Computation of three-dimensional hydrostatic menisci
C. Pozrikidis · IMA Journal of Applied Mathematics · 2009
A numerical method is developed for computing the shape of an infinite three-dimensional hydrostatic meniscus originating from interior contact lines whose projection in the horizontal plane has a specified shape. The Laplace–Young equation determining the meniscus shape is solved in orthogonal curvilinear coordinates generated by conformal mapping using a finite-difference method. The elevation of the contact lines is either prescribed or computed as part of the solution to ensure a specified contact angle. The method is applied to study the hydrostatic meniscus developing around an elliptical vertical cylinder using elliptic coordinates and between two parallel vertical circular cylinders using bipolar coordinates. The results illustrate variations in the contact angle or contact line distribution due to the boundary geometry and furnish numerical estimates for the capillary force and torque.