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This study seeks to understand the role of photodegradation of aqueous polymers in drop splashing. Polymer drop impact commonly occurs in various industrial applications such as inkjet printing, spray coating, and agrochemical sprays. In agrochemicals, the various constituent components (e.g., adjuvants) imparts multiple changes to the fluid dynamics and the wetting behaviors of the drops, as well as interacting with the environmental conditions. The environmental conditions (e.g., thermal-degradation, photo-degradation, and oxidation) of the chemicals affect the shelf stability of the intended physicochemical properties of the chemicals, which are added to stabilize drift from the spray nozzles and minimize drop bouncing from leaves. The aging effects of the adjuvants in tandem with the already low pesticide delivery efficiency has an unknown effect on the agrochemical delivery efficiency and the related environmental burden from the increased run off. Herein, we systematically photo-degraded polyethylene oxide (PEO) to probe the drop splashing behavior as a result of the simulated aging conditions. Dye was added to accelerate the degradation of the polymers and caused drops to splash at Weber numbers where the pure PEO case did not, confirming the need to consider environmental factors which contributes to adjuvant aging in agrochemical applications. We have also conducted experiments with various concentrations of PEO to probe the changes in the splash dynamics as well as including surfactants, which played a marginal role in altering the splash dynamics under our parameter space. The significance of the study is that the degradation of the polymers influences the splashing and increases the amount of splashed droplets, indicating the importance of controlling the environmental conditions under which polymer solutions are stored. 

Understanding the peripheral capillary wave propagation during droplet impact is crucial for comprehending the physics of wetting onset and droplet fragmentation. Although Newtonian droplets have been extensively studied, we show how capillary waves deform non-Newtonian droplets in such a way that rheological features, such as the critical concentrations for the overlap (c*) and entangled polymer molecules (c**), may be directly obtained from the deformation history. Determining these critical concentrations is essential as they mark transitions in the rheological behavior of aqueous polymeric solutions, influencing viscosity, elasticity, and associated fluid dynamics. We have also compared capillary waves among Newtonian, shear-thinning, and Boger fluid droplets and found that although the fluid kinematics appear to be purely biaxial extensional flow, the infinite-shear properties of the droplets dominate the physics of capillary wave formation and propagation. 

In many commercial applications, polymer–dye interactions are frequently encountered from food to wastewater treatment, and while shear rheology has been well characterized, the extensional properties are not well known. The extensional viscosity ηE and relaxation time λE are the extensional rheological parameters that provide valuable insights into how aqueous polymers respond during deformation, and this study investigated the effect of dyes on the extensional rheology of three different aqueous polymer solutions (e.g., anionic, cationic, and neutral) paired with two different dye salts (e.g., anionic and cationic) using drop pinch-off experiments. We have found that the influence of dyes on the pinch-off dynamics is complex but generally leads to a decrease in, for example, the apparent extensional relaxation time. We have utilized the dripping-onto-substrate method to probe the uniaxial deformation of widely used polymers such as xanthan gum (XG), poly(diallyldimethylammonium chloride) (PDADMAC), and poly(ethylene oxide) (PEO) as the anionic, cationic, and neutral polymers, respectively, paired with either fluorescein (Fl) or methylene blue (MB) as the anionic and cationic dyes, respectively. Polymer–dye pairs with opposite charges (e.g., XG–MB and PDADMAC–Fl) displayed a pronounced decrease in pinch-off times, but even PEO, which is a neutral polymer, resulted in decreased pinch-off times, which was restored by the addition of NaCl. The pinch-off times for the Boger fluid (mixture of poly(ethylene glycol) and PEO), however, were surprisingly uninfluenced by dyes. These results showed that not only did the small addition of dyes strongly decrease the polymer relaxation times, but the relative importance of the dye salts on the polymer pinch-off dynamics was also different from that of pure salts such as NaCl. 

Comparing spherical probability distributions is of great interest in various fields, including geology, medical domains, computer vision, and deep representation learning. The utility of optimal transport-based distances, such as the Wasserstein distance, for comparing probability measures has spurred active research in developing computationally efficient variations of these distances for spherical probability measures. This paper introduces a high-speed and highly parallelizable distance for comparing spherical measures using the stereographic projection and the generalized Radon transform, which we refer to as the Stereographic Spherical Sliced Wasserstein (S3W) distance. We carefully address the distance distortion caused by the stereographic projection and provide an extensive theoretical analysis of our proposed metric and its rotationally invariant variation. Finally, we evaluate the performance of the proposed metrics and compare them with recent baselines in terms of both speed and accuracy through a wide range of numerical studies, including gradient flows and self-supervised learning. Our code is available at https://github.com/mint-vu/s3wd. 

Recent studies have revealed the air-cushioning effect of droplet impact upon various surfaces and although pure water droplets have extensively been studied, the air entrainment dynamics for aqueous polymeric droplets was the focus of this study. Herein, droplets of low to moderate Weber numbers, [Formula: see text], displayed air film thickness gradients which was strongly influenced by the viscoelastic properties of the aqueous polymeric droplets in the dilute to the semidilute unentangled regimes. Aqueous polyethylene oxide droplets impacting a smooth thin oil film surface formed a submicrometer air layer, moments prior to impact, which was tracked by a high-speed total internal reflection microscopy technique. The radial changes in the air film thickness were related to the polymer concentration, thus providing an alternative tool for comparing the rheometer-derived overlap concentrations with a contactless optical technique.