| The rapid emergence of microfluidics may well mean that the early part of the 21st century will witness an explosion of novel pocket-sized biomedical devices. Similar to the development of large-scale integration that allowed the miniaturization of electronics, it is hoped that many of the large, expensive chemical and biological analyses that are currently being performed can be replaced by microfluidic devices. These devices not only reduce the need for large laboratory-sized instrumentation, space and expenses, but also help in expediting many of the slow chemical processes by integrating multiphysics components---such as automation electronics, microfluidics, photonics and quantum-mechanical components on a single platform measuring a few square centimeters of area. Rapid simulation and design of such devices call for "fast", "multiphysics" computational tools. This work aims at the development of an environment to simulate the different physical domains that interplay in a complex Lab-on-Chip environment. The end goal here is to develop a technology for systems where a number of physical effects participate in tandem.;Novel schemes are introduced to address various theoretical problems that arise in EM and microhydrodynamics. Boundary element methods are used to develop a robust electromagnetic engine for predicting the EM forces produced by distributed electrode structures. Fast multipole method for low to high-frequency structures are demonstrated. Fast spherical transforms introduced by Driscoll and Healy are used as a means of quadrature, interpolation and setup of translation operators. For treating a variety of potentials arising in multiphysics, fast multipole operators based on ultraspherical harmonics are proposed. These are used for fast computation of Stokes and molecular dynamics fields. In addition, 3-D models of enclosed microfluidic channels are presented, and fast BEM technology for such systems is discussed. This enables the treatment of a wide class of electro-microfluidic systems. In cell handling devices, particularly, particle dynamics under combined action of external forces is treated. |
