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

Published online by Cambridge University Press:  14 January 2019

Evgeniy Boyko Open the ORCID record for Evgeniy Boyko [Opens in a new window] ,
Ran Eshel ,
Khaled Gommed ,
Amir D. Gat Open the ORCID record for Amir D. Gat [Opens in a new window]  and
Moran Bercovici Open the ORCID record for Moran Bercovici [Opens in a new window]
Evgeniy Boyko
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 3200003, Israel
Ran Eshel
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 3200003, Israel
Khaled Gommed
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 3200003, Israel
Amir D. Gat*
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 3200003, Israel
Moran Bercovici*
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 3200003, Israel Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas, TX 78712, USA
*
†Email addresses for correspondence: amirgat@technion.ac.il, mberco@technion.ac.il
†Email addresses for correspondence: amirgat@technion.ac.il, mberco@technion.ac.il
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Abstract

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.

JFM classification

Low-Reynolds-number flows: Hele-Shaw flows Micro-/Nano-fluid dynamics: MEMS/NEMS Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 862 , 10 March 2019 , pp. 732 - 752
Copyright
© 2019 Cambridge University Press 

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Boyko et al. supplementary movie 1

The evolution of pressure and deformation fields, resulting from two square-shaped regions with opposite signs of zeta potential, subjected to an electric field suddenly applied at t=0.

Download Boyko et al. supplementary movie 1(Video)
Video 9.4 MB

Boyko et al. supplementary movie 2

The steady-state oscillations of pressure and deformation fields, resulting from a single square region with a fixed zeta potential, subjected to an oscillating electric field.

Download Boyko et al. supplementary movie 2(Video)
Video 9.3 MB
Supplementary material: PDF

Boyko et al. supplementary material

Supplementary material

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