Measurement of flow in microfluidic networks with micrometer-sized flow restrictors

The fluid dynamics in micrometer-sized flow restrictors was evaluated, to test the predictions of the Hagen-Poiseuille equation in small microchip devices. A photobleaching, time-of-flight linear flow rate measurement method was developed for the evaluation of flow in slot-shaped channels with at least one dimension in the size range of 1-3 mu m. For a linear flow rate range in the narrowest dimension of 0.3 to 16 mm/s (volumetric flow rates of 0.6 to 32 nL/s, maximum Reynolds number of 0.3), observed flow rates agreed with theoretical predictions within experimental error (2-3%). An empirical equation for the geometric form factor of a D-shaped channel was developed, providing a useful working curve for use of the Hagen-Poiseuille equation in microfluidics design. The Hagen-Poiseuille solution can be used to design multiport devices with intersecting flow channel networks, achieving the intended flow rate ratios in channels with differing flow resistance with an accuracy of 1-2%. Despite the differences between achieved etched dimensions and the nominal design values a deviation of only 1-4% in the flow ratios was also achieved. This observation provides a useful guideline for predicting tolerance sensitivity in device manufacture. (c) 2005 American Institute of Chemical Engineers AIChE J, 52:75-85,2006.