NUMERICAL SOLUTION OF THE PROBLEM ON STABILITY OF A LIQUID BRIDGE BETWEEN TWO COAXIAL CYLINDERS

Abstract

The problem on equilibrium shapes and stability of axially symmetric liquid bridge between the end faces of two coaxial vertical cylinders of equal radius in gravitational field is considered. A scheme of spline type for numerical solving of the problem is developed. Construction of the scheme is based on an approximation of the free surface by parametric cubic splines which exactly satisfy equations of the differential problem at grid nodes. Equilibrium free-surface shapes in a wide range of problem parameters are obtained. Critical values of the bridge height corresponding to the loss of equilibrium stability depending on the Bond number are determined.