Capillary interaction between a small thin solid plate and a liquid

Micromechanical systems are increasingly being used in microfluidic and biological applications where solid-liquid interaction phenomena become important. Here, we present an analytical/computational study on the interaction force between a thin solid plate interfacing with a liquid, and forming a meniscus under uniform gravitational field. The height of the plate from the liquid surface is prescribed. We assume that the contact angle is fixed, and must be satisfied by all possible menisci. The interaction force and the profile of the meniscus are determined using Young-Laplace equation represented in an Eulerian coordinate. For a long narrow thin plate, the results are obtained in closed form. For a circular plate, the solution is obtained numerically, where we find that the stability of the meniscus is strongly dependent on the radius of the plate. The findings of this study have relevance to the quantification of force between an AFM tip and the thin layer of moisture on the surface that it scans, as well as in the design of MEMS actuators that manipulate objects in liquids without inundating themselves.