Flows in rectangular microchannels driven by capillary force and gravity

Capillary phenomena was studied and discussed by the scholars about 200 years ago, but the progress was slow due to the limited equipment and manufacture precision of the microchannel. In recent years, because of the rapid development of MEMS and micromachining, many applications of the capillary flow is widely developing in some modern processes, such as underfilling of flip chip, flow in microfluidic chip or biochip, and a variety of other fields. In this study, the theoretical mathematical model of flow in microchannel driven by capillary force and gravity is formulated from the Navier–Stokes equations. A close form solution to predict flow time was developed, and experiments have been set up to investigate and verify the flow times in microchannels. From the results, the predicted flow times show reasonably good agreement with the corresponding experimental flow times. Moreover, when the microchannel height is small, the effects of gravity force become less obvious; namely, the capillary becomes the dominant source to drive microfluidic.