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Effects of Polydispersity and Concentration on Elastocapillary Thinning of Dilute Polymer Solutions

Vincenzo Calabrese, Amy Q. Shen, and Simon J. Haward

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Phys. Rev. X 15, 021025 – Published 23 April, 2025

DOI: https://doi.org/10.1103/PhysRevX.15.021025

Abstract

The self-thinning of liquid bridges under the action of capillarity occurs in widespread processes like jetting, dripping, and spraying and gives rise to a strong extensional flow capable of stretching dissolved polymers. If the resulting elastic stress exceeds the viscous stress, an exponential “elastocapillary” (EC) thinning regime arises, yielding a timescale τEC that is commonly considered equivalent to the longest relaxation time of the polymer λ. A long-standing question is why τEC depends strongly on the polymer concentration, even at high dilutions where λ should be constant in theory. To date, this is understood in terms of intermolecular interactions that arise due to “self-concentration” effects as polymers stretch. However, λ depends on the polymer molecular weight M, and we show how the concentration dependence of τEC can be explained by considering the molecular weight distribution (MWD) inherent in real polymer samples, without the need to invoke self-concentration. 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 τEC for each blend in capillary thinning experiments. Through a simple model that qualitatively reproduces the experimental results, we show how elastic stresses generated by the polymer build up prior to the EC regime due to the sequential stretching of progressively 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 in the solution. For higher c, the EC regime is induced by stretching of a higher-M (longer λ) fraction of the MWD and results in a longer measurement of τEC. 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.

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The thinning and breakup of liquid bridges under capillary forces play a crucial role in various natural and industrial processes, such as spraying, printing, and additive manufacturing. While the thinning of simple fluids like water follows predictable dynamics, more complex fluids such as paints and inks behave differently due to the stretching of polymers or proteins. Monitoring the thinning rate of polymeric liquid bridges is a key method for studying polymer relaxation times, but the impact of molecular weight distribution, or polydispersity, on these dynamics remains unclear. This study investigates how capillary thinning is influenced by the spread of molecular weights in polymer samples.

Through capillary thinning measurements on bimodal polymer solution blends, we find that polymer concentration and polydispersity play crucial roles in determining the thinning rate. At high polymer concentrations, high molecular weight polymers dominate the thinning process, leading to slower thinning due to their longer relaxation times. Conversely, at lower concentrations, low molecular weight polymers, with their shorter relaxation times, control the thinning, resulting in faster rates. These results suggest that capillary thinning is governed by a complex interplay between polymer concentration and the distribution of molecular weights.

This work provides new insights into the dynamics of capillary thinning processes and raises important questions about using capillary thinning as a method for characterizing complex fluids. Future studies should focus on understanding how factors like polymer concentration and polydispersity influence these processes, with the aim of improving experimental, numerical, and theoretical models for complex fluid behavior.

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Phys. Rev. X 15, 021025– Published 23 April, 2025
  • Received 11 July 2024
  • Accepted 13 February 2025
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