Marangoni-based geometrical low-pass-filter

Smooth surfaces are central in a variety of applications, including optics, friction reduction, and anti-fouling surfaces. Current methods for fabrication of smooth surfaces rely almost entirely on mechanical polishing processes, and alternative methods for creating smooth surfaces are highly desirable. Liquid interfaces are a natural candidate, owing to their natural smoothness. We consider a thin liquid film suspended on top of a rigid surface of arbitrary topography and present a novel approach that utilizes the Marangoni effect and capillary forces to replicate the baseline surface. When radiating the liquid with a constant heat flux, Marangoni forces act to shape the interface to match that of the underlying surface, while capillary forces act to smooth high spatial frequencies. In this way, a rough surface created, for example, by 3D printing could be transformed into a smooth surface while preserving the desired shape. We derive and scale the governing evolution equation of the thin film along with the energy equation under constant and uniform heat flux. Analyzing these equations, we identify a non-dimensional parameter that controls the threshold frequency of spatial waves, similar to a low pass filter. This result allows to define conditions for replication and smoothing of the base line substrate using a thin film. We demonstrate and verify this result by multiple experiments.