Effects of polydispersity and concentration on elastocapillary thinning of dilute polymer solutions

TL;DR

This study explains how molecular weight distribution influences the elastocapillary thinning timescale in dilute polymer solutions, revealing that concentration affects the activation of different molecular species during stretching.

Contribution

It introduces a model linking molecular weight distribution to elastocapillary timescale, clarifying the concentration dependence of $ au_{EC}$ in polymer solutions.

Findings

Molecular weight distribution explains concentration dependence of $ au_{EC}$.

Blending experiments confirm sequential stretching of polymer species.

A simple model reproduces experimental trends.

Abstract

The thinning of liquid bridges under capillary stress occurs in widespread processes like jetting, dripping, and spraying, and creates a strong extensional flow capable of stretching dissolved polymers. If the elastic stress exceeds the viscous stress, an exponential `elastocapillary' (EC) thinning regime arises, yielding a timescale $\tau_{EC}$ commonly considered to be the longest relaxation time of the polymer $\lambda$. A longstanding question is why $\tau_{EC}$ depends on the polymer concentration, even at high dilutions where $\lambda$ should be constant in theory. To date this is understood in terms of intermolecular interactions that arise as polymers stretch. However, we show how the concentration dependence of $\tau_{EC}$ can be explained by considering the molecular weight distribution (MWD) inherent in real polymer samples. We demonstrate this by blending low-$M$ and high-$M$ polymer samples with narrow MWDs at dilute concentrations and in different proportions, and by measuring $\tau_{EC}$ for each blend in capillary thinning experiments. A simple model qualitatively reproduces the experimental results, showing how elastic stresses generated by the polymer build up prior to the EC regime due to sequential stretching of decreasing molecular weight species in the MWD. Since the elastic stress generated by each species depends on its concentration, the fraction of the MWD that is required to stretch in order to induce the EC regime depends on the total polymer concentration $c$. For higher $c$ the EC regime is induced by stretching of a higher-$M$ (longer $\lambda$) fraction of the MWD, and results in a longer measurement of $\tau_{EC}$. Our results have significant implications for the application of capillary thinning measurements to extensional rheometry, for the interpretation of such measurements, and for the understanding of elastocapillary thinning dynamics in general.