Temporal instability analysis of power-law fluid jets in quiescent air under symmetric (varicose) perturbations
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Karthick Sundaresan
,
Dineshwar Murugan
Abstract
Power-law fluids, such as paints, silica suspensions, and polymers, are frequently employed in industrial processes such as spray painting, agricultural spraying, and fuel injection, which disintegrate liquid sheets into smaller droplets. Their flow characteristics are distinct and intricate because of the absence of fixed viscosity. In contrast to Newtonian fluids, power-law fluid atomization is significantly influenced by the non-linear relationship between shear stress and shear rate. With an emphasis on the interaction of fluid rheology, sheet dynamics, and instability processes, this work explores the primary breakup of power-law liquid sheets. Using linear stability analysis, a theoretical attempt has been made to capture the primary breakup characteristics of these liquids in stagnant air under the influence of symmetric(varicose) mode of interfacial instability. Combining the continuity equation, linearised momentum equation, and the relevant boundary conditions, the dispersion relation for predicting the stability of the tested mode has been arrived. The stability variables namely the temporal growth rate, the breakup frequency, and the critical wave number were determined. On plotting the primary breakup variables in the dimensionless form, regression functions have attained a superior correlation coefficient for both shear-thinning and shear-thickening liquids.
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Use of Large Language Models, AI, and Machine Learning Tools: Not Applicable.
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Conflict of interest: The authors state there is no conflict of interest.
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Research funding: None declared.
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Data availability: Not applicable.
Nomenclature
- h
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Surface perturbation/interface shape
- k
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Wavenumber
- K
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Consistency index
- K crit
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Critical Wavenumber
- M
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Mode of interfacial disturbance
- n
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Power law index/flow behavior index
- Oh
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Ohnesorge number
- R or R o
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radius of jet
- U 0
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base velocity profile
- U l
-
liquid velocity
- We
-
liquid Weber number
- μ
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Dynamic viscosity of a liquid
- μ eff
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Effective dynamic viscosity of a liquid
- ν
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Kinematic viscosity of liquid
- ρ
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Density of liquid
- γ̇
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Shear rate
- σ
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Surface tension
- ω r
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Breakup frequency
- ω i
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Amplification factor
- Ω
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Temporal growth rate
- χ
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Dimensionless breakup frequency
- ξ
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Dimensionless critical wave number
- η 0
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Initial interfacial displacement
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