## Abstract

We consider a Newtonian fluid owing at low Reynolds numbers along a spatially periodic array of cylinders of diameter proportional to a small nonzero parameter ∈. Then for ∈ 6≠ 0 and close to 0 we denote by K_{II} [∈] the longitudinal permeability. We are interested in studying the asymptotic behavior of K_{II} [∈] as ∈ tends to 0. We analyze K_{II} [∈] 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 K_{II} [∈] can be written as the sum of a logarithmic term and a power series in ∈^{2}. 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).

Original language | English |
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Article number | A290 |

Pages (from-to) | 1-20 |

Number of pages | 20 |

Journal | Electronic Journal of Differential Equations |

Volume | 2015 |

Publication status | Published - 20 Nov 2015 |

## Keywords

- Asymptotic expansion
- Integral equations
- Logarithmic capacity
- Longitudinal permeability
- Rectangular array
- Singularly perturbed domain