Viscoelastocapillary extensional De-Oh or VE-DeOh stringiness of unentangled polymer solutions

Abstract

Characterization, control, and calibration of stringiness, the propensity to form long, thin, persistent threads, are key to the design and application of polymer solutions and formulations transferred to substrates by dropwise dispensing, jetting, spraying, or coating, and are used in manufacturing fibers, membranes, or spray-dried products. For Newtonian fluids, enhancing shear viscosity translates into increasing stringiness as can be easily perceived during dripping of water vs. sugar syrups or glycerol-water mixtures. In contrast, even polymer solutions with comparable shear viscosity can display a significant contrast in extensional rheology and apparent stringiness. However, there are no quantitative maps, formulas, or scales for stringiness, which motivates this study. In this contribution, we contrast the stringiness for a series of aqueous polymer solutions by determining the filament lifespan using dripping-onto-substrate (DoS) rheometry and filament length and lifespan in using dripping-into-air (DiA). We investigate the influence of polymer chemistry and molecular weight on stringiness and rely on DoS rheometry to characterize pinching dynamics and extensional rheology response. We show that an increase in stringiness correlates with steady, terminal extensional viscosity, and extensional relaxation time, respectively. Lastly, we provide a framework, which compares the stringiness of different polymer solutions through an extensional Ohnesorge-Deborah ($Oh-De$) plot or $Oh_E-De_E$ map, by computing the two dimensionless groups $Oh_E$ using steady, terminal extensional viscosity and $De_E$ using extensional relaxation time, respectively