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

Kira Lewis; Takeshi Matsuura

doi:10.1021/acsomega.2c04359

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

ACS Omega. 2022 Oct 7;7(41):36510-36518. doi: 10.1021/acsomega.2c04359. eCollection 2022 Oct 18.

Authors

Kira Lewis¹, Takeshi Matsuura²

Affiliations

¹ Horace Mann School, 231 West 246th Street, Bronx, New York10471, United States.
² Department of Chemical and Biological Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, OntarioK1N 6N5, Canada.

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.