A mathematical model for the motion analysis of embedded straight microcantilevers under a pressure-driven flow

The empirical optimisation of a cantilever design for microfluidic control applications is a time consuming process that requires considerable testing. The use of finite element analysis tools is a common alternative to determine the effect of each design parameter. However, the prediction of the motion of an embedded cantilever within a microfluidic channel is a very complex problem. The coupled geometrical and fluidic variables make the simulation difficult using these tools. In this paper, a mathematical model is presented that couples the geometrical and fluidic features of the system. Therefore, it allows the determination of the way and extent to which each design parameter should be modified in order to achieve the desired performance. To the knowledge of the authors, this is the first example of a mathematical model that explains the motion and forces acting on a cantilever embedded in a microchannel. Furthermore, it does not require specific knowledge of the flow conditions in the vicinity of the structure, which improves its practical use during the early stages of design. Predictions have been made for two straight cantilevers under a range of pressures and compared against measurements obtained in Part I of this article. The results obtained show very good agreement with real measurements from experiments.