Elastic deformations driven by non-uniform lubrication flows. (5th January 2017)

• Record Type: Journal Article
• Authors: Rubin, Shimon; Tulchinsky, Arie; Gat, Amir D.; Bercovici, Moran
• Is Part Of: Journal of fluid mechanics. Volume 812(2017)
• Page Start: 841
• Page End: 865
• Publication Date: 2017-01-05
• Subjects: fluid–structure interactions, -- Hele-Shaw flows, -- microfluidics; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2016.830
• Languages: English
• ISSNs: 0022-1120

Abstract

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.