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Withdrawal from a fluid of finite depth through a line sink, including surface-tension effects


Hocking, GC and Forbes, LK, Withdrawal from a fluid of finite depth through a line sink, including surface-tension effects, Journal of Engineering Mathematics, 38, (1) pp. 91-100. ISSN 0022-0833 (2000) [Refereed Article]

DOI: doi:10.1023/A:1004612117673


The steady withdrawal of an inviscid fluid of finite depth into a line sink is considered for the case in which surface tension is acting on the free surface. The problem is solved numerically by use of a boundary-integral-equation method. It is shown that the flow depends on the Froude number, F B = m(gH B 3 ) -1/2 , and the nondimensional sink depth λ = H S /H B , where m is the sink strength, g the acceleration of gravity, H B is the total depth upstream, H S is the height of the sink, and on the surface tension, T. Solutions are obtained in which the free surface has a stagnation point above the sink, and it is found that these exist for almost all Froude numbers less than unity. A train of steady waves is found on the free surface for very small values of the surface tension, while for larger values of surface tension the waves disappear, leaving a waveless free surface. It the sink is a long way off the bottom, the solutions break down at a Froude number which appears to be bounded by a region containing solutions with a cusp in the surface. For certain values of the parameters, two solutions can be obtained.

Item Details

Item Type:Refereed Article
Research Division:Engineering
Research Group:Fluid mechanics and thermal engineering
Research Field:Microfluidics and nanofluidics
Objective Division:Environmental Management
Objective Group:Other environmental management
Objective Field:Other environmental management not elsewhere classified
UTAS Author:Forbes, LK (Professor Larry Forbes)
ID Code:18425
Year Published:2000
Web of Science® Times Cited:7
Deposited By:Mathematics
Deposited On:2000-08-01
Last Modified:2022-07-08

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