Frontiers in Physics (Sep 2019)
Mathematical Model for Simulating the Movement of Water Droplet on Artificial Leaf Surface
Abstract
To understand the mechanism of how a droplet of pesticide, nutrient or water is imbibed via the leaf surface, a simple model-based mathematics for simulating a realistic water droplet motion over the artificial leaf surface is introduced. The preliminary object of this model is to reconstruct the leaf surface, so an interpolation finite element method so-called hybrid Clough–Tocher (CT) radial basis function (RBF) with a cubic polynomial (CT-MRBFC) has recently been proposed by the authors [1] for this purpose. The surface consists of a triangular element over which the method of CT-MRBFC is applied. In the presented droplet motion model, the forces that influence the motion are supposed to be the internal force due to the drag force and external force caused by gravity. As outcomes of the proposed model, the droplet model captures realism fairly well and generates a genuine motion over the surface. More significantly, the droplet movements pursue the surface contours and falls from the leaf mesh depending on the model parameters. Furthermore, the droplet height is computed over every triangle and the droplet vanishes or stops moving if a set tolerance is greater than the droplet height.
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