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Journal of Porous Media
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ISSN Druckformat: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.2019024801
pages 1371-1382

NUMERICAL APPLICATION OF INCOMPLETE ELLIPTIC INTEGRALS TO INVESTIGATE THE CAPILLARY PHENOMENA IN A PENDULAR STATE BETWEEN TWO IDENTICAL SPHERES IN CONTACT

Hyuk Jin Lee
Department of Civil Engineering, Techsquare Co., Ltd., 3rd Fl., Automobile Hall, Banpo-daero, Seoch-gu, Seoul, Republic of Korea
John S. Tyner
Department of Biosystems Engineering and Soil Science, University of Tennessee, 2506 E. J. Chapman Drive, Knoxville, TN, USA
Jaehoon Lee
Department of Biosystems Engineering and Soil Science, University of Tennessee, 2506 E. J. Chapman Drive, Knoxville, TN, USA

ABSTRAKT

This study provides a new mathematical description of pendular rings that allows for continuous solutions of the geometric and physical properties (i.e., volume, meridional curvature, azimuthal curvature, pressure difference, and total capillary force) that were previously not fully understood due to difficulty in obtaining the mathematical solutions. This new solution has also allowed for calculation of volume limit for a pendular ring, beyond which the dimensionless mean curvature obtained by iterative calculation does not converge. The new continuous solutions were validated by comparison to previously published results of an analytical solution for a succinct number of tabular input values. The resulting fits are excellent with root-mean square error of 0.00021.

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