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Amy Li*Wellesley College*

Friday, August 10, 15:30 - 16:30
	Building 101 Lecture Room D
	Gaithersburg

Friday, August 10, 13:30 - 14:30
	Building 1 Room 4072
	Boulder

**Advisors:** Tony Kearsley and Paul Patrone

**Abstract:** Operation of microfluidic devices requires precise control over, and thereby measurement of, flow rates on the order of nL/min. At such scales, measurement signals are weak and require amplification. Current methods address this problem by relying on expensive microscopes, a detailed mathematical model of system geometry, and/or high resolution of the microfluidic device. However, such approaches are sensitive to uncertainties associated with device characterization, which propagate into final measurements.

Here, we expand on a recently proposed technique that overcomes such limitations by modelling flow rates in terms of the fluorescence intensity of dissolved fluorophores. In particular, this method relies solely on the observation that fluorescence efficiency, i.e. the measurement signal, is a one-to-one function of dosage, which is inversely proportional to flow rate. Critically, this property is robust: it holds irrespective of uncertainties in the device geometry and operating conditions. To further improve accuracy and facilitate uncertainty quantification, we argue that fluorescence efficiency is also a convex function of dosage. This allows us to apply powerful tools in convex optimisation to model the measurement signal, restrict the class of admissible fit-functions, and tighten uncertainty bounds.

We demonstrate convexity by showing that the second derivative of fluorophore concentration in dosage exists and is strictly positive. We recast this problem in terms of an existence proof of solutions to nonlinear integral equations, using Picard iteration. The proof does not require assumptions that compromise the robustness of the model. Experimental results confirm the validity of this approach.

**Bio:** Amy Li is an undergraduate at Wellesley College, majoring in mathematics and physics. She has worked in the Wellesley physics department, designing and building a fluorescence correlation spectrometer. Her interests include analysis and applied mathematics. This summer, she is part of the SURF program, advised by Dr. Tony Kearsley and Dr. Paul Patrone.

**Note:** Visitors from outside NIST must contact Cathy Graham; (301) 975-3800; at least 24 hours in advance.
  Mathematics and statistics

    
    Contacts
      
        

Paul Patrone
    
      
  paul.patrone@nist.gov
  (301) 975-5551

Created August 2, 2018, Updated June 2, 2021
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