Steady vapor bubbles in rectangular microchannels

We consider vapor bubbles in microchannels in which the vapor is produced by a heater element and condenses in cooler parts of the interface. The free boundary problem is formulated for a long steady-state bubble in a rectangular channel with a heated bottom. Lubrication-type equations are derived for the shape of the liquid-vapor interface in a cross-sectional plane and in the regime for which the vapor phase fills most of the cross section. These equations are then solved numerically over a range of parameter values with given temperature profiles in the walls and subject to a global integral condition requiring evaporation near the heater to balance condensation in colder areas of the interface. Our results show that depending on the temperature, the side walls can be either dry or covered with a liquid film and we identify criteria for these two different regimes. The asymptotic method breaks down in the limit when capillary condensation becomes important near the bubble top and a different approach is used to determine the shape of the bubble in this limit. Solutions here involve localized regions of lar mass fluxes, which are asymptotically matched to capillary-statics regions where the heat transfer is negligible. (C) 2001 Academic Press.