Numerical simulation of hydrogel-based pH-responsive biosensors in BioMEMS

Applications of hydrogels in BioMEMS as mircoscale sensors/actuators have increasingly driven wide range effort of researchers since the bio-stimuli-responsive phenomena of hydrogels are observed, including the stimulation of pH, antigens, glucose, temperatures, pressure, etc. However, most of the studies are conducted through experimental works. A few theoretical works done are based on some over simplified assumptions. In this paper, a mathematical model, based on the chemo-electro-mechanical coupling formulations, is presented and known as the Multi-Effect-Coupling for pH-stimulus (MECpH) model. The MECpH model is developed to simulate the response of pH-sensitive hydrogels stimulated by pH value of the surrounding solution. This mathematical model is constructed from the nonlinear partial differential Nernst-Planck diffusive equations for diffusing ion species, and coupled with both the Poisson equations for electric potential and mechanical equilibrium equation for deformation of hydrogels. In order to solve the present MECpH model, consisting of a set of coupled nonlinear partial differential equations, a novel meshless technique, Hermite-Cloud method, is employed to simulate the responsive performance of the pH-sensitive hydrogels with varying pH in the bathing solution. Finally, one-dimensional steady-state simulations are carried out and compared with experimental results. It is shown that the presently developed MECpH model can simulate numerically and predict accurately the swelling response of the pH-responsive hydrogel.