Advanced models for the calculation of capillary attraction in axisymmetric configurations

• A new analytical method is developed for the determination of the exact shape of a liquid meniscus.
• Axisymmetric configurations are considered.
• Comparisons with approximate solutions are proposed.
• An improved simplified method is proposed.
• A FE procedure is proposed which can be applied to non-symmetric geometries.

The proper estimate of capillary attraction is of great importance in many situations, for example the reliability assessment of Micro- Electro-Mechanical Systems (MEMS) with respect to spontaneous adhesion. In spite of many theoretical studies, there is a lack of general methods for obtaining the exact shape of the liquid meniscus between the asperities of rough surfaces. In this paper, a new analytical method is developed for the specific case of axysimmetric configurations. The outcomes of such a method are critically compared with the approximate solution which is usually proposed in the literature. Moreover, an improved simplified method is constructed and validated. Finally, a more general procedure (based on the Finite Element Method) is proposed, with possible application to non-symmetric geometries.