The retraction of jetted slender viscoelastic liquid filaments

Abstract

Long and slender liquid filaments are produced during inkjet printing, which can subsequently either retract to form a single droplet, or break up to form a primary droplet and one or more satellite droplets. These satellite droplets are undesirable since they degrade the quality and reproducibility of the print, and lead to contamination within the enclosure of the print device. Existing strategies for the suppression of satellite droplet formation include, among others, adding viscoelasticity to the ink. In the present work, we aim to improve the understanding of the role of viscoelasticity in suppressing satellite droplets in inkjet printing. We demonstrate that very dilute viscoelastic aqueous solutions ( $\text {concentrations} \sim 0.003\,\%$ wt. polyethylene oxide, corresponding to nozzle Deborah number $De_{n}\sim 3$ ) can suppress satellite droplet formation. Furthermore, we show that, for a given driving condition, upper and lower bounds of polymer concentration exist, within which satellite droplets are suppressed. Satellite droplets are formed at concentrations below the lower bound, while jetting ceases for concentrations above the upper bound (for fixed driving conditions). Moreover, we observe that, with concentrations in between the two bounds, the filaments retract at velocities larger than the corresponding Taylor–Culick velocity for the Newtonian case. We show that this enhanced retraction velocity can be attributed to the elastic tension due to polymer stretching, which builds up during the initial jetting phase. These results shed some light on the complex interplay between inertia, capillarity and viscoelasticity for retracting liquid filaments, which is important for the stability and quality of inkjet printing of polymer solutions.

Temperature-controlled dripping-onto-substrate (DoS) extensional rheometry of polymer micelle solutions

“…For example, ejecting a polymer solution with a long extensional relaxation time from a nozzle can result in filament formation and droplet retraction back into the nozzle, rendering it unsuitable for printing. 10–12 In spraying polymer solutions, the mean droplet size has been shown to increase with extensional relaxation time. 13…”

Taylor–Culick retractions and the influence of the surroundings

“…A natural extension of the present work would be to understand the retraction of non-Newtonian sheets and filaments (Sen et al 2021) in similar surroundings. In such scenarios, the retraction dynamics will depend not only on capillarity and viscosity as described in this work, but also on the rheological properties of both the film and the surroundings.…”

“…For instance, Sen et al. (2021) showed that viscoelastic filaments can retract at velocities higher than the Newtonian Taylor–Culick limit due to elastic tension. Moreover, the retraction dynamics of liquids have also been studied in the context of dewetting for a wide range of scenarios (Redon, Brochard-Wyart & Rondelez 1991; Brochard-Wyart, Martin & Redon 1993; Shull & Karis 1994; Andrieu, Sykes & Brochard 1996; Lambooy et al.…”

“…The rheological properties of the film also influence the retraction dynamics (Dalnoki-Veress et al 1999;Tammaro et al 2018;Villone, Hulsen & Maffettone 2019;Kamat, Anthony & Basaran 2020). For instance, Sen et al (2021) showed that viscoelastic filaments can retract at velocities higher than the Newtonian Taylor-Culick limit due to elastic tension. Moreover, the retraction dynamics of liquids have also been studied in the context of dewetting for a wide range of scenarios (Redon, Brochard-Wyart & Rondelez 1991;Brochard-Wyart, Martin & Redon 1993;Shull & Karis 1994;Andrieu, Sykes & Brochard 1996;Lambooy et al 1996;Haidara, Vonna & Schultz 1998;Buguin, Vovelle & Brochard-Wyart 1999;Péron, Brochard-Wyart & Duval 2012;Peschka et al 2018;Kim et al 2020).…”

Transition to the viscoelastic regime in the thinning of polymer solutions

“…A better understanding of the transition between the Newtonian and the viscoelastic regimes could be benficial to applications that require the break-up of ligaments of polymer solutions, 50 and the atomization into droplets. [51][52][53][54]…”