Under microgravity conditions, the dynamics of a thin condensate film on a curved surface is determined by the capillary pressure gradient proportional to the mean surface curvature gradient. A one-parameter family of axisymmetric surfaces is found for which the gradient of mean curvature is constant. The dimensionless equation for rotation angle of the generatrix curve is found. There is a single generatrix curve for an axisymmetric surface for which the rotation angle at the inflexion point assumes a predetermined value. Due to the constant gradient of capillary pressure on such a surface, a stable condensate flow is ensured under microgravity conditions. A similar curve for the planar case, known as the clothoid or "Cornu spiral", is used to find the best transition curve to get the smoothest traffic on the roads. A numerical model for film-wise vapor condensation on such surface has been built. The film thickness distribution and mass flow rate of the HFE-7100 along the cooled curvilinear fin have been calculated. Calculations were done both for terrestrial gravity and microgravity. This work proposes a particular surface shape, found numerically, for conducting experiments on the pure vapor condensation under microgravity conditions in Parabolic Flight Campaigns and onboard the International Space Station.

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