Three analytical solutions describing the 2D Stokes flow in a peristaltic micro-channels are presented. The paper is concerned with pure hydrodynamics discarding any other physical phenomenon like electrical forces. This allows the derivation of analytical results when the problem is share into three main parts: the effect of the contraction on its vicinity, the squeezing of the fluid near the contraction and the effect of wavy walls that is related to the problem of the wall quality which depends on the elaboration process. The results can be considered as reference touch stones for these flows at Reynolds number smaller than one. They allow some physical discussions on the phenomena.

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