Effects of unrelaxed stress tension on the weakly nonlinear instability of viscoelastic sheets

Droplet atomization through aerobreakup is omnipresent in various natural and industrial processes. Atomization of Newtonian droplets is a well-studied area; however, non-Newtonian droplets have received less attention despite their being frequently encountered. By subjecting polymeric droplets of different concentrations to the induced airflow behind a moving shock wave, we explore the role of elasticity in modulating the aerobreakup of viscoelastic droplets. Three distinct modes of aerobreakup are identified for a wide range of Weber number $({\sim }10^2\unicode{x2013}10^4)$ and elasticity number $({\sim }10^{-4}\unicode{x2013}10^2)$ variation: these modes are vibrational, shear-induced entrainment and catastrophic breakup modes. Each mode is described as a three-stage process. Stage I is droplet deformation, stage II is the appearance and growth of hydrodynamic instabilities and stage III is the evolution of liquid mass morphology. It is observed that elasticity plays an insignificant role in the first two stages but a dominant role in the final stage. The results are described with the support of adequate mathematical analysis.

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“…2011; Yang, Tong & Fu 2013; Xie et al. 2016). The resolution for this discrepancy comes in terms of unrelaxed tension (Xie et al.…”

Section: Resultsmentioning

confidence: 99%

“…The resolution for this discrepancy comes in terms of unrelaxed tension (Xie et al. 2016) in the liquid phase. The role of elasticity changes from a destabilizing to a stabilizing agent if the unrelaxed tension is accounted for in the relevant stability analysis.…”

Section: Resultsmentioning

confidence: 99%

Shock-induced aerobreakup of a polymeric droplet

et al. 2023

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“…Another interesting observation is the formation of a bead on a string structure (BOAS), reported widely in extensional flows of dilute polymeric solutions model these complex phenomena, especially the fragment size at high We. There are theoretical studies related to the breakup of viscoelastic sheets and ligaments, but the results are ambiguous in a sense that, some literature reported elasticity as a destabilizing agent [42][43][44] , whereas others reported it as a stabilizing agent [45][46][47][48][49] . The resolution for this discrepancy comes in terms of unrelaxed tension 49 in the liquid phase.…”

Section: Stage-ii: Rt Instabilitymentioning

confidence: 99%

“…There are theoretical studies related to the breakup of viscoelastic sheets and ligaments, but the results are ambiguous in a sense that, some literature reported elasticity as a destabilizing agent [42][43][44] , whereas others reported it as a stabilizing agent [45][46][47][48][49] . The resolution for this discrepancy comes in terms of unrelaxed tension 49 in the liquid phase. The role of elasticity changes from destabilizing to stabilizing agent if the unrelaxed tension is accounted in the relevant stability analysis.…”

Section: Stage-ii: Rt Instabilitymentioning

confidence: 99%

Shock induced aerobreakup of a polymeric droplet

Chandra¹,

Sharma²,

Basu³

et al. 2022

Preprint

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Droplet atomization through aerobreakup is omnipresent in various natural and industrial processes. Atomization of Newtonian droplets is a well-studied area; however, non-Newtonian droplets have received less attention despite their frequent encounters. By subjecting polymeric droplets of different concentration to the induced airflow behind a moving shock wave, we explore the role of elasticity in modulating the aerobreakup of viscoelastic droplets. Three distinct modes of aerobreakup are identified for a wide range of Weber number (∼ 10 2 − 10 4 ) and Elasticity number (∼ 10 −4 − 10 2 ) variation; these modes are-vibrational, shear-induced entrainment and catastrophic breakup mode. Each mode is described as a three stage process. Stage-I is the droplet deformation, stage-II is the appearance and growth of hydrodynamic instabilities, and stage-III is the evolution of liquid mass morphology. It is observed that elasticity plays an insignificant role in the first two stages, but a dominant role in the final stage. The results are described with the support of adequate mathematical analysis.

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“…2015; Xie et al. 2016), and its real physical meaning is unclear. Secondly, the elastic tension decays exponentially with an increase in the distance from the nozzle.…”

Section: Introductionmentioning

confidence: 99%

Linear instability analysis of a viscoelastic jet in a co-flowing gas stream

Ding

et al. 2022

J. Fluid Mech.

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The instability characteristic of a viscoelastic jet in a co-flowing gas stream is studied comprehensively. The important role of the non-uniform basic velocity in the instability analysis of viscoelastic jets is clarified, which first induces an unrelaxed elastic tension, and then produces a coupling term between the elastic tension and perturbation velocity. The elastic tension promotes the instability of the jet, while the coupling term exhibits a stabilizing effect, which is essentially related to the nonlinear constitutive relation of viscoelastic fluids and the non-uniform basic velocity. The competition between these two factors leads to the non-monotonic effect of fluid elasticity on the disturbance growth rate, which can be divided into two different regimes characterized by the Weissenberg number with values smaller or larger than unity. In different regimes, the structure of the eigenspectrum is also significantly different. Furthermore, three instability mechanisms are identified using the energy budget analysis, corresponding to the predominance of the surface tension, elastic tension and shear and pressure of the external gas, respectively. By analysing the variations of the growth rate and phase speed of the disturbances, the general features of viscoelastic jet instability are obtained. Finally, the transitions of instability modes in parameter spaces are investigated theoretically and the transition boundaries among them are provided. This study provides guidance for understanding the underlying mechanism of instability of a viscoelastic jet surrounded by a co-flowing gas stream and the transition criterion of different instability modes.

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Effects of unrelaxed stress tension on the weakly nonlinear instability of viscoelastic sheets

Cited by 12 publications

References 23 publications

Shock-induced aerobreakup of a polymeric droplet

Shock-induced aerobreakup of a polymeric droplet

Shock induced aerobreakup of a polymeric droplet

Linear instability analysis of a viscoelastic jet in a co-flowing gas stream

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