The propagation of surface waves in adsorbed superfluid helium film occurs at temperatures considerably lower than Tλ. The thickness of film d is a function of density ρ. When the ratio between density and saturated vapor density ρ₀ drops below some value, the superflow properties are found to vanish. The differential equation of the motion of the superfluid component of the bose system characterized by different models for the superfluid condensate is reviewed. The theory indicates that the onset thickness be proportional to the coherence length in agreement with experimental observations. The model proposed by Sarfatt and Cummings for the motion of the condensate mode is simplified to a set of two nonlinear ordinary differential equations. A computer program based on the method of quasilinearization is developed to solve a system of ordinary differential equations in general. This computer program is then applied to the Sarfatt-Cummings model to solve for the order parameter and chemical potential. The solution was repeated for the several coherence lengths and the results were tabulated and analyzed. The results of measurements of third-sound velocity in adsorbed superfluid helium show that the average superfluid fraction is nonvanishing at the superflow onset thickness and has a value about three eighths of its bulk value . There is a parametric agreement between the Sarfatt-Cummings model and the experimental results similar to the agreement obtained from the Ginzburg-Pitaevski model.
