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Thwarting Marangoni instability in a viscoelastic liquid film via parametric forcing
Phys. Rev. Fluids 10, 044001 – Published 17 April, 2025
DOI: https://doi.org/10.1103/PhysRevFluids.10.044001
Abstract
We explore how fluid elasticity affects the stabilization of an inherently unstable Marangoni-driven thin-film system through the application of parametric forcing. In the absence of elasticity, parametric forcing increases the threshold for the long-wave Marangoni instability mode in a thin liquid film, thereby stabilizing the system. A quiescent stable state is achievable within a finite forcing amplitude range, provided the forcing frequency is below a critical value. Outside this parameter range, the system is unstable on account of either Marangoni or Faraday instability. We find that the behavior for a film of viscoelastic liquid is different in two significant ways, as a result of fluid elasticity. Firstly, the neutral stability diagram in the amplitude versus frequency plane displays an island of stability, bounded by an upper and a lower frequency, as opposed to the Newtonian case, which displays only an upper frequency bound. Below the lower frequency bound and above the upper frequency bound, the film can be simultaneously subject to both Maranogni and Faraday instability. Secondly, fluid elasticity lowers the forcing amplitude at the neutral stability bound for both the Marangoni and Faraday instabilities, with a more significant reduction in the latter. As a result, both the threshold amplitude and the amplitude range for full stabilization of the thin-film system are reduced, which is attributed to the memory effect imparted by fluid elasticity.
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References (20)
- S. J. Vanhook, M. F. Schatz, J. B. Swift, W. D. McCormick, and H. L. Swinney, Long-wavelength surface-tension-driven Bénard convection: Experiment and theory, J. Fluid Mech. 345, 45 (1997).
- P. Chen, T. Liu, P. Wu, C. Tseng, and C. Leu, Drying-induced birefringence of polyimide optical films, AIChE J. 56, 790 (2010).
- I. B. Ignatius, B. Dinesh, G. F. Dietze, and R. Narayanan, Influence of parametric forcing on Marangoni instability, J. Fluid Mech. 981, A8 (2024).
- U. Thiele, J. M. Vega, and E. Knobloch, Long-wave Marangoni instability with vibration, J. Fluid Mech. 546, 61 (2006).
- S. Shklyaev, A. A. Alabuzhev, and M. Khenner, Marangoni convection in a thin film on a vertically oscillating plate, Phys. Rev. E 92, 013019 (2015).
- K. Kumar and L. S. Tuckerman, Parametric instability of the interface between two fluids, J. Fluid Mech. 279, 49 (1994).
- A. Morozov and S. E. Spagnolie, Introduction to complex fluids, Complex Fluids in Biological Systems: Experiment, Theory, and Computation (Springer New York, NY, 2015).
- L. Scriven and C. Sternling, On cellular convection driven by surface-tension gradients: Effects of mean surface tension and surface viscosity, J. Fluid Mech. 19, 321 (1964).
- A. H. Nayfeh, Perturbation Methods (John Wiley & Sons, 1981).
- A. Sobti, A. P. Toor, and R. K. Wanchoo, Oscillatory and steady shear rheological properties of aqueous polyacrylamide solutions, Chem. Data Coll. 17-18, 356 (2018).
- Y. Hirata, Y. Kato, N. Andoh, N. Fujiwara, and R. Ito, Measurements of thermophysical properties of polyacrylamide gel used for electrophoresis, J. Chem. Eng. Japan 26, 143 (1993).
- W. Guo, G. Labrosse, and R. Narayanan, The Application of the Chebyshev-Spectral Method in Transport Phenomena (Springer Science & Business Media, Berlin and Heidelberg, 2012).
- D. Getachew and S. Rosenblat, Thermocapillary instability of a viscoelastic liquid layer, Acta Mech. 55, 137 (1985).
- P. Dauby, P. Parmentier, G. Lebon, and M. Grmela, Coupled buoyancy and thermocapillary convection in a viscoelastic Maxwell fluid, J. Phys.: Condens. Matter 5, 4343 (1993).
- R. Sarma and P. K. Mondal, Marangoni instability in a heated viscoelastic liquid film: Long-wave versus short-wave perturbations, Phys. Rev. E 100, 013103 (2019).
- R. Sarma and P. K. Mondal, Marangoni instability in a viscoelastic binary film with cross-diffusive effect, J. Fluid Mech. 910, A30 (2021).
- H. Müller and W. Zimmermann, Faraday instability in a linear viscoelastic fluid, Europhys. Lett. 45, 169 (1999).
- S. Kumar, Parametrically driven surface waves in viscoelastic liquids, Phys. Fluids 11, 1970 (1999).
- A. Lindner and C. Wagner, Viscoelastic surface instabilities, C. R. Phys. 10, 712 (2009).
- F. Schön and M. Bestehorn, Instabilities and pattern formation in viscoelastic fluids, Eur. Phys. J.: Spec. Top. 232, 375 (2023).
