  Drop condensation and evaportation as a result of the gradient in vapor
concentration are important in both engineering and natural systems. One of the
interesting natural examples is transpiration on plant leaves. Most of water in
the inner space of the leaves escapes through stomata, whose rate depends on
the surface topography and a difference in vapor concentrations inside and just
outside of the leaves. Previous research on the vapor flux on various surfaces
has focused on numerically solving the vapor diffusion equation or using
scaling arguments based on a simple solution with a flat surface. In this
present work, we present and discuss simple analytical solutions on various 2D
surface shapes (e.g., semicylinder, semi-ellipse, hair). The method of solving
the diffusion equation is to use the complex potential theory, which provides
analytical solutions for vapor concentration and flux. We find that a high mass
flux of vapor is formed near the top of the microstructures while a low mass
flux is developed near the stomata at the leaf surface. Such a low vapor flux
near the stomata may affect transpiration in two ways. First, condensed
droplets on the stomata will not grow due to a low mass flux of vapor, which
will not inhibit the gas exchange through the stomatal opening. Second, the low
mass flux from the atmosphere will facilitate the release of high concentrated
vapor from the substomatal space.
