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With the developments in nanotechnology, nanofibrous materials attract great attention as possible platforms for fluidic engineering. This requires an understanding of droplet interactions with fibers when gravity plays no significant role. This work aims to classify all possible axisymmetric configurations of droplets on fibers. The contact angle that the drop makes with the fiber surface is allowed to change from 0° to 180°. Nodoidal apple-like droplets with inverted menisci cusped toward the droplet center and unduloidal droplets with menisci cusped away from the droplet center were introduced and fully analyzed. The existing theory describing axisymmetric droplets on fibers is significantly enriched introducing new morphological configurations of droplets. It is experimentally shown that the barreled droplets could be formed on non-wettable fibers offering contact angles greater than 90°. The theory was quantitatively confirmed with hemispherical droplets formed at the end of a capillary tube and satisfying all the boundary conditions of the model. It is expected that the developed theory could be used for the design of nanofiber-based fluidic devices and for drop-on-demand technologies. 

Chaplygin’s hodograph method of classical fluid mechanics is applied to explicitly solve the Plateau problem of finding minimal surfaces. The minimal surfaces are formed between two mirror-symmetric polygonal frames having a common axis of symmetry. Two classes of minimal surfaces are found: the class of regular surfaces continuously connecting the supporting frames forming a tube with complex shape; and the class of singular surfaces which have a partitioning film closing the tube in between. As an illustration of the general solution, minimal surfaces supported by triangular frames are fully described. The theory is experimentally validated using soap films. The general solution is compared with the known particular solutions obtained by the Weierstrass inverse method.