Abstract
Scientists must overcome fundamental measurement problems if microfluidic devices are to become reliable and commercially viable. In particular, microfluidic devices require precise control over operating conditions such as flow-rate, υυ , which is difficult to measure continuously and in situ. Given the small scales involved, state-of-the-art approaches generally require accurate models to infer υυ on the basis of indirect measurements. However, such methods necessarily introduce model-form errors that dominate at the nL/min scale being targeted by the community. To address these problems, we develop a robust and largely assumption-free scaling method that relates the fluorescence efficiency II<math><mi>I</mi></math> of fluorophores to υυ through a dosage parameter ξ, which depends on the flow rate and laser power. Notably, we show that this scaling relationship emerges as a universal feature from a general class of partial differential equations (PDEs) describing the experimental setup, which consists of an excitation beam and fluorescence detector. As a result, our approach avoids uncertainties associated with most modeling assumptions, e.g. the exact system geometry, the flow profile, the physics of fluorescence, etc. Moreover, the corresponding measurements remain valid down to the scale of 10 nL/min, with some devices potentially capable of reaching 1 nL/min. As an added benefit, the measurement procedure is mathematically simple, requiring a few trivial computations, as opposed to the full solution of a PDE. To support these claims, we discuss and quantify uncertainties associated with our method and present experimental results that confirm its validity.