Modeling of evaporation of a pure liquid within a capillary tube of circular cross section is a classic problem which has been the subject of many studies. Here we consider the case of tubes of polygonal cross section. This case leads to much greater evaporation rates owing to the liquid flow along the tube edges induced by the capillary forces. We concentrate on slow evaporation situations for which evaporation is controlled by mass transfer. Various evaporation regimes are distinguished depending on the competition between capillary, gravity and viscous forces. When the capillary forces are dominant, it is shown that the position of the bulk meniscus scales linearly with time (and not as the square root of time as in a capillary tube of circular cross section). The effect of viscous or gravity forces is to thin out the corner liquid fingers as the bulk meniscus recedes into the tube. This contributes to reduce the evaporation rate compared to the capillarity dominated regime. Then the case of faster evaporations inducing significant temperature variations is briefly discussed.

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