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Elastic deformations driven by non-uniform lubrication flows

Published online by Cambridge University Press:  05 January 2017

Shimon Rubin ,
Arie Tulchinsky ,
Amir D. Gat  and
Moran Bercovici
Shimon Rubin
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa, Israel
Arie Tulchinsky
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa, Israel
Amir D. Gat*
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa, Israel
Moran Bercovici*
Affiliation:
Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa, Israel
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

The ability to create dynamic deformations of micron-sized structures is relevant to a wide variety of applications such as adaptable optics, soft robotics and reconfigurable microfluidic devices. In this work, we examine non-uniform lubrication flow as a mechanism to create complex deformation fields in an elastic plate. We consider a Kirchhoff–Love elasticity model for the plate and Hele-Shaw flow in a narrow gap between the plate and a parallel rigid surface. Based on linearization of the Reynolds equation, we obtain a governing equation which relates elastic deformations to gradients in non-homogeneous physical properties of the fluid (e.g. body forces, viscosity and slip velocity). We then focus on a specific case of non-uniform Helmholtz–Smoluchowski electro-osmotic slip velocity, and provide a method for determining the zeta-potential distribution necessary to generate arbitrary static and quasi-static deformations of the elastic plate. Extending the problem to time-dependent solutions, we analyse transient effects on asymptotically static solutions, and finally provide a closed form solution for a Green’s function for time periodic actuations.

JFM classification

Low-Reynolds-number flows: Hele-Shaw flows Micro-/Nano-fluid dynamics: Microfluidics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 812 , 10 February 2017 , pp. 841 - 865
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Copyright
© 2017 Cambridge University Press 

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