Steady flow and evaporation of a volatile liquid in a wedge

We develop a lubrication-type model of a liquid flow in a wedge in the limit of small capillary numbers and negligible gravity. Liquid flows under the action of capillary pressure gradients and thermocapillary stresses, and evaporates due to heating from the solid walls on which a constant axial temperature gradient is imposed. Steady vapor-liquid interface shapes are found for different wedge angles and material properties of the liquid. In the limit of weak evaporation (e.g., in the adiabatic region of a heat pipe) and negligible Marangoni number, the flow rate 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 finite 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 conditions. Somewhat counterintuitively, we find that the dry-out point shifts toward the region of higher temperature as evaporation intensity is increased. The effect of thermocapillary stresses on the vapor-liquid interface shape is also investigated in the limit of negligible evaporation. Since thermocapillarity generally opposes the capillary flow, it leads to shorter wetted lengths. The implications of the results for design and optimization of micro heat pipes are discussed. (c) 2006 American Institute of Physics.