A modified finite element method for determining equilibrium capillary surfaces of liquids with specified volumes

This paper describes a modified finite element method (MFEM) for determinin g the static equilibrium shape of the capillary surface of a liquid with a prescribed volume constrained by rigid boundaries with arbitrary shapes. It is assumed that the liquid is in static equilibrium under the influence of surface tension, adhesion, and gravity forces. This problem can be solved by employing the conventional FEM; however, a major difficulty arises due t o the presence of the volume (integral) constraint and usually requires the use of the Lagrange multiplier method, the sequential unconstrained minimi zation technique, or the augmented Lagrange multiplier method. With the MFE M, the space variables defining the equilibrium surfaces (or curves) are ex panded in terms of parametric interpolation functions, which are designed s uch that the boundary conditions and the integral constraint equation are a utomatically satisfied during each iteration of a direct numerical search p rocess. Hence, there is no need to include Lagrange multipliers and/or pena lty factors and the problem can be treated more simply as one involving unc onstrained optimization. This investigation indicates that the MFEM is more efficient and reliable than the other methods. Results are presented for s everal case study problems involving liquid solder drops. Copyright (C) 200 0 John Wiley & Sons, Ltd.