Droplet-induced anomalous deformation of a thin micro-plate

The surface tension of liquid is generally negligible at macroscopic scale but can cause a lot of anomalous deformation of slender structures at small scales. In this study, we presented the analytical deflection solutions of a rectangular plate with two clamped ends and a clamped circular plate based upon the principle of superposition, where a droplet was deposited onto the micro-plate surfaces. In the light of these analytical solutions, the abnormal bending of the plate when the droplet is placed at different positions of the top or bottom surface of the plate was discussed in detail. The FEM (finite element method) simulation was also conducted, and the results show excellent agreement with our analytical solutions. We also put to use the FEM simulation to explore the displacement field of a more general plate with complex boundary conditions and complicated loads originating from the droplet, and the folding of a soft membrane caused by a droplet was also simulated. This investigation is beneficial to understand the physical mechanisms underlying the droplet-induced deformation of slender structures, and is of great interest for the design of new materials and devices by utilizing the effects of surface tension at micro and nano scales.

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► Approximate analytical deflection solution of a clamped-clamped plate is presented.
► Analytical deflection solution of a clamped circular plate is derived.
► The displacement field of a general plate is simulated by FEM (finite element method).
► The analytical and numerical results show excellent agreement with each other.