Image-analyzing interferometry technique is successfully used to study microscale transport processes related to a curved microfilm on a solid substrate. Digital image processing is used to analyze the images of interference fringes, leading to the evaluation of liquid (heptane) film thickness and curvature profiles at different inclinations on a high refractive index glass surface. The curvature profiles obtained at different inclinations clearly demonstrate that there is a maximum in curvature near the junction of the adsorbed film (of uniform thickness) and the curved film, and then it becomes constant in the thicker portions of the film. The adsorbed film thickness is measured for horizontal as well as inclined positions. Experimentally obtained values of the dispersion constants are compared to those predicted from the Dzyaloshinskii-Lifshitz-Pitaevskii (DLP) theory, and reasonable agreements were obtained. A parameter alpha is defined and experimentally evaluated to quantify the closeness of the system to equilibrium. The nonequilibrium behavior of this parameter alpha is also observed with certain heat input at a particular inclination. A small thermal perturbation is used to force the liquid meniscus to undergo a cycle of alternating condensation and evaporation. High-speed video-microscopy and subsequent image analysis are used for data analysis. The numerical solution of a model that takes into account the balance between the suction and the capillary force is compared with the data to elicit new insights into the evaporation/condensation phenomena and to estimate the interfacial temperature differences for near-equilibrium situations.