Critical condition for bubble breakup in a microfluidic flow-focusing junction
Xiaoda Wanga, Taotao Fua, Xiqun Gaob, 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 critical condition for bubble breakup in a microfluidic flow-focusing junction was investigated experimentally by means of a high-speed digital camera. The experiments were carried out in a square microchannel with width of 400 mm, which were fabricated in a polymethyl-methacrylate (PMMA) microfluidic chip. This microfluidic chip could perform a variety of functions, such as the formation, breakup and coalescence of bubble and droplet. In presented study, our attention was only paid to the bubble behaviors of breakup and non-breakup in the second flow-focusing junction of the microfluidic chip, as shown in Figure 1. N2 and the glycerol-water mixtures were used as the dispersed and continuous phase, respectively. The viscosity of the continuous phase was modified by varying the mass fraction of the glycerol from 0 to 62%. Sodium dodecyl sulfate (SDS) was added into the glycerol-water mixtures to stabilize the flow patterns.
The effects of five factors on the critical condition for bubble breakup were studied, including the length of the bubble, the flow velocity of the continuous phase from the side channels of the microfluidic flow-focusing junction (or the flow velocity of the second continuous phase), the viscosity of the continuous phase, the movement velocity of the bubble and the concentration of the surfactant. The experimental results showed that: (I) the increase of the first three factors would promote the bubble breakup; (II) the bubble broke more easily at lower movement velocity; (III) the concentration of the surfactant hardly affected the transition between breakup and non-breakup.
The critical condition for bubble breakup was closely related to two time-scales: the breakup time and deformation time. The periods of breakup and deformation processes were determined, respectively, by tracing the evolution of the dynamical gas-liquid interface shape of the bubble flowing through the flow-focusing junction. The breakup time was defined to characterize the process of breakup, and it referred to the time duration from the moment that the bubble head arrived at the exit of the flow-focusing junction to the moment that the bubble broke into two ones. The deformation time was defined for the case of non-breakup, and it referred to the time duration from the moment that the bubble head arrived at the exit of the flow-focusing junction to the moment that the bubble rear left the entry of the flow-focusing junction.
Two mathematical models were constructed for the breakup time Tb and the deformation time Td by analyzing the effects of every factor on these two time-scales: Tb/Tc = 8.25¦Á2-all-0.74Ca2-0.23 and Td/Tc = 14.47¦Á2-all-0.12(l0/wc)0.91 Here, Tc (= (¦Ñwc3/¦")1/2) is the capillary time, Ca2 is the capillary number of the second continuous phase, ¦Á2-all is the flow ratio of the second continuous phase to all fluids, l0 is the length of the bubble, wc is the width of the microchanenl, ¦Ñ is the density of the liquid and ¦" is the surface tension. From these two time models, a criterion equation to predict the critical condition was deduced for the bubble breakup in a flow-focusing junction: l0/wc = 0.54¦Á2-all-0.68 Ca2-0.25.
Keywords: bubble; breakup; microfluidic; flow-focusing; critical condition.
Figure 1 Schematic diagram of the microfluidic chip. The microfluidic device is 71 mm long, 43 mm wide and 10 mm high. All the cross-sections of the microchannels are 400 µm (height) ´ 400 µm (width). We focused on the bubble behaviors in the second flow-focusing junction.
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