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

[Image: see text] 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 u...

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Autores principales: Lewis, Kira, Matsuura, Takeshi
Formato: Online Artículo Texto
Lenguaje:English
Publicado: American Chemical Society 2022
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9583325/
https://www.ncbi.nlm.nih.gov/pubmed/36278068
http://dx.doi.org/10.1021/acsomega.2c04359
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author Lewis, Kira
Matsuura, Takeshi
author_facet Lewis, Kira
Matsuura, Takeshi
author_sort Lewis, Kira
collection PubMed
description [Image: see text] 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.
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spelling pubmed-95833252022-10-21 Calculation of the Meniscus Shape Formed under Gravitational Force by Solving the Young–Laplace Differential Equation Using the Bézier Curve Method Lewis, Kira Matsuura, Takeshi ACS Omega [Image: see text] 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. American Chemical Society 2022-10-07 /pmc/articles/PMC9583325/ /pubmed/36278068 http://dx.doi.org/10.1021/acsomega.2c04359 Text en © 2022 The Authors. Published by American Chemical Society https://creativecommons.org/licenses/by-nc-nd/4.0/Permits non-commercial access and re-use, provided that author attribution and integrity are maintained; but does not permit creation of adaptations or other derivative works (https://creativecommons.org/licenses/by-nc-nd/4.0/).
spellingShingle Lewis, Kira
Matsuura, Takeshi
Calculation of the Meniscus Shape Formed under Gravitational Force by Solving the Young–Laplace Differential Equation Using the Bézier Curve Method
title Calculation of the Meniscus Shape Formed under Gravitational Force by Solving the Young–Laplace Differential Equation Using the Bézier Curve Method
title_full Calculation of the Meniscus Shape Formed under Gravitational Force by Solving the Young–Laplace Differential Equation Using the Bézier Curve Method
title_fullStr Calculation of the Meniscus Shape Formed under Gravitational Force by Solving the Young–Laplace Differential Equation Using the Bézier Curve Method
title_full_unstemmed Calculation of the Meniscus Shape Formed under Gravitational Force by Solving the Young–Laplace Differential Equation Using the Bézier Curve Method
title_short Calculation of the Meniscus Shape Formed under Gravitational Force by Solving the Young–Laplace Differential Equation Using the Bézier Curve Method
title_sort calculation of the meniscus shape formed under gravitational force by solving the young–laplace differential equation using the bézier curve method
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9583325/
https://www.ncbi.nlm.nih.gov/pubmed/36278068
http://dx.doi.org/10.1021/acsomega.2c04359
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