Pattern formation in plants via instability theory of hydrogels

Abstract

In this paper, we demonstrate how deformation patterns of leaves and fruits in growing and drying processes can be described via the inhomogeneous field theory. The distorted deformation of ribbed leaves and the ridge formation on fruit surfaces can be understood as the energy-minimizing mechanical buckling patterns. The swelling and de-swelling induced instabilities of various membrane structures or elastic sheets on elastic or gel-like substrates are simulated using the inhomogeneous field theory of a polymeric network in equilibrium with solvent and mechanical constraints. The article describes briefly the inhomogeneous field theory of hydrogel deformation and the buckling patterns of thin hydrogel films on thick substrates. The theory is then adopted to simulate the growth and drying processes of leaves and fruits through the buckling phenomena observed in the film gel of various shapes, geometric proportions, chemical potentials and mechanical constraints. The key idea is to show that the hydrogel deformation theory can capture the deformation process and various states of plant growth or drying. The study has been made in an attempt to mimic the shapes of fruits and leaves from the swelling/deswelling patterns of hydrogel films. The study provides the possibility of exploring the origin of the intriguing natural phenomena of leaves and fruits.