Modeling, analysis and design of centrifugal force driven transient filling flow into rectangular microchannel

Recently, centrifugal pumping has been discovered to be an excellent alternative method for controlling the fluid flow inside microchannels. In this paper, we have developed the physical modeling and carried out the analysis for the centrifugal force driven transient filling flow into a rectangular microchannel. Two types of analytic solutions for the transient flow were obtained: (1) a pseudo-static approximate solution, and (2) an exact solution. Analytic solutions include expressions for flow front advancement, detailed velocity profile and pressure distribution. The obtained analytical results show that the filling flow driven by centrifugal force is affected by three dimensionless parameters which combine fluid properties, rectangular channel geometry and processing condition of rotational speed. Effects of inertia, viscous and centrifugal forces were also discussed based on the parametric study. Furthermore, we have also successfully provided a simple and convenient analytical design tool for such rectangular microchannels, demonstrating two design application examples.