Electro-fluidic microsystem modeling based on Kirchhoffian network theory

We describe a comprehensive methodology for setting up physical-based, consistent full system models for the effort-economizing and yet accurate numerical simulation of microsystems. In this approach, the microsystem is partitioned into so-called lumped elements, which interact with each other as constituent parts of a Kirchhoffian network. For each of them, a compact model with only few degrees of freedom is formulated. This is achieved by using a flux-conserving discretization of the system of balance equations governing the flow of the relevant physical quantities such as volume, charge, mass, heat etc. caused by the respective driving forces which, in continuum theory, are the gradients of the spatial distributions of pressure, voltage, chemical potentials, temperature etc. In this sense, Kirchhoffian network theory is the discrete counterpart of continuum transport theory and relies on the same basic physical conservation laws as described by the principles of irreversible thermodynamics. The adequate formal representation of the system description is provided by VHDL-AMS (Analog Hardware Description Language), which is used to code the models of the individual system components as well as to assemble the full system by linking the constituent parts. The general principles underlying our approach are exemplified with reference to an electrofluidic micropump macromodel.