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Action of a force near the planar surface between semi-infinite immiscible liquids at very low Reynolds numbers: Addendum

Published online by Cambridge University Press:  17 April 2009

K. Aderogba  and
J.R. Blake
K. Aderogba
Affiliation:
Engineering Analysis Unit, University of Lagos, Lagos, Nigeria
J.R. Blake
Affiliation:
CSIRO, Division of Mathematics and Statistics, Canberra, ACT.
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In the paper by Aderogba and Blake [1], the first order approximation to the shape of the interface between two immiscible liquids, at which surface tension acted, was obtained in the case of a point force directed parallel to the interface. In the case of the normal force no solution was obtained due to the logarithmic singularity associated with problems of this type. However, the problem is not physically well-posed in the case of the normal force. Surface tension is not suitable because it cannot alone balance the induced stress on the interface due to a point force. We need an additional force to balance the action of the point force on the interface. The obvious solution is to include a density difference Δρ* between the two fluids

where and are the densities of the lower and upper fluid respectively.

Type
Addendum
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 2 , October 1978 , pp. 309 - 318
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Aderogba, K. and Blake, J.R., “Action of a force near the planar surface between two semi-infinite immiscible liquids at very low Reynolds numbers”, Bull. Austral. Math. Soc. 18 (1978), 345–356.CrossRefGoogle Scholar