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首页> 外文期刊>Physics of fluids >Understanding flow features in drying droplets via Euler characteristic surfaces-A topological tool
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Understanding flow features in drying droplets via Euler characteristic surfaces-A topological tool

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摘要

In this paper, we propose a mathematical picture of flow in a drying multiphase droplet. The system studied consists of a suspension of microscopic polystyrene beads in water. The time development of the drying process is described by defining the "Euler characteristic surface," which provides a multiscale topological map of this dynamical system. A novel method is adopted to analyze the images extracted from experimental video sequences. Experimental image data are converted to binary data through appropriate Gaussian filters and optimal thresholding and analyzed using the Euler characteristic determined on a hexagonal lattice. In order to do a multiscale analysis of the extracted image, we introduce the concept of Euler characteristic at a specific scale r > 0. This multiscale time evolution of the connectivity information on aggregates of polysterene beads in water is summarized in a Euler characteristic surface and, subsequently, in a Euler characteristic level curve plot. We introduce a metric between Euler characteristic surfaces as a possible similarity measure between two flow situations. The constructions proposed by us are used to interpret flow patterns (and their stability) generated on the upper surface of the drying droplet interface. The philosophy behind the topological tools developed in this work is to produce low-dimensional signatures of dynamical systems, which may be used to efficiently summarize and distinguish topological information in various types of flow situations.

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