Limitations of Matching Condensing Film Profile on a Micro Fin with the Groove: Critical Effect of Disjoining Pressure

ABSTRACT Condensation on a fin top terminating with a groove involves several simultaneous phenomena including vapor–liquid boundaries whose shapes are unknown a priori, fluid flow due to capillary and disjoining pressure gradients, and condensation over thin films. This problem occurs in grooved heat pipes, where the condensation is predominantly present on fin tops due to the thinner liquid film – having a lower thermal resistance compared to inside the groove where the fluid is substantially thicker. Majority of the studies in the literature assume an approximate profile for the liquid film surface and apply an integral balance for conservation laws, accounting for the effect of the capillary pressure only. In addition, this approximate profile is matched with the liquid profile inside the groove, which serves as a boundary condition. Although intuitive, validity of the matching is not straightforward, and its limitations have never been discussed in the literature, despite the presence of experimental findings to the contrary. In the current study, the effect of disjoining pressure and matching conditions with the groove is investigated using a comprehensive model. The results suggest that for small temperature differences and small slopes, the effect of disjoining pressure is non-negligible, and beyond limiting values of edge angles, the effect of disjoining pressure precludes solutions where the fin top film matches the groove in a smooth transition.