The profile of a dew drop
作者:
Feredoon Behroozi,
Hilliard K. Macomber,
Jack A. Dostal,
Cyrus H. Behroozi,
Brian K. Lambert,
期刊:
American Journal of Physics
(AIP Available online 1996)
卷期:
Volume 64,
issue 9
页码: 1120-1125
ISSN:0002-9505
年代: 1996
DOI:10.1119/1.18332
出版商: American Association of Physics Teachers
关键词: DROPLETS;SHAPE;SURFACE TENSION;VARIATIONAL METHODS;NUMERICAL SOLUTION;POTENTIAL ENERGY;SURFACE ENERGY;01.55;03.40;60.
数据来源: AIP
摘要:
A stationary dew drop assumes a shape that minimizes the sum of its gravitational and surface energies. This shape, however, cannot be described by a mathematical function in closed form because the governing differential equations of the drop do not admit of an analytical solution but must be integrated numerically to yield the drop profile. Hence, this problem provides a good case for using the calculus of variations to obtain the governing differential equations and presents advanced students with an opportunity to gain insight and experience in numerical computations involving a real and interesting physical problem. In this paper we obtain the differential equations governing the shape of the drop in two ways: (i) by considering the balance of forces on the drop in static equilibrium; (ii) by seeking the profile which minimizes the total energy of the drop through the use of the calculus of variations. The resulting differential equations are then integrated numerically to obtain the theoretical profile. Two computational strategies, one for each of the two classes of wetting and nonwetting drops, are discussed. Further, it is shown how one may obtain the values of the surface tension and the contact angle for a liquid drop by matching the computed profile to the experimentally observed shape.
点击下载:
PDF
(529KB)
返 回