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 μm. 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. © 2005 American Institute of Chemical Engineers AIChE J, 2006

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