Calculation of the Meniscus Shape Formed under Gravitational Force by Solving the Young-Laplace Differential Equation Using the Bézier Curve Method

Abstract

This work presents a method to calculate the meniscus shape by solving the differential equation based on the Young-Laplace equation. More specifically, the differential equation is solved by applying the cubic Bézier curve. A complicated nonlinear differential equation is solved using the Bézier control points and the least-squares method while maintaining computational simplicity. The results show all of the expected features of the meniscus under the gravitational force. A brief discussion is also made on the effect of the errors on the results. The method is further validated by its agreement with the numerical solutions reported in the existing literature.