Description of a Hydrogel-Based Micro-Valve As a Library Element for Matlab Simulink

Abstract

We propose a planar hydrogel-based micro-valve design which is modeled as a library element for Matlab Simulink. For this test case, a pressure pump (voltage source) in series with a micro-valve model (variable fluidic resistance) is built up. The micro-valve subsystem is separated in four main parts. Based on the applied temperature stimulus, the equilibrium length is determined according to an experimentally verified fit function. Furthermore, the equilibrium length considers a static hysteresis effect which is modeled in analogy to the saturation of magnetization in electric transformers. In a second step, the transient behavior follows a first order differential equation, but the cooperate diffusion coefficient is size dependent affecting the rise time of the system. This causes a faster swelling than deswelling of the hydrogel. In the third section, the stiffness property is implemented to calculate the maximum sealing pressure and the resulting gap between the hydrogel and the wall. The fluidic resistance of the micro-valve considers a three-dimensional geometry and is calculated based on a look-up table, extracted from a fluid-structure-interaction (FSI) model generated from a finite element structure. The proposed model allows a full description of the fluidic hydrogel-based micro-valve and is part of an upcoming microfluidic toolbox for Matlab Simulink containing passive elements and optional chemical reactions like mixing fluids and enzyme reactions for future applications.