Analysis of a Moving Meniscus in Narrow Gap between Parallel Plates by Boundary Element Method.

Abstract

When we fill the narrow gap between two parallel plates with a viscous fluid, the meniscus of the free surface forms a concave shape due to capillary action. Air enters the gap with the movement of the viscous fluid when the gap between the two plates is increased at a certain speed. In this paper, the appearance of a moving meniscus is simulated by the boundary element method for two situations : two-dimensional flow and axisymmetric flow. First, the solutions obtained as fundamental solutions satisfying the Stokes approximation equation were quantitatively compared with experimental results with respect to the tip of the moving meniscus. Second, a new fundamental solution for the axisymmetric boundary element method was used for the direct evaluation of a singular integral. Numerical results showed a good agreement with experimental ones.