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Viscoelastic Ligament Dynamics in Free Liquid Jet Experiments

Abstract : The widely-used experimental methods to determine the relaxation time of viscoelastic solutions are based on ligament thinning measurements. The CaBER (Capillary Breakup Extensional Rheometer) produces a stretched liquid filament between two plates and deduces the solution relaxation time from its diameter temporal decrease. However this technique does not suit dilute polymer solutions for which the jet rheometer such as the ROJER (Rayleigh Ohnesorge Jetting Extensional Rheometer) is seen as a promising alternative. The measurement principle consists in analyzing the temporal evolution of the neck diameter of a liquid jet experiencing a capillary instability. However, this technique is known to be difficult to implement and has revealed a dependence between the measured relaxation time and the operating conditions involving the jet velocity, the perturbation frequency and initial amplitude. In the present work an experimental protocol is reported to extract the relaxation time of a dilute polymer solution from its jet behavior. The main features are the use of free liquid jets which simplifies the control of the operating conditions and of a multi-scale analyzing tool which simplifies the measurement to be performed on the jets. Twenty one experiments with various jet diameters and velocities were performed. The results explain why the relaxation time measurement cannot be performed on any jets and allow elaborating a precise procedure for a confident measurement of the relaxation time. Keywords: dilute polymer solution, ligament behavior, jet break-up Introduction Viscoelastic liquids have specific shear thinning and strain-hardening properties that confer on them characteristic behaviors while atomizing. For instance, laminar viscoelastic liquid jets break up with formation of beads-on-strings structures composed of large spherical beads and thin cylindrical threads. These threads might be the seat of an elongational flow where capillary and elastic forces are in balance, the first being the driving force, the second the resistive one, that leads to a specific decrease of their diameter with time. This decrease is controlled by the stress relaxation time scale tr of the viscoelastic solution. The knowledge of this time scale is therefore of paramount importance in the context of atomization but its experimental determination remains challenging especially for very dilute polymer solutions. The Capillary Breakup Extensional Rheometer (CaBER) performs this measurement by detecting and analyzing the elasto-capillary thinning of a filament formed by stretching a liquid bridge between two coaxial cylindrical plates. For dilute polymer solutions, Rodd and al. [1] have shown that the CaBER have limitations: there is a lower shear viscosity limit and a lower relaxation time limit for which the relaxation time measurement is not possible due to the fast thinning of the filament and the lack of resolution of the device. Moreover, liquid shape oscillations are introduced due to the fast transition of the plates from their initial positions to their final configurations for which the liquid bridge is unstable and thins down [2]. These oscillations persist for multiples of the capillary time and corrupt the CaBER measurement if the breakup occurs before they vanish. These limitations have been overcome in part with the use of the Slow Retraction Method and the use of a high speed camera, but there is a progressive appearance of beads-on-strings structures at the final steps of the filament thinning resulting from an iterated elastic instability [3]. Another technic based on jet experiments have been developed [4-8]. For dilute polymer solutions, the jet rheometer is seen as a promising alternative to the liquid filament rheometer [7]. Up so far, the jet rheometer considers the behavior of a cylindrical liquid jet forced at a given perturbation amplitude and frequency [4-6, 8]. However, this technic remains tricky in particular because the resulting relaxation time might report a dependence on the jet operating conditions, i.e. the jet velocity and the initial disturbance amplitude and frequency [6]. Recently, new results suggest however the existence of an operating domain free of these dependences [8].
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Christophe Tirel, Marie-Charlotte Renoult, Christophe Dumouchel. Viscoelastic Ligament Dynamics in Free Liquid Jet Experiments. International Conference on Liquid Atomization and Spray Systems, Jul 2018, Chicago, United States. ⟨hal-01844090⟩

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