Evaluation of axisymmetric equilibrium capillary surface with pseudo Newton-Raphson method

Determination of an axisymmetric equilibrium capillary surface of a liquid con-tained in a vessel is, in brief, selecting a surface, from a parametric family of surfaces which satisfies a set of prescribed physical constraints. The parametric family of surfaces arises from an unknown parameter in the governing equations. Slobozhanin and Tyuptsov [5] proposed the graphic technique to determine the equilibrium free surface. The graphic technique requires plotting a dense family of curves and relies a great deal on visual estimation of the satisfaction of the physical constraints which makes the process time consuming and the solution imprecise. The work described in this thesis follows the graphic technique’s methodology and implements a pseudo Newton-Raphson method to quickly and accurately determine the equilibrium free surface. A computer program was developed to determine an equilibrium free surface and generate a series of free surfaces under a varying parameter to simulate the effect of the parameter on the surface shape.