Modeling of capillary coaxial gap filling with viscous liquid

A variational formulation of the boundary value problem on the motion of a viscous incompressible fluid with a free surface and changing dynamic boundary angles is proposed. The mathematical description of the process is based on the equations of motion, continuity and natural boundary conditions on the free surface. The traditional feature of the mathematical model on the three-phase contact lines (LTPC) is eliminated by the slip condition. The boundary angle on the LTPC is included in the variational formulation of the problem by replacing the curvature of the free boundary by the Laplace - Beltrami operator and using integration in parts. To describe the dynamic conditions on the LTPC, linking the speed of the LTPC and the dynamic edge angles on the solid walls of the cylinders, the empirical Jiang ratio is used. The numerical solution of the problem is based on the mixed finite element method with approximation of the main variables of the problem (velocity and pressure vector) satisfying the compatibility condition (LBB - condition)...