Allaire – Briane Homogenization Method for Studying Aerodynamics Around a Plant Leaf with Trichomes
Abstract
A new mathematical model describing airflow near a plant leaf surface with trichomes is elaborated. The leaf is modeled as an elastic plate with closely placed and rigidly attached elastic cylinders. The cylinders have small diameters and finite hights. They model trichomes, i.e., fibers on the leaf surface. We suppose that there are two distinct types of trichomes on the leaf surface: closely placed thin and short ones and sparse thick and long ones. Flow of a viscous compressible fluid (air) around the leaf is considered. It is strongly desirable to derive a homogenized model that would allow us to find velocities distribution of air particles on the macroscopic scale, i.e., on the whole leaf without consideration of distinct trichomes. In the paper, such model is elaborated by systematic use of the Allaire Briane homogenization method. It appears to be a three-scale three-velocity homogenized model describing velocity distributions on macro-, meso-, and microscopic scales.
DOI 10.14258/izvasu(2016)1-31
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References
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