We develop a lubrication type model of a liquid flow in a wedge in the limit of small capillary numbers and negligible gravity. The model incorporates the effects of capillary pressure gradients and evaporation. Steady vapor-liquid interface shapes are found for a range of parameters. In the limit of weak evaporation the flow is the same in all cross-sections and can be controlled by changing the wedge angle. We find the wedge angle that results in the maximum value of the flow rate for a given contact angle. For high evaporation rates, both the flow rate and the amount of liquid in each cross-section along the wedge decrease until the point of dry-out is reached. The location of the dry-out point is studied as a function of evaporation. Practical suggestions about optimization of micro heat pipes are given.

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