Journal
JOURNAL OF FLUID MECHANICS
Volume 812, Issue -, Pages 841-865Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2016.830
Keywords
fluid-structure interactions; Hele-Shaw flows; microfluidics
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Funding
- European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme [678734]
- Israel Science Foundation [818/13]
- Technion fellowship from the Lady Davis Foundation
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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 flefinholtz Smoluchowski clectro-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 (ireen's function for time periodic actuations.
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