Supplementary Material for Reviewers
Following the two reviewer’s comment, additional experiments were carried out. As a summary,
the color flip-over experiment shows that the mixing characteristics are the same. Experiments
were done too while changing the viscosity ratio. The conclusion is the same as before. But, due to
the early mixing upon exiting the T-junction, the intermediate cases were not well resolved.
However, the 1:1 and 1:28 cases show the same behavior. Hence the conclusion in the original
manuscript is the same. In the following the experimental condition and the results are described.
Experiment: mixing of the drops composed of fluids with various viscosity ratios
Materials: Same chemicals are used
Glycerin (Cat. No. G33-1, Thermo Fisher Scientific Inc.)
Silicone oil (Cat. No. S159-500, Thermo Fisher Scientific Inc.)
Food coloring (SpiceTime)
Microchannel: Width and height of the main stream: 1.55 mm and 0.56 mm, width and height of
the discontinuous stream: 0.55mm, 0.39mm (cf. For the case of original manuscript: Width and
height of the continuous stream: 1.59 mm and 0.53 mm; Width and height of the discontinuous
stream: 0.62mm, 0.29 mm)
- Viscosities are measured by using AR2000 (60mm flat steel plate) at the same time with the
mixing experiment.
Table 1. Viscosity ratio of the prepared fluids
Volume fraction of glycerin [%]
Viscosity ratio with water
0
1
20
1.9
50
7.8
70
28.4
75
44.7
- Fluids are dyed with the food coloring (yellow and red) and ejected through the same order of
inlets with the original experiments.
- Another set of experiment with two colored water streams are conducted with different inlet orders.
- The Lagrangian image analysis is performed to compare the mixing efficiency depending on the
viscosity ratio of the drop composing fluids.
- The intensity profiles of the Lagrangian images are acquired in both flow and transverse directions.
- Skewness is calculated after normalizing the consecutive intensity profiles to quantify the mixing
efficiency.
- Microchannel with a smaller size is used. Hence direct comparison of the effective mixing in the
microchannels is difficult.
- Re (= Channel height * velocity*density of oil / Viscosity of oil): 0.0026
Ca (= Viscosity of oil * velocity / Interfacial tension of water/oil): 0.02
Pe (= Channel height * velocity / Molecular diffusivity of glycerin in water): 1.3E3
Pe (= Channel height * velocity / Self diffusivity of water): 0.6E3
Figures and Discussions
Figure 1. Lagrangian images (a - f) of the drops with varying viscosity ratio in RGB channel (a)
Viscosity ratio 1 (inlet 1: red), (b) Viscosity ratio 1(inlet 1: yellow), (c) Viscosity ratio
1.9, (d) Viscosity ratio 7.7, (e) Viscosity ratio 28.1, (f) Viscosity ratio 44.4. (c - f) inlet 1:
yellow. (g) The image of microchannel with traveling drops. The age of the drops and
name of the inlets are marked on the image.
- The location of the water with red dye in the drop is inverted as the order of inlet streams is
changed. (Fig 1 a and b)
- The overall mixing process remains the same for the drops composed of two water streams (Fig 1
a and b).
- Slightly bigger drops are generated as the viscosity ratio of the drop composing fluids becomes
higher. Bigger viscous force resists to the capillary force detaching the drops at the T-junction.
(0.90, 0.90, 0.93, 1.05, 1.10 microliter for the cases of the viscosity ratio of 1, 1.9, 7.7, 28.1, 44.4
respectively)
- For the cases of the drops composed of fluids with a viscosity ratio higher than one, more
premixing occurs except the water/water mixture as the viscosity ratio of fluids becomes smaller
(Fig 1 c-f).
Figure 2. Skewness of intensity profiles in transverse direction
- The distribution of the fluid dyed in red is represented by the pixel intensity in transverse and flow
directions. The skewness data are computed from the pixel intensity profile of each frame.
- Premix occurs before the drops are detached at the T-junction. Less distinct color variation in the
drop at the initial stage and smaller values of skewness are obtained due to the premixing.
- As stated in the original manuscript, two fluids with same viscosities align comparably parallel to
the direction of the flow at the T-junction which gives strongly tilted intensity profile in the
transverse direction.
- The solid and open circles in Figure 2 are skewness profiles of the drops composed of two water
streams with different orders of inlet streams, water colored in red from inlet 1 and inlet 2
respectively.
- The positive and negative values of the skewness with similar absolute values (around 0.5) are
obtained when the water dyed in red is ejected through inlet 1 and inlet 2 respectively.
- For the cases of the drops composed of fluids of viscosity ratio higher than one, the skewness
values in transverse direction approaches zero much faster compared to those of the drops with the
same viscosity fluids.
Figure 3. Skewness of intensity profiles in flow direction
- The fluids with different viscosities align in the perpendicular direction to the flow direction in the
drop. Hence, the skewness deviates from zero much more as the drops pass the microchannel for
the cases of the viscosity ratio higher than one than the skewness in the transverse direction.
- As the viscosity ratios of the drop composing fluids become smaller, the initial skewness values in
flow direction increase, which means that the composing fluid dyed in red is distributed more in
flow direction initially (the color intensity profile is less tilted.).
Figure 4. Residence time required for effective mixing estimated from the skewness profiles.
- Because of the less distinct color contrast as a result of premixing, the skewness values are smaller
than the original work. Here, the required drop age for effective mixing is estimated by computing
the drop age when the skewness profiles become steady and the absolute values are less than 0.035
which is the value used to estimate the effective mixing time in the original work.
- Figure 4 shows that about 12 second is required for the drops composed of two water streams to be
mixed. About 4 seconds are required for the drops composed of fluids with viscosity ratio of
higher than one, which means that the drop composing fluids are mixed as the drops pass the 90
degree corner.
- The overall time scales of mixing are smaller for these sets of experiments compared with those of
the original work due to the different size of the microchannel.
- It takes about 4 seconds for the drops to pass the first 90 degree of curve after drop generation for
the cases with various viscosity ratios of the drop composing fluids. Hence, it can be said that the
first 90 degree of curve effectively mixes the drop composing materials although the initial mixing
conditions are different.