Formalizing the movement of microparticles in a continuous flow microfluidic device for field flow fractionation

Abstract

The movement of microparticles in a continuous flow microfluidic device employing dielectrophoresis for purposes of field-flow fractionation is a challenging problem since there are several forces incorporated. For instance, forces due to inertia, gravity, buoyancy, dielectrophoresis and virtual mass are accounted for in this system. The governing equations for particle movement are solved conventionally using finite difference method. This device is designed to be used in biomedical engineering for separation of cancer cells from blood. As per the model, the levitation height is independent of the radius, volumetric flow rate and microchannel height, under steady state conditions, of the microparticles when subjected to dielectrophoresis. On the other hand, it is dependent on the applied voltage and electrode/gap length. While the levitation height, under transient conditions, is dependent on all these parameters. This shows that understanding the particle movement at high level of abstraction is necessary in order to avoid fundamental errors in the design of systems that can make use of this behavior. In this paper we use Event-B formal methods in order to formalize and validate the movement of microparticles under DEP. This is achieved by modeling the dynamic behavior that can predict the trajectory of microparticles as a transition state based system. The proposed model can provide early understanding of the behavior of the system at high level of abstraction, and therefore, can help validating several aspects of the design which is beneficial to designers of DEP-FFF microdevice at early stages of the design process.