

Preprint 78/2011
Capillary Forces on Partially Immersed Plates
Robert Finn
Contact the author: Please use for correspondence this email.
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.