An analytical model for the bending and reaction force of hygroscopic bilayers upon water adsorption

Hygroscopic bilayers replicating the morphing capability of plants upon hydration (e.g., pinecone scales, chiral seed pods) have gained much attention in robotics and material science research in the past decade. Due to variations in humidity, hygroscopic bilayers - comprising a passive substrate and an active porous coating - can convert the chemical potential difference of adsorbate species between the surrounding environment and the pore space to mechanical energy, resulting in development of curvature and forces. In this paper, we present a closed-form analytical model that considers the pore structure of the active layer for predicting the morphing of hygroscopic bilayers subjected to adsorption. For free-end cases, the curvature evolution as a function of relative humidity is predicted by combining a bilayer beam theory and a linear surface poroelasticity model for the active porous layer. For fixed-end scenarios, the reaction force generated by the bilayer is predicted using Castigliano's second theorem with the same constitutive model. For validation, we consider two types of hydroscopic bilayers with microporous and mesoporous coatings, as tested by Boudot et al. (2016). A new isotherm equation is introduced to capture the adsorption characteristics of mesoporous media at all humidity levels. The predicted curvature and reaction force curves compared well against the experimental data. Finally, the effects of substrate Young's modulus and the coating's thickness on the response of the bilayer are studied. The proposed model offers straightforward mechanistic description of hydroscopic bilayers, thereby aiding in the future optimization and design of these systems for engineering applications.