Capillary Forces on Partially Immersed Plates

Robert Finn

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Submission date: 01. Dec. 2011
published in: Differential and difference equations with applications : contributions from the international conference on differential & difference equations and applications ; [conference in honor of Professor Ravi P. Agarwal ; Ponta Delgada, Portugal ; July 4 - 8, 2011] / S. Pinelas (ed.)
Berlin : Springer, 2013. - P. 13 - 25
(Springer proceedings in mathematics ; 47) 
DOI number (of the published article): 10.1007/978-1-4614-7333-6_2
Bibtex

Abstract:
This is a partly historical outline of material related to the general question of mutual attraction and repulsion of bodies floating on an unbounded fluid surface in the presence of a gravity field and subject to surface tension interactions with the free surface interface. Discussion centers on a simplified model originally introduced by Laplace, and later re-introduced in more detailed studies, initially by the author and then by the author with Devin Lu, concerning the horizontal forces that can arise when two parallel plates of perhaps differing materials are dipped vertically into an unbounded fluid bath, in the presence of a gravity field. Despite the conceptual simplifications intrinsic to the model, a remarkable variety of behavior can occur, encompassing a singular perturbation that leads to strikingly discontinuous limiting behavior as the plates approach each other.