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Behavior of liquid menisci formed during the extraction of a vertical rod from the free surface of a liquid contained in a finite basin (Part 1)
Author(s) -
Su J.,
Nigro N. J.
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2214
Subject(s) - curvature , radius , geometry , surface (topology) , structural basin , finite element method , extraction (chemistry) , parametric statistics , free surface , mechanics , radius of curvature , mathematics , geology , materials science , physics , chemistry , thermodynamics , mean curvature , chromatography , computer science , geomorphology , computer security , statistics , mean curvature flow
Many studies involving the shapes and stability of liquid menisci formed during the extraction of a vertical rod from a liquid basin (rod‐in‐free‐surface problem) have been reported in the literature. However, the vast majority of these were conducted under the assumptions that the radius of the basin ( R ) is infinite and that, at its extremity, both the slope and curvature of the liquid surface are zero. Recently, a few studies involving finite basins have been reported; however, these were conducted under the assumption that the displaced volume of the liquid in the basin is prescribed. In this study, a parametric finite element method was employed to determine the behavior (shape and stability) of liquid menisci formed during the extraction of a vertical rod with circular cross‐section from a liquid contained in a circular basin with finite radius. The plots presented in this paper enable investigators to predict the critical extraction height ( a priori ) as a function of the radius ratio ( R / r ) and Bond number (β 0 =ρ gr 2 /γ) for the case where the contact angle (θ 2 ) at the outer extremity of the basin is 90 ∘ . Theoretical and experimental results obtained for arbitrary values of θ 2 will be presented in a Part 2 paper. Copyright © 2010 John Wiley & Sons, Ltd.