Breakup Dynamic of Viscoelastic Thread for Droplet Formation in a Flow-Focusing Device
Wei Dua, Xiqun Gaob, Taotao Fua, Chunying Zhua, Youguang Maa*
a State Key Laboratory of Chemical Engineering, Collaborative Innovation Center of Chemical science and Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, P. R. China
* Corresponding author: email@example.com
b Yifang Industry Corporation, Liaohua Petrochemical Fiber Company, Liaoyang 111003, P. R. China
The breakup dynamic of viscoelastic thread for droplet formation was investigated by a high-speed digital camera in a flow-focusing device with square cross-section of 400°Á400µm. Dilute polyethylene oxide (PEO) - glycerol aqueous solution was used as the dispersed phase, while mineral oil with 4% (wt) surfactant sorbitanlauric acid ester (Span 20) was used as the continuous phase. Viscoelastic droplets were generated at the intersections of microﬂuidic device (Fig. 1).
The flow regime could be categorized into two patterns based on a critical droplet length: (i) dripping with satellites, (ii) dripping without satellites. In the regime with satellites droplets, the pinch-off of the viscoelastic thread of the dispersed phase would take place at both ends or at either end of the thread. While in the regime without satellite droplets, the rupture always occurs firstly at the upstream end of the thread.
For both flow patterns, the breakup processes of thread could be divided into two stages by a critical 'pinch time' tp: 'pre-stretch' stage (t < tp) and the 'elastocapillary balance' stage (t > tp). In the 'pre-stretch' stage, the variation of the minimum width of the dispersed thread with the remaining time (tp ¨C t) could be scaled as a power¨Claw relationship: wm/wc°Ø(tp ¨C t)¦Á, here ¦Á=0.36±0.03. In the 'elastocapillary balance' stage, it would exhibit an exponentially relationship between the minimum width of the thread and time: wm/wc°Øexp(-t/3¦Ë). In which the effective relaxation time ¦Ë extracted from the exponentially evolution of the thread is larger than the estimated Zimm relaxation time for the viscoelastic fluid.
Whether the satellite droplets could be generated or not depends primarily on the initial aspect ratio of the thread at the beginning of the 'elastocapillary balance' stage and afterward the evolution dynamics of the thread. For the regime with satellite droplets, the thread would firstly undergo a rapid stretching stage and then a linearly slow stretching process. For the regime without satellite droplets, it would undergo a rapid stretching stage at first and then a self-similar "elastic drainage" process with a constant length.
This study on breakup dynamic of viscoelastic thread for droplet formation in a flow-focusing device is conducive to the fully understanding of the rupture process, it would provide a perfect way to gain insight into the viscoelastic droplet formation with monodispersity and at same time provide the foundation for further theoretical and experimental investigations on the droplet formation and breakup processes for soft matter synthesis and design in microfluidic devices.
Keywords£ºmicrofluidic, viscoelastic, interface, pinch-off, satellite droplet.
Fig. 1 (a) Schematic diagram of the microfluidic device. All the cross-sections of these microchannels are 400 µm (height) ´ 400 µm (width). Unit: mm. (b) 30w PEO/ glycerol/Water droplets are generated at the intersections of microﬂuidic device (dashed line box in Fig. 1 (a)).