Bayesian Uncertainty Quantification for Microfluidics: Assessing and Improving the Reliability of Reduced-Order Models and Sample Detection Schemes

• Applicant: Dr.-Ing. Henning Bonart
• Subject Area: Fluid Mechanics
• Term: from 2021 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 459970841

• Final Report Year: 2024

Final Report Abstract

In this project, we collected experimental data, developed models describing the data, processed the data using Bayesian methods, and developed a new software toolkit for Bayesian inference. The new software is freely available and can be used to construct Bayesian inference and stochastic surrogates based on monotone triangular transport maps. Microfluidic systems with very small length scales or strong influence of surface tension effects were researched in great detail. This included holes in liquid films on a vibrated surface exhibiting capillary waves and sample concentration and transport in microchannels using isotachophoresis. Experimental data was collected using camera imagining, laser profilometer, and laser-induced fluorescence microscopy. For the holes in liquid films, Bayesian modeling including prior information and measurement error models as well as model comparison were used to guide the development of a theory and model purely based on physics describing the shrinkage of holes with vibration parameters. The final model without any fitting parameters is based on the Young-Laplace equation and an effective capillary length, and is validated against two independent measurements (hole diameter and wave energy). For the sample concentration and transport in microchannels, Bayesian modeling and inference were used to extract the sample signals completely hidden in noise. In addition, the detection decision was based on Bayesian statistics including the full uncertainty of the sample intensity estimation. The final algorithm exhibit a signal-to-noise ratio in dependence on the square root of the number of images. Using only 200 images of the traveling sample in the microchannel resulted in a reduction of the detectable concentration by two orders of magnitude. Based on the results of this project, we hope that in the future Bayesian methods, especially based on transport maps, will be applied more often to analyse noisy experimental data, develop and validate models as well as for decision-making in microfludic basic research and applications.

Publications

• Microfluidic isotachophoresis in constant-current mode with Alexa Fluor 647 carboxylic acid. July 2022
  Henning Bonart, Florian Gebhard, Lukas Hecht, Tamal Roy, Benno Liebchen & Steffen Hardt
  
• MParT: Monotone Parameterization Toolkit. Journal of Open Source Software, 7(80), 4843.
  Parno, Matthew; Rubio, Paul-Baptiste; Sharp, Daniel; Brennan, Michael; Baptista, Ricardo; Bonart, Henning & Marzouk, Youssef
  
• Detecting Isotachophoresis Zones Hidden in Noise Using Signal Processing. Analytical Chemistry, 95(19), 7575-7583.
  Bonart, Henning; Gebhard, Florian; Hecht, Lukas; Roy, Tamal; Liebchen, Benno & Hardt, Steffen
  
• Detecting Isotachophoresis Zones Hidden in Noise Using Signal Processing. Analytical Chemistry, 95(19), 7575-7583.
  Henning Bonart, Lukas Hecht & Florian Gebhard
  
• Disorder-to-order transition of long fibers contained in evaporating sessile drops. Soft Matter, 20(14), 3107-3117.
  Sannyamath, S.; Vetter, R.; Bonart, H.; Hartmann, M.; Ganguly, R. & Hardt, S.
  
• Isotachophoresis with Oscillating Sample Zones to Control the Spatial Overlap of Co-focused Species. Analytical Chemistry, 96(11), 4446-4454.
  Gebhard, Florian; Bonart, Henning; Roy, Tamal; Meckel, Tobias & Hardt, Steffen
  
• Liquid Surfaces with Chaotic Capillary Waves Exhibit an Effective Surface Tension. Physical Review Letters, 133(3).
  Bisswanger, Steffen; Bonart, Henning; Khaing, Pyi Thein & Hardt, Steffen