Analytical approximate capillary surfaces

• Datum: 2020
• Автори та афіліації: E.M. Tkachenko — Institute of Mathematics; A.N. Timokha — Institute of Mathematics
• Ключові слова: keywords
• Hauptverfasser: Tkachenko, E.M., Timokha, A.N., Ткаченко, Е.Н., Тимоха, А.Н., Ткаченко, Є.М., Тимоха, О.М.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2020
• Online Zugang: https://trim.imath.kiev.ua/index.php/trim/article/view/432
• Назва журналу: Transactions of Institute of Mathematics of NAS of Ukraine

Analytical approaches to capillary (meniscus) problem in infinite horizon- tal channel and axisymmetric container are developed. For these cases, finding the menisci reduces to free-boundary problems for specific systems of ordinary differential equations. Their solutions describe capillary curves, resulted from intersection of menisci and (depending on the container type) either cross-section or meridional plane. Further studies on capillary waves require to know analytical approximations in the Cn, n 3 metrics. An objective consists of constructing analytical approximate solutions. The paper focuses on limits of applicability of Taylor-polynomial and Pad ́e approximations, which were proposed for this class of capillary problems in 1984 by Barnyak & Timokha.