Analytical approximate capillary surfaces
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Original versionProceedings of the Institute of Mathematics of NAS of Ukraine. 2018, 15 (1), .
Analytical approaches to hydrostatic capillary (meniscus) problem in infinite horizontal channel and axisymmetric container are developed. For these geometric cases, finding the capillary menisci reduces to freeboundary problems for special systems of ordinary differential equations. Their solutions describe capillary curves, which appear as intersections of the capillary menisci and (depending on the container type) either crosssection or meridional plane. Further studies on capillary waves require to know analytical approximations of these capillary curves in the C n , n ≥ 3 metrics. An objective may consists of constructing analytical approximate solutions of the corresponding systems of ordinary differential equations. The present paper focuses on limits of applicability of the Taylorpolynomial and Pad´e approximations, which were proposed for this class of capillary problems in 1984 by Barnyak & Timokha.