Behaviour of free falling viscoelastic liquid jets

Abstract

In a recent work, a protocol to measure the relaxation time of dilute polymer solutions, known to be challenging, has been established [1]. This protocol is based on a 2D multi-scale description of free-falling low velocity viscoelastic liquid jets. Although the relaxation time reached an asymptotic value for high jet velocities, a significant dependence with the jet velocity is observed for low velocities. The present work reconsiders these previous experimental data using a 3D multi-scale analysis in order to identify the origin of the dependence between the relaxation time and the jet velocity. The 3D analysis demonstrates the importance of a velocity-dependent coalescence mechanism in the jet behaviour. Thanks to a simple model of jet deformation it is demonstrated that this coalescence mechanism prevents the elasto-capillary contraction of the smallest scales from occurring when the jet velocity is reduced. KeywordsDilute polymer solutions, Viscoelasticity, Jet break-up, Multi-scale analysis IntroductionContrary to Newtonian fluids, the atomisation of a cylindrical jet of a viscoelastic solution presents long life time cylindrical ligaments connecting spherical beads, the so called beads-on-a-string (BOAS) structures [2]. These structures are observed at times prior jet breakup. It is well known that the thinning evolution of the ligaments diameter is controlled by the elasticity of the liquid [3]. The decrease is exponential, with a relaxation time depending only on the physical properties of the liquid. The measurement of this relaxation time is also known to be particularly challenging for dilute polymer solutions [4] for which the relaxation time is very short (micro-second or under). Previous studies [5][6][7][8] have investigated the possibility to use a cylindrical jet to measure this quantity, a method that could be suitable to probe very short times [4]. Yet, it was shown that the relaxation time obtained with this method depends on the jet operating conditions, i.e. the jet velocity, the amplitude and the frequency of the initial disturbance [6][7][8], thus limiting the development of this experimental method. Until recently, new results [4] suggest that an operating domain where these dependences vanish may exist. In this context, a multi-scale analysis of the behaviour of free falling jets of a dilute viscoelastic solution was performed, allowing measurements of the relaxation time [1]. The dynamics of the smaller scales was monitored and an exponential decrease was observed from which a relaxation time was extracted. It was found that the measured relaxation time decreases with increasing jet velocity, reaching a plateau for sufficiently high velocities. This behaviour was related to the influence of the initial amplitude disturbance as reported in [6][7][8]. The higher jet velocity was imposed, the larger initial amplitude was observed on jet images and the lower relaxation time was measured in agreement with [6][7][8]. To date, the dependence of the relaxation time with the jet veloci...