Collocation based meshless methods for microelectromechanical systems.

摘要

Multiphysics and multiscale analysis, which is essential for microelectromechanical systems (MEMS), is radically simplified by meshless techniques, which are appealing in adaptive techniques. In this work, the mathematical expressions for the meshless approximation and global error bound for the finite cloud method (FCM) have been derived. The point distribution in a cloud significantly affects the condition number of the final matrix which is directly related to the global error of the solution. Based on the analysis, certain positivity conditions were proposed as a criteria to monitor the cloud quality and special weighting functions to satisfy the positivity conditions. In order to minimize solution errors, modifications to the fixed kernel approximation were proposed, and more sophisticated collocation schemes were studied.; After the theoretical study of the meshless methods, the FCM and boundary cloud method (BCM) were applied to solve the fluid flow in the MEMS devices. Combining the fluid flow module with the solver for the Poisson and Nernst-Planck (PNP) equations, a tool for the simulation of ion transport in the framework of the meshless methods has been developed. Furthermore, this tool has been used to study the electrokinetic transport in a hybrid micro-nanofluidic interconnect device, which is capable of controlling analyte transfer between the microchannels through a nanochannel under rest, injection and recovery stages of operation by varying the applied potential bias. During the injection stage, the phenomenon of ion accumulation and depletion is observed at the micro-nano interface region. Net volume charge in the depletion region gives rise to nonlinear electrokinetic transport during the recovery stage due to induced pressure, induced electroosmotic flow of the second kind and complex flow circulations. Analytical expressions derived for ion current variation are in agreement with the simulated results. In the presence of multiple accumulation or depletion regions, a hybrid micro-nano device can be designed to function as a logic gate.