Multiphysics Equivalent Circuit of a Thermally Controlled Hydrogel-Micro Valve

Hydrogels consist of a network of cross-linked polymers that swell when put into water. For temperature-sensitive smart hydrogels the equilibrium hydrogel size depends on the temperature of the liquid. These hydrogels are used to build temperature-controlled fluidic valves. Here we present an equivalent circuit model of such a hydrogel valve. The transient behavior is based on the model by Tanaka with three additional assumptions: 1. Only the fundamental mode of the deformation field, i.e. the slowest-decaying exponential temporal behavior, is relevant. 2. There are distinct equilibrium sizes for the swollen and the de-swollen state. 3. As observed in experiment, the swollen gel and the de-swollen gel have different elastic moduli, which affect the time constants of swelling vs. de-swelling. The resulting network model includes three physical subsystems: the thermal subsystem, the polymeric subsystem and the fluidic subsystem. The thermal subsystem considers the temperature of the heater, of the adhesive and of the hydrogel. It is assumed that adhesive, housing and hydrogel act as heat capacities in combination with heat resistors. The modeled polymeric subsystem causes in addition time delays for swelling and de-swelling of first order with different delay constants. The fluidic subsystem basically includes the fluidic channel between hydrogel and housing with time varying cross section, which is modeled as controlled source. All subsystems are described and coupled within one single circuit. Thus the transient behavior of the hydrogel can be calculated using a circuit simulator. Simulation results for an assumed hydrogel setup are presented.