The ability to create dynamic deformations of micron-sized structures isrelevant to a wide variety of applications such as adaptable optics, softrobotics, and reconfigurable microfluidic devices. In this work we examinenon-uniform lubrication flow as a mechanism to create complex deformationfields in an elastic plate. We consider a Kirchoff-Love elasticity model forthe plate and Hele-Shaw flow in a narrow gap between the plate and a parallelrigid surface. Based on linearization of the Reynolds equation, we obtain agoverning equation which relates elastic deformations to gradients innon-homogenous physical properties of the fluid (e.g. body forces, viscosity,and slip velocity). We then focus on a specific case of non-uniformHelmholtz-Smoluchowski electroosmotic slip velocity, and provide a method fordetermining the zeta-potential distribution necessary to generate arbitrarystatic and quasi-static deformations of the elastic plate. Extending theproblem to time-dependent solutions, we analyze transient effects onasymptotically static solutions, and finally provide a closed form solution fora Green's function for time periodic actuations.
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