Semi-Analytical Modelling of Evaporating Power-Law Thin Films in Inclined Micro-Channels

The evaporation of a thin liquid film representative of power-law rheology flowing along an inclined channel wall under the combined influence of gravity and surface tension is investigated using a semi-analytical modelling framework. The evolution of film thickness, heat transfer characteristics, and dry-out behaviour are examined as functions of the power-law exponent, Weber number, and inlet film thickness. The results show that a decrease in the power-law exponent leads to a slower reduction in film thickness, resulting in a significant increase in the dry-out length for a fixed value of consistency. This behaviour is attributed to the large effective viscosity developing near the free surface for shear-thinning fluids, in contrast to the negligible surface viscosity observed for shear-thickening fluids. The local Nusselt number increases gradually along the flow direction, followed by a sharp terminal rise marking the onset of dry-out. The mean Nusselt number decreases with increasing power-law exponent, which is consistent with the dry-out length variation with the power-law exponent. The dry-out length is found to be largely insensitive to surface tension for a fixed normalised inlet film thickness, while exhibiting an approximately linear dependence on the inlet film thickness that is nearly independent of the power-law index. Overall, the study establishes a hierarchy of controlling parameters for evaporating power-law films in inclined micro-channels, demonstrating that inlet film thickness primarily governs the dry-out location, while rheology and surface tension exert secondary influences within the parameter ranges considered.