Thin film instabilities and pattern formation
Thin film instabilities and pattern formation We recently derived a novel equation describing how the thickness of a viscous film evolves with time, as a by-product of our work on the effects of oscillatory airflow on capillary instabilities related to airway closure. This is a modified Kuramoto-Sivashinsky equation which can also describe the Rayleigh-Taylor instability of a two-fluid system between horizontal plates consisting of a viscous film bounded below by a rigid oscillating plate and above by a heavier fluid. For some parameter values, the growth of waves at the air-liquid interface saturates and capillary instabilities promote chaotic waves. Numerical solutions on extended spatial intervals reveal interesting time-asymptotic regimes in which averaged properties of the extensive spatiotemporal chaos are not steady but oscillate in time. A comprehensive parametric study is being undertaken with the aim of identifying and classifying a wide range of flow patterns that may have biomedical and industrial applications. Extensions to other coating flow problems, including three-dimensional instabilities, are also being considered.
This work is being done in collaboration with A.L. Frenkel.
Frenkel, A.L. and Halpern, D. (2000) On saturation of Rayleigh-Taylor instability.In: IUTAM Symposium on Nonlinear Waves in Multiphase Flow.Editor, Chang, H.-C, Volume 57, pp. 69-79. Publishers: Kluwer Academic, Dordrecht, The Netherlands. PDF.
Faybishenko, B., Babchin, A.J., Frenkel, A.L., Halpern, D. and Sivashinsky, G.I. A model of chaotic evolution of an ultrathin film down an inclined plane. Colloids & Surfaces 192: 377-385, 2001. SummaryPlus | Full Text + Links | PDF.
Halpern, D. and Frenkel, A.L. Saturated Rayleigh-Taylor instability of an oscillating Couette film flow. J. Fluid Mech.446: 67-93, 2001. [PDF].
Frenkel, A.L. and Halpern, D. Stokes-flow instability due to interfacial surfactant. Phys. Fluids.14(7), L45-L48, 2002. [PDF].
Halpern, D. and Frenkel, A.L. Destabilization of a creeping flow by interfacial surfactant: Linear theory extended to all wavenumbers. J. Fluid Mech. 485: 191-220, 2003. [PDF].
Frenkel, A.L and Halpern, D. Effect of inertia on the insoluble-surfactant instability of a shear flow.Phys. Rev. E 71, 016302, 2005. [PDF].
Frenkel, A.L and Halpern, D. Strongly nonlinear nature of interfacial-surfactant instability of Couette flow. Int. J. Pure Appl. Math, 29(2), 205-224, 2006 or arXiv:nlin/0601025
Halpern, D. and Frenkel, A. L. Nonlinear evolution, travelling waves, and secondary instability of sheared-film flows with insoluble surfactants. J.Fluid Mech., 594, 125-156, 2008. [PDF].
Frenkel, A.L. and Halpern, D. Surfactant and gravity dependent instability of two-layer Couette flows and its nonlinear saturation. J. Fluid Mech., 826, 158-204, 2017. [PDF].
Frenkel, A.L., Halpern, D. and Schweiger, A.J. Surfactant and gravity dependent instability of two-layer channel flows: Linear theory covering all wave lengths. arXiv preprint arXiv:1801.09290, 2018.
Frenkel, A., Halpern, D., & Schweiger, A. (2019). Surfactant- and gravity-dependent instability of two-layer channel flows: Linear theory covering all wavelengths. Part 1. ‘Long-wave’ regimes. Journal of Fluid Mechanics, 863, 150-184. doi:10.1017/jfm.2018.990.
Frenkel, A., Halpern, D., & Schweiger, A. (2019). Surfactant- and gravity-dependent instability of two-layer channel flows: Linear theory covering all wavelengths. Part 2. Mid-wave regimes. Journal of Fluid Mechanics, 863, 185-214. doi:10.1017/jfm.2018.991.