Analysis and modeling of flow in rotating spiral microchannels: towards math-aided design of microfluidic systems using centrifugal pumping

This paper describes the experimental measurement and mathematical modeling of centrifugally-pumped flow in spiral microchannels. Here, the liquid is delivered by the rotation of a circular microchip as depicted before (X. Y. Peng, P. C. H. Li, H. Z. Yu, M. Parameswaran and W. L. Chou, Sens. Actuators, B, 2007, 128, 64-69). The spiral microchannel in it was specially designed to produce a constant centrifugal force component. From experimental measurements, it was found that the flow velocity inside the spiral microchannels was associated with the rotation speed only, but not with the length of the liquid column. The mathematical modeling of liquid flow was constructed based on solving the Navier-Stokes equations of incompressible flow formulated in a new orthogonal curvilinear coordinate system aligned with the channel geometry. The governing equations were simplified under various assumptions, rendering a mathematically-tractable physical model. In addition, a commercial computational fluid dynamics (CFD) program was used to simulate the flow in the spiral microchannel. The predicted liquid flow velocities from the mathematical model and the CFD program showed reasonable agreement with the experimental data. Under proper assumptions, the mathematical model gave a flexible and rather accurate analytical solution using much less computing power. The proposed study demonstrated the effectiveness of the spiral microchannel design in microfluidic applications using centrifugal force. With modifications, this study could be adapted to the simulation and modeling of other centrifugal-pumping microflow systems.