3D spherical-cap fitting procedure for (truncated) sessile nano- and micro-droplets & -bubbles

In the study of nanobubbles, nanodroplets or nanolenses immobilised on a substrate, a cross-section of a spherical-cap is widely applied to extract geometrical information from atomic force microscopy (AFM) topographic images. In this paper, we have developed a comprehensive 3D spherical cap fitting procedure (3D-SCFP) to extract morphologic characteristics of complete or truncated spherical caps from AFM images. Our procedure integrates several advanced digital image analysis techniques to construct a 3D spherical cap model, from which the geometrical parameters of the nanostructures are extracted automatically by a simple algorithm. The procedure takes into account all valid data points in the construction of the 3D spherical cap model to achieve high fidelity in morphology analysis. We compare our 3D fitting procedure with the commonly used 2D cross-sectional profile fitting method to determine the contact angle of a complete spherical cap and a truncated spherical cap. The results from 3D-SCFP are consistent and accurate, while 2D fitting is unavoidably arbitrary in selection of the cross-section and has a much lower number of data points on which the fitting can be based, which in addition is biased to the top of the spherical cap. We expect that the developed 3D spherical-cap fitting procedure will find many applications in imaging analysis.Comment: 23 pages, 7 figure

Evaporation-triggered microdroplet nucleation and the four life phases of an evaporating Ouzo drop

Evaporating liquid droplets are omnipresent in nature and technology, such as in inkjet printing, coating, deposition of materials, medical diagnostics, agriculture, food industry, cosmetics, or spills of liquids. While the evaporation of pure liquids, liquids with dispersed particles, or even liquid mixtures has intensively been studied over the last two decades, the evaporation of ternary mixtures of liquids with different volatilities and mutual solubilities has not yet been explored. Here we show that the evaporation of such ternary mixtures can trigger a phase transition and the nucleation of microdroplets of one of the components of the mixture. As model system we pick a sessile Ouzo droplet (as known from daily life - a transparent mixture of water, ethanol, and anise oil) and reveal and theoretically explain its four life phases: In phase I, the spherical cap-shaped droplet remains transparent, while the more volatile ethanol is evaporating, preferentially at the rim of the drop due to the singularity there. This leads to a local ethanol concentration reduction and correspondingly to oil droplet nucleation there. This is the beginning of phase II, in which oil microdroplets quickly nucleate in the whole drop, leading to its milky color which typifies the so-called 'Ouzo-effect'. Once all ethanol has evaporated, the drop, which now has a characteristic non-spherical-cap shape, has become clear again, with a water drop sitting on an oil-ring (phase III), finalizing the phase inversion. Finally, in phase IV, also all water has evaporated, leaving behind a tiny spherical cap-shaped oil drop.Comment: 40 pages, 12 figure

Reply to [arXiv:1105.5147] "Are GRB 090423 and Similar Bursts due to Superconducting Cosmic Strings?"

The GRB outflow driven by superconducting cosmic strings is likely to be an arc rather than a usually-considered spherical cap. In such a case, the afterglows of the cosmic string GRBs could be basically consistent with the observation of the high-redshift GRBs.Comment: 2 pages, 1 figure, to appear in Phys. Rev. Let