Swelling response of functionally graded temperature-sensitive hydrogel valves: Analytic solution and finite element method

Abstract

Temperature-sensitive hydrogels are classified as high stretchable materials undertaking large recoverable deformation under thermomechanical loadings. Due to vast applications of these materials in microfluidic valves and stress/deformation discontinuity observed in multi-layered structures, understanding of thermomechanical behavior of functionally graded hydrogels is of great practical interest. In this article, the swelling of these materials is analyzed considering various types of micro-valves including solid cylinder, hollow cylinder, and Jacket-pillar cylinder. Accordingly, analytical solutions are developed for swelling behavior of diverse types of cylinders composed of functionally graded temperature-sensitive hydrogel. The distribution of the cross-link density alters along the radial direction in exponential and linear trends. Besides, finite element analysis is presented to evaluate the proposed analytical solution in different case studies. Then, to account for more realistic environmental conditions, heat transfer equation is also solved along with the mechanical equilibrium equation to propose a novel analytical solution validated by finite element method. Clarifying the micro-valves mechanism and illustrating the capability and accuracy of the analytical method, the effects of material and environmental variables are studied in detail; continuous stress and deformation fields are observed opposed to the multi-layered structures which normally involve stress discontinuity.