(257z) Critical Condition for Bubble Breakup in a Microfluidic Flow-Focusing Junction

Critical condition for bubble breakup in a microfluidic flow-focusing junction

Xiaoda Wang^a, Taotao Fu^a, Xiqun Gao^b,
Chunying Zhu^a, Youguang Ma^a*

^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: ygma@tju.edu.cn

^bYifang Industry Corporation, Liaohua Petrochemical Fiber Company, Liaoyang 111003, P.
R. China

Abstract:

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 T_b and the
deformation time T_d by
analyzing the effects of every factor on these two time-scales: T_b/T_c = 8.25¦Á_2-all^-0.74Ca₂^-0.23 and T_d/T_c = 14.47¦Á_2-all^-0.12(l₀/w_c)^0.91 Here, T_c (= (¦Ñw_c³/¦")^1/2) is the capillary
time, Ca₂ is the capillary
number of the second continuous phase, ¦Á_2-all
is the flow ratio of the second continuous phase to all fluids, l₀ is the length of the
bubble, w_c
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/w_c
= 0.54¦Á_2-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.