Determining the flow-related cap deformation of Taylor droplets at low Ca numbers using ensemble-averaged high-speed images

• Published in: Experiments in fluids 2019-07, Vol.60 (7), p.1-17, Article 113
• Main Authors: Helmers, Thorben, Kemper, Philip, Thöming, Jorg, Mießner, Ulrich
• Format: Article
• Language: English
• Subjects: Curvature; Deformation; Droplets; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Fluid- and Aerodynamics; Heat and Mass Transfer; Image contrast; Image processing; Mass transfer; Microreactors; Pressure drop; Refractivity; Research Article
• ISSN: 0723-4864; 1432-1114
• DOI: 10.1007/s00348-019-2757-7

Droplets of microscopic Taylor flows can act as stirred batch microreactors, while the continuous phase compartments supply good mixing and mass transfer to the channel walls. The design of reliable reactors, however, requires a priori information about droplet formation frequency and droplet length, which is difficult to obtain. Here, we report about a new method to reliably describe the droplet deformation, which could act as a flow indicator. The flow-related interface shape deformation of liquid–liquid Taylor flows in square micro channels for R e < 5 and C a < 0.02 is quantified by experimental studies and ensemble image averaging. We deduce an easy-to-access droplet cap deformation model, which allows reducing the complex interface curvature information to an ellipse and provide correlation functions to link this deformation ratio to the flow conditions quantitatively. In addition, we introduce an experimental approach using a ternary liquid–liquid material system that allows adjusting Re and Ca numbers independently without surfactant addition by changing the mass fraction of two liquids forming the continuous phase. In combination, we suggest an image processing method to overcome the optical issues arising from the poor image contrast of Taylor droplets with low differences of refractive index to the bulk material. The presented approach opens the possibility to benchmark numerical studies of the interface deformation and paves the way for improved flow modeling, e.g., pressure drop or relative velocity of Taylor droplets, since the flow-induced curvature could serve as an indicator of the forces acting on the droplet front and rear. Graphic abstract