Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 290, pp. 120.
Asymptotic behavior of the longitudinal permeability of a periodic
array of thin cylinders
Paolo Musolino, Vladimir Mityushev
Abstract:
We consider a Newtonian fluid flowing at low Reynolds numbers
along a spatially periodic array of cylinders of diameter proportional
to a small nonzero parameter
.
Then for
and close to 0 we denote by
the longitudinal permeability.
We are interested in studying the asymptotic behavior of
as
tends to 0. We analyze
for
close to 0 by an approach based on functional analysis and potential theory,
which is alternative to that of asymptotic analysis. We prove that
can be written as the sum of a logarithmic term and a
power series in
.
Then, for small
,
we provide an
asymptotic expansion of the longitudinal permeability in terms of the sum
of a logarithmic function of the square of the capacity of the cross section
of the cylinders and a term which does not depend of the shape of the unit
inclusion (plus a small remainder).
Submitted June 17, 2015. Published November 20, 2015.
Math Subject Classifications: 76D30, 76D05, 35J05, 35J25, 31B10, 45A05.
Key Words: Longitudinal permeability; asymptotic expansion; rectangular array;
singularly perturbed domain; integral equations; logarithmic capacity.
Show me the PDF file (315 KB),
TEX file, and other files for this article.

Paolo Musolino
Department of Mathematics
University of Padova, Italy
email: musolinopaolo@gmail.com


Vladimir Mityushev
Department of Computer Science and Computational Methods
Pedagogical University of Cracow, Poland
email: mityu@up.krakow.pl

Return to the EJDE web page