Analytical computation of arc menisci configuration under primary drainage in convex capillary cross sections

We analyze the geometric set-up of Lindquist’s “The Geometry of Primary Drainage” (J Colloid Interface Sci 296(2):655–668, 2006) and show that his main equation, which models the arc menisci configuration under primary drainage in capillary tube cross sections, can be solved analytically for the special case of a convex cross section and the wetting angle being assumed 0. Our approach relies on the Voronoi diagram of the cross section and runs in O(n log n) time for an n-segment cross section. It requires only the solution of n − 2 second-degree polynomial equations.