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Relaxation times and dynamic behavior of an optofluidic flow meter in the nanoliter per minute regime



Nicholas Drachman, Paul Patrone, Gregory A. Cooksey


Accuracy and temporal resolution of flow meters are often unacceptable below the microliter per minute scale, limiting their ability to evaluate the real-time performance of many microfluidic devices. For conventional flow meters, this problem arises from uncertainties that depend on physical effects, such as evaporation, whose relative impacts scale inversely with flow rate. More advanced techniques that can measure nanoliter per minute flows are often not dynamic and require specialized equipment. Herein, we report on new experimental and theoretical results that overcome both limitations using an optofluidic flow meter. Previously, we showed that this device can measure flow rates as low as 1 nl/min with roughly 5% relative uncertainty by leveraging the photobleaching rate of a fluorescent dye. We now extend that work by determining the flow meter's relaxation time over a wide range of flow rates and incident irradiances. Using a simplified analytical model, we deduce that this time constant arises from the interplay between the photobleaching rate and transit time of the dye through the optical interrogation region. This motivates us to consider a more general model of the device, which, surprisingly, implies that all time constants are related by a simple scaling relationship depending only on the flow rate and optical irradiance. We experimentally validate this relationship to within 5% uncertainty down to 1 nl/min. Additionally, we measure a relaxation time of the flow meter on the order of 100 ms for 1 nl/min flows, demonstrating the ability to make dynamic measurements of small flows with unprecedented accuracy.
Physics of Fluids


optofluidics, flow metrology, dynamics, nanoflow


Drachman, N. , Patrone, P. and Cooksey, G. (2024), Relaxation times and dynamic behavior of an optofluidic flow meter in the nanoliter per minute regime, Physics of Fluids, [online],, (Accessed April 15, 2024)
Created February 29, 2024, Updated March 18, 2024