Iterated stretching of viscoelastic jets (original) (raw)
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Dynamics of bead formation, filament thinning and breakup in weakly viscoelastic jets
Journal of Fluid Mechanics, 2010
The spatiotemporal evolution of a viscoelastic jet depends on the relative magnitude of capillary, viscous, inertial and elastic stresses. The interplay of capillary and elastic stresses leads to the formation of very thin and stable filaments between drops, or to 'beads-on-a-string' structure. In this paper, we show that by understanding the physical processes that control different stages of the jet evolution it is possible to extract transient extensional viscosity information even for very low viscosity and weakly elastic liquids, which is a particular challenge in using traditional rheometers. The parameter space at which a forced jet can be used as an extensional rheometer is numerically investigated by using a one-dimensional nonlinear free-surface theory for Oldroyd-B and Giesekus fluids. The results show that even when the ratio of viscous to inertio-capillary time scales (or Ohnesorge number) is as low as Oh ∼ 0.02, the temporal evolution of the jet can be used to obtain elongational properties of the liquid.
Influence of viscosity on the capillary instability of a stretching jet
Journal of Fluid Mechanics, 1987
The hydrodynamic stability of a rapidly elongating, viscous liquid jet such as obtained in shaped charges is presented. The flow field depends on three characteristic timescales associated with the growth of perturbations (due esaentially to the effect of the surface tension), the elongation of the jet, and the inward diffusion of vorticity from the free surface, respectively. The latter process introduces a time lag resulting in the current values of the free-surface perturbation and its time derivative being a function of their past history. Solutions of the integro-differential equation for the evolution of disturbances exhibit a novel dual role played by the viscosity : besides the traditional damping effect it is associated with a destabilizing mechanism in the elongating jet. The wavelength of maximum instability is also a function of time elapsed since the jet formation, longer wavelengths becoming dominant at later stages. Understanding of these instability processes can help in both promoting and delaying instability as required by specific applications.
Collision of viscoelastic jets and the formation of fluid webs
Applied Physics Letters, 2005
This letter reports experimental observations of the flow kinematics and stability of thin fluid sheets produced by impinging obliquely aligned laminar jets of a series of viscoelastic worm-like micelle solutions. As the velocity of the impinging jets is increased, the sheets of viscoelastic fluid grow larger and eventually become unstable. High speed imaging reveals a transition to a striking new flow structure resembling fluid webs, previously unobserved for Newtonian or non-Newtonian fluids. These newly discovered flow structures are complex and comprised of highly interconnected filaments created by the growth of multiple internal failures within the fluid sheet. Increasing viscoelasticity of the test fluid was found to stabilize the sheets and the fluid webs while increasing the drop size produced by their eventual breakup under capillary stresses.
On the evolution of thin viscous jets: filament formation
Mathematical Methods in the Applied Sciences, 2004
In this paper, we have studied the evolution of thin uid jets, paying special attention on the limit of very large viscosity. Local well-posedness of the one-dimensional system describing this evolution as well as the existence of break-up (at least as t → ∞) under quite general conditions is proved. In addition, we have proved the well-known experimental fact that in the limits of very large viscosities the solutions develop very long and thin ÿlaments previous to break-up and a complete detailed description of their structure is given.
Behaviour of free falling viscoelastic liquid jets
Proceedings ILASS–Europe 2017. 28th Conference on Liquid Atomization and Spray Systems, 2017
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 whenthe jet velocity is reduced.DOI: http://dx.doi.org/10.4995/ILASS2017.2017.4700
Instability of viscoelastic curved liquid jets
Applied Mathematical Modelling, 2014
The industrial prilling process is a common technique to produce small pellets which are generated from the break-up of rotating liquid jets. In many cases the fluids used are molten liquid and/or contain small quantities of polymers and thus typically can be modelled as non-Newtonian liquids. Industrial scale setups are costly to run and thus mathematical modelling provides an opportunity to assess methods of improving efficiency and introduces greater levels of precision. In order to understand this process, we will consider a mathematical model to capture the essential physics related to a cylindrical drum, which is rotated about its axis. In this paper, we will model the viscoelastic nature of the fluid using the Oldroyd-B model. An asymptotic approach is used to simplify the governing equations into 1D equations. Moreover, a linear instability analysis is examined and the most unstable modes are found to grow along the jet. Furthermore, the non-linear instability is investigated by using a finite difference scheme to find break-up lengths and droplet formation.
Break-up and no break-up in a family of models for the evolution of viscoelastic jets
Zeitschrift für angewandte Mathematik und Physik, 2003
The goal of this paper is to study the conditions under which break-up of a thin viscoelastic jet is inhibited or, oppositely, to provide families of self-similar break-up solutions emerging in the evolution. The fluid is a polymeric solution and the constitutive relation we consider is of the Johnson-Segalman type which contains one parameter. The models under consideration are the limits of the well know one-dimensional model when the viscosity of the solvent goes to zero or to infinity and when the Deborah number is very large. Some considerations on the stationary and travelling wave solutions of the models are also presented.
Journal of Rheology, 2012
This paper develops a model for fast filament stretching, thinning, and break-up for Newtonian and non-Newtonian fluids, and the results are compared against experimental data where fast filament relaxation occurs. A 1D approximation was coupled with the arbitrary Lagrangian Eulerian (ALE) formulation to perform simulations that captured both filament thinning and break-up. The modeling accounts for both the initial polymer stretching processes from the precise movement of the two moving pistons and also the subsequent thinning when the pistons are at rest. The simulations were first validated for a low viscosity Newtonian fluid matched to experimental data obtained from a recently developed apparatus, the Cambridge Trimaster. A non-Newtonian polymer fluid, with high frequency linear viscoelastic behavior characterized using a piezoaxial vibrator rheometer, was modeled using both an Oldroyd-B and FENE-CR single-mode constitutive models. The simulations of the filament deformation were compared with experiment. The simulations showed a generally reasonable agreement with both the stretch and subsequent relaxation experimental responses, although the mono mode models used in this paper were unable to capture all of the details for the experimental time evolution relaxation profile of the central filament diameter. V C 2012 The Society of Rheology.
Viscoelastic Ligament Dynamics in Free Liquid Jet Experiments
2021
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 ...