Electrofluidic full-system modelling of a flap valve micropump based on Kirchhoffian network theory

We describe a comprehensive methodology for setting up physically based consistent full-system models for the effort-economizing and yet accurate numerical simulation of microsystems and we demonstrate its practicality with reference to an electrofluidic micropump macromodel. In this approach, the microsystem is partitioned into functional blocks (lumped elements), which interact with each other as constituent parts of a generalized Kirchhoffian network. For each of them, a compact model with only a few degrees of freedom is formulated. This is achieved by using a flux-conserving discretization of the system of balance equations which govern the flow of the relevant physical quantities. In the case of a micropump, these quantities are the flows of volume, charge and momentum caused by the respective driving forces which, in continuum theory, are the gradients of the spatial distributions of pressure, voltage and velocity. In this sense, generalized 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. An adequate formal representation of the system description is provided by an appropriate analog hardware description language such as VHDL-AMS, as it allows the models of the individual system components to be coded as well as the full system to be assembled by linking the constituent parts. Again, the general principles underlying our approach are exemplified by a full-system transient analysis of our benchmark problem, the electrostatically driven micropump.