Instability of a thin viscous film flowing under an inclined substrate: the emergence and stability of rivulets

2020 ◽  
Vol 904 ◽  
Author(s):  
Pier Giuseppe Ledda ◽  
Gaétan Lerisson ◽  
Gioele Balestra ◽  
François Gallaire
Keyword(s):  
Viscous Film

Abstract

Formation, Rupture, and Healing of an Annular Viscous Film

2020 ◽  
Vol 124 (22) ◽  
Author(s):  
Fan Yang ◽  
Howard A. Stone
Keyword(s):  
Viscous Film

scholarly journals Elastohydrodynamics of a pre-stretched finite elastic sheet lubricated by a thin viscous film with application to microfluidic soft actuators

2019 ◽  
Vol 862 ◽  
pp. 732-752 ◽  
Author(s):  
Evgeniy Boyko ◽  
Ran Eshel ◽  
Khaled Gommed ◽  
Amir D. Gat ◽  
Moran Bercovici
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Finite Domain ◽  
Viscous Film ◽  
Elastic Sheet ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Wide Range ◽  
Soft Actuators ◽  
Von Kármán

The interaction of a thin viscous film with an elastic sheet results in coupling of pressure and deformation, which can be utilized as an actuation mechanism for surface deformations in a wide range of applications, including microfluidics, optics and soft robotics. Implementation of such configurations inherently takes place over finite domains and often requires some pre-stretching of the sheet. Under the assumptions of strong pre-stretching and small deformations of the lubricated elastic sheet, we use the linearized Reynolds and Föppl–von Kármán equations to derive closed-form analytical solutions describing the deformation in a finite domain due to external forces, accounting for both bending and tension effects. We provide a closed-form solution for the case of a square-shaped actuation region and present the effect of pre-stretching on the dynamics of the deformation. We further present the dependence of the deformation magnitude and time scale on the spatial wavenumber, as well as the transition between stretching- and bending-dominant regimes. We also demonstrate the effect of spatial discretization of the forcing (representing practical actuation elements) on the achievable resolution of the deformation. Extending the problem to an axisymmetric domain, we investigate the effects arising from nonlinearity of the Reynolds and Föppl–von Kármán equations and present the deformation behaviour as it becomes comparable to the initial film thickness and dependent on the induced tension. These results set the theoretical foundation for implementation of microfluidic soft actuators based on elastohydrodynanmics.

Instability of a thin viscous film flowing under an inclined substrate: steady patterns

2020 ◽  
Vol 898 ◽  
Author(s):  
Gaétan Lerisson ◽  
Pier Giuseppe Ledda ◽  
Gioele Balestra ◽  
François Gallaire
Keyword(s):  
Viscous Film ◽  
Image Position

scholarly journals The transition from sheet to cloud cavitation

2017 ◽  
Vol 817 ◽  
pp. 439-454 ◽  
Author(s):  
P. F. Pelz ◽  
T. Keil ◽  
T. F. Groß
Keyword(s):  
Reynolds Number ◽  
Cavitation Number ◽  
Wall Friction ◽  
Bubble Collapse ◽  
Penetration Length ◽  
Cloud Cavitation ◽  
Viscous Film ◽  
History Of ◽  
Good Agreement

Recent studies indicate that the transition from sheet to cloud cavitation depends on both cavitation number and Reynolds number. In the present paper this transition is investigated analytically and a physical model is introduced. In order to include the entire process, the model consists of two parts, a model for the growth of the sheet cavity and a viscous film flow model for the so-called re-entrant jet. The models allow the calculation of the length of the sheet cavity for given nucleation rates and initial nuclei radii and the spreading history of the viscous film. By definition, the transition occurs when the re-entrant jet reaches the point of origin of the sheet cavity, implying that the cavity length and the penetration length of the re-entrant jet are equal. Following this criterion, a stability map is derived showing that the transition depends on a critical Reynolds number which is a function of cavitation number and relative surface roughness. A good agreement was found between the model-based calculations and the experimental measurements. In conclusion, the presented research shows the evidence of nucleation and bubble collapse for the growth of the sheet cavity and underlines the role of wall friction for the evolution of the re-entrant jet.

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