Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stokes force on a cylinder in the presence of fluid confinement   In this note, we present Stokes' calculation of the force exerted by the
fluid on an oscillating cylinder. While the calculation of the similar problem
in the case of the sphere is treated in several textbooks, the case of the
cylinder is absent from these textbooks. Because modified Bessel functions were
not defined in 1851 when Stokes made this calculation, Stokes was not able to
express his results in closed forms but he gave asymptotic formulas valid in
the two limits $a\ll \delta$ and $a \gg \delta$, where $a$ is the cylinder
radius and $\delta$ is the viscous penetration depth. The closed form results
were given by Stuart in 1963. We recall this calculation and we compare Stokes'
asymptotic formulas to these exact results. Using modified Bessel functions, it
is possible to calculate the force when the fluid is confined by an external
cylinder of radius $b$ sharing the same axis: we review previous publications
which have treated this problem and we present an exact calculation of this
force which is also developed in powers of $\delta/a$, with the expansion
coefficients being functions of the ratio $\gamma= a/b$ of the cylinder radii.

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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: math
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph