A novel quantitative analysis of the local deformation of the air-water surface by a floating sphere

• Novel algorithm for solving Young-Laplace equation is proposed.
• Novel algorithm for processing and correcting interface images is developed.
• Interface deformation is quantified using the Levenberg–Marquardt algorithm.
• Interface deformation and contact angle are reliably determined.

The Young-Laplace equation (YLE) for the deformation of external menisci governs many amazing interfacial phenomena and processes, from the walking on the surface of water by arthropods to the separation of coal and valuable minerals worth billions of dollars annually. A quantitative analysis of the phenomena suffers from problems of YLE which is a highly nonlinear differential equation with one of the two boundary conditions occurred at infinity. Available numerical solutions cannot be used for the numerical fitting of the meniscus profiles to quantify experimental results. Here we present a novel qualitative analysis involving novel numerical algorithms, which are fast and stable and, therefore, suitable for the numerical fitting to match the theoretical and experimental results to quantify the meniscus deformation. The application of the algorithms is successfully demonstrated using the experimental data for the deformation of the air-water interface around a sphere.

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