In the present study on the linear stability of gravity-driven Newtonian films flowing over inclined topographies, we consider a fundamental question: Is there a universal principle, being valid to describe the parametric evolution of the flow’s stability chart for variations of different system parameters? For this sake, we first screened all experimental and numerical stability charts available in the literature. In a second step, we performed experiments to fill the gaps which remained. Variations of the fluid’s viscosity and the topography’s specific shape, amplitude, wavelength, tip width, and inclination were considered. That way, we identified a set of six characteristic patterns of stability charts to be sufficient to describe and unify all results on the linear stability of Newtonian films flowing over undulated inclines. We unveiled a universal pathway—the stability cycle—along which the linear stability charts of all considered Newtonian films flowing down periodically corrugated inclines evolved when the system parameters were changed.
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January 2018
Research Article|
January 11 2018
The stability cycle—A universal pathway for the stability of films over topography
Mario Schörner
;
Mario Schörner
Department of Applied Mechanics and Fluid Dynamics, University of Bayreuth
, D-95440 Bayreuth, Germany
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Nuri Aksel
Nuri Aksel
Department of Applied Mechanics and Fluid Dynamics, University of Bayreuth
, D-95440 Bayreuth, Germany
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Physics of Fluids 30, 012105 (2018)
Article history
Received:
September 06 2017
Accepted:
December 14 2017
Citation
Mario Schörner, Nuri Aksel; The stability cycle—A universal pathway for the stability of films over topography. Physics of Fluids 1 January 2018; 30 (1): 012105. https://doi.org/10.1063/1.5003449
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