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

      research-article
      Author(s): † , ‡ ,
      Publication date (Electronic):
      Journal: ACS Omega
      Publisher: American Chemical Society

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          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.

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          The Surface Evolver

          Kenneth Brakke (1992)
          Article 0 comments Cited 99 times – based on 0 reviews     Review now
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            Solid–Liquid Work of Adhesion

            Priyanka S. Wasnik, Jie Liu, Hartmann N’guessan … (2017)
            We establish a tool for direct measurements of the work needed to separate a liquid from a solid. This method mimics a pendant drop that is subjected to a gravitational force that is slowly increasing until the solid-liquid contact area starts to shrink spontaneously. The work of separation is then calculated in analogy to Tate's law. The values obtained for the work of separation are independent of drop size and are in agreement with Dupré's theory, showing that they are equal to the work of adhesion.
            Article 0 comments Cited 30 times – based on 0 reviews     Review now
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              Open Problems in Wetting Phenomena: Pinning Retention Forces.

              Rafael Tadmor (2021)
              We review existing explanations for drop pinning and the origin of the force required to initiate the sliding of a drop on a solid surface (depinning). Theories that describe these phenomena include de Gennes', Marmur's, Furmidge's, the related Furmidge-Extrand's, and Tadmor's theory. These theories are all well cited but generally do not address each other, and usually papers that cite one of them ignore the others. Here, we discuss the advantages and disadvantages of these theories and their applicability to different experimental systems. Thus, we link different experimental systems to the theories that describe them best. We describe the force laws that can be deduced should these theories be united and the major open problems that remain. We describe a physical meaning that can be extracted from retention force measurements, specifically, the interfacial modulus that describes the tendency of a solid to conform to the liquid. This has implications for various wetting phenomena such as adhesion robustness, drug penetration into biological tissues, and solid robustness/resilience versus solid degradation over time as a result of its contact with a liquid.
              Article 0 comments Cited 25 times – based on 0 reviews     Review now
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                Author and article information

                Journal
                Journal ID (nlm-ta): ACS Omega
                Journal ID (iso-abbrev): ACS Omega
                Journal ID (publisher-id): ao
                Journal ID (coden): acsodf
                Title: ACS Omega
                Publisher: American Chemical Society
                ISSN (Electronic): 2470-1343
                Publication date (Electronic): 07 October 2022
                Publication date Collection: 18 October 2022
                Volume: 7
                Issue: 41
                Pages: 36510-36518
                Affiliations
                [† ]Horace Mann School , 231 West 246th Street, Bronx, New York10471, United States
                [‡ ]Department of Chemical and Biological Engineering, University of Ottawa , 161 Louis Pasteur, Ottawa, OntarioK1N 6N5, Canada
                Author notes
                Author information
                https://orcid.org/0000-0002-1461-7904
                Article
                DOI: 10.1021/acsomega.2c04359
                PMC ID: 9583325
                PubMed ID: 36278068
                SO-VID: 28c6c780-c795-4f02-b816-edbdc2cea0b8
                Copyright © © 2022 The Authors. Published by American Chemical Society
                License:

                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/).

                History
                Date received : 10 July 2022
                Date accepted : 22 September 2022
                Categories
                Subject: Article
                Custom metadata
                document-id-old-9 ao2c04359
                document-id-new-14 ao2c04359
                ccc-price

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