A novel approach to determining the hydrodynamic resistance of droplets in microchannels using active control and grey-box system identification

Inaccurate prediction of droplet hydrodynamic resistance has a profound impact on droplet chip performance and lengthens the iterative design process. Previous studies measuring droplet resistance use various approaches such as interface comparison to quantify flow rate, and pressure taps; all these methods are classified as passive. Although each study supports well their own findings, the wide variety of conditions such as channel geometry and use of surfactant in combination with the difficulty in quantifying the droplet resistance leads to poor consensus across the different studies. Overall guidelines would be broadly beneficial to the community, but are currently fairly crude, with a rule of thumb of 2 to 5 times resistance increase. The active droplet control platform previously developed enables a novel approach that is herein confirmed as promising. This proof-of-concept study focuses on verifying this approach that employs a system identification method to determine the hydrodynamic resistance of a channel containing a single droplet, from which the droplet resistance is retrieved. This method has the potential to be further applied to a large variety of conditions, and most importantly, to non-Newtonian fluids once key limitations are overcome to improve measurement resolution. The current results qualitatively agree with the literature and demonstrate the promising future for this novel active approach to quantifying droplet resistance.