Hydrogels have many applications, ranging from industrial to biological fields, due to
their specific triphasic structure and response to different environmental conditions. The
field theory framework for the deformation of pH-sensitive hydrogel is presented coupling electro-magnetic (EM) field (external or internal) and diffusion of mobile ionic
species through an irreversible thermodynamics. The diffusion of mobile ionic species
from the solution to hydrogel, and an evolution of electric potential field within hydrogel
are captured by Poisson-Nernst-Plank and Maxwell equations, respectively. The evolution of fixed-charge inside the hydrogel is modelled by Langmuir monolayer adsorption theory. The Cauchy stress tensor constitutive relation coupling EM field and
species diffusion through Maxwell’s stress and spherical tensors is derived. The resulting hydrogel swelling is finally computed by mechanical equilibrium equation through traction boundary conditions. The simulation of one-dimensional pH-sensitive hydrogel is firstly performed, by strong-form local differential quadrature method, varying solution pH and initial fixed-charge concentration inside the hydrogel. The simulation of two-dimensional pH-sensitive hydrogel is secondly performed varying solution pH, initial fixed-charge concentration and Young’s modulus of hydrogel. The constitutive relations derived in the present work are also verified with the other published results. All the presented simulation results successfully demonstrate the multi-physics coupling of hydrogel deformation with diffusion (osmosis) and EM field. The primary focus of the present work has been the multi-physics coupling between mechanical, diffusion, and EM phenomenon driving hydrogel deformation, the presented results are thus obtained within the scope of small deformation regime of hydrogel.
The micro-electro-mechanical (MEM) beam and column structures, made of hydrogel-like material (polyelectrolyte), are analyzed finally in details containing fixed charge(+ve or - ve). The transverse deflection of this column, due to the presence of fixed charge concentration and axial compressive force, is studied for linear elastic and viscoelastic cases. An analytical solution of critical buckling load P supported by MEM column, with initial imperfections due to the presence of fixed-charge in the column (simply-supported), is derived. A pull-in instability of MEM beam is studied under the
influence of external electric field, and a critical voltage V without any instability is obtained varying fixed-charge concentration inside beam. All the presented formulations are extended to finite deformation setting (incorporating von Karman strain field), as the beam rotation becomes significant at higher fixed-charge values. All the presented results are also verified with the published literature wherever it was possible. The presented work thus can be reasonably employed in the design of MEM micro-switches.