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


Elastic stress concentration at the 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 the tips has not been analyzed. Here, we theoretically investigate elastic stress development at the 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 the tips, find thresholds for large stress development depending on orientation, and calculate greater stress accumulation near the tips of cylinders oriented parallel to the motion over perpendicular.

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