parameters.

Findings

Stress concentration at tips depends on object orientation.

Thresholds for large elastic stress are identified.

Greater stress accumulates when objects are oriented parallel to motion.

Abstract

Elastic stress concentration at tips of long slender objects moving in viscoelastic fluids has been observed in numerical simulations, but despite the prevalence of flagellated motion in complex fluids in many biological functions, the physics of stress accumulation near tips has not been analyzed. Here we theoretically investigate elastic stress development at tips of slender objects by computing the leading order viscoelastic correction to the equilibrium viscous flow around long cylinders, using the weak-coupling limit. In this limit nonlinearities in the fluid are retained allowing us to study the biologically relevant parameter regime of high Weissenberg number. We calculate a stretch rate from the viscous flow around cylinders to predict when large elastic stress develops at tips, find thresholds for large stress development depending on orientation, and calculate greater stress accumulation near tips of cylinders oriented parallel to motion over perpendicular.