Analytical approximate capillary surfaces
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 curve...
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| Date: | 2020 |
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| Main Authors: | , , , , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2020
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| Online Access: | https://trim.imath.kiev.ua/index.php/trim/article/view/432 |
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| Journal Title: | Transactions of Institute of Mathematics of NAS of Ukraine |
| Download file: |  |
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Transactions of Institute of Mathematics of NAS of Ukraine| Summary: | 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.
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