Three-dimensional Finite Element Model of Three-phase Contact Line Dynamics and Dynamic Contact Angle

Abstract

An unconventional model of three-phase contact liny dynamics is suggested for the numerical solution of the boundary value problem of dipping and spreading. The numerical modeling is conducted with the use of the finite-element method in Lagrange variables. The mathematical model of the process is described by the equation of motion, continuity, and natural boundary conditions on the free surface. To exclude the ity of viscous stresses in the mathematical model on three-phase contact lines (TPCL) there was suggested a gridded model of gliding that takes into consideration peculiarities of dissipative processes in the neighborhood of TPCL at the microlevel. To reduce oscillations of pressure in the neighborhood of TPCL, a finite element is used. The suggested method allows for natural monitoring of free surface and TPCL with an unconventional model for dynamic contact micro-angle. A stable convergent algorithm is suggested that is not dependent on the grid step size and that is tested through the example of a three-dimensional semispherical drop and a drop in the form of a cube. The investigations obtained are compared to well-known experimental and analytical results demonstrating a high efficiency of the suggested model of TPCL dynamics at small values of capillary number.