(a) Simple two-region model considering diffusion of .... cSO2â. 3. = 130 mM. The concentrations of the other chemicals were the same as those described in the ...
1 Supplementary Figures
5 0 5 0 5 0 5 0 5 0
T =10 min T =4 min T =1 min T =0.1 min approx. 0
20
[min]
40
60
b
1
Norm. difference 2| 2(eq)| of u2 from approx
2 [mM]
a
0 0.1
1
10 100 [min]
Supplementary Figure 1. Numerical characterisation of the droplet open-reactor system. (a) Numerical simulations of the autocatalytic reaction shown in Eq. 2 (in the main text) in the droplet open-reactor system. The simulations were performed using the general form shown in Eq. 1 (in the main text) for T = 0.1–10 min, and using the approximate form represented by Eq. 6 (in the main text) for “approx.” (Details are given in the Methods section in the main text). T j = T and w j = w for all j. w/T = 0.5 (fixed), which results in convergence to a steady state. (b) Normalised difference of u2 from “approx.”! in (a), which is calculated as the time-averages of the difference of u2 normalised by dividing by " the steady state values of u2 (approx.); i.e. u2,T (t) − u2,approx. (t) /u2,approx. (t = 60). A value of 1 means that the difference is ±100%, whereas t a value of 0 indicates no difference. The solid line is provided as a guide for the eyes.
2
a
b
40 mm
Zigzag channel
1.8 mm Top sealing area
1.8 mm
T-junction
40 mm
Oil
8 mm
Electrode
Foil
3 mm Y
Aq.2 Transporter Faq2 Reactor
Aq.1
Faq1
c
550 μm
Electrode
e
d
5 mm
1.8 mm X 3 mm
3.9 mm
500 μm
125 μm
2.2 mm 2.2 mm
550 μm
100 μm
550 μm
Y
Y
550 μm
Outlet 800 μm
X 550 μm
X
550 μm
g
f Oil inlet hole
500 μm
Y
800 μm
X
h
Hole for Outlet hole electrodes
1 mm
Outlet 800 μm
Outlet
800 μm
500 μm
500 μm
Aqueous inlet hole
500 μm
Z Y
X
1 mm (upper plate)
Hole for square chamber
1 mm (lower plate)
Z
1 mm X
Z 1 mm
500 μm
Y X
i
550 μm Y
j Electrode 40 mm
Cellophane tape for top sealing Square chamber Electrode
Supplementary Figure 2. Design details of microfluidic device for droplet open-reactor system. (a) Schematic diagram of microfluidic device. (b) Top view. (c) Enlarged top view of T-junction for transporter generation. (d) Enlarged top view of zig-zag channel for mixing. (e) Enlarged top view of square chamber for reactor. (f) and (g) 3D wide views. The microchannel was fabricated in the upper plate. The lower plate was attached to the upper plate by thermal compression bonding. (h) Enlarged 3D view of the square chamber for a reactor. The design and illustration were created using 3D CAD software (Rhinoceros 3D, Robert McNeel & Associates). (i) and (j) Photographs of fabricated microfluidic system.
3
d
3.0 3
Duration, w w [s] [s] Duration,
c
b
2.0 2 1.0 1 0.0 0
0 10 20 30 20 30 FoilF[μL Oil Oil flowflow rate, min-1] rate, oil [µL/min]
e
-2 s
0s
2s
enlarged view
Fluorescence int. [a.u.]
a
1.0 0.8 0.6 0.4 30 μL min-1 15 μL min-1
0.2 0.0
0 20 40 60 80 100
Number of fusion times
10 s
22 s
42 s
60 s
Supplementary Figure 3. Experimental characterisation of the droplet open-reactor system. (a) Generation of a transporter at the T-junction. Scale bar: 500 µm. (b) Solution mixing in the transporters in the zigzag mixing channel. Scale bar: 1 mm. (c) Control of w by Foil . T set j = 8s (fixed). (d) Solution exchange by successive multiple fusions. (e) Fluorescently observed diffusion of chemicals in the reactor immediately after a single fusion-fission event. The mixing time (∼ 60 s) was much faster than that of the simple diffusion of molecules (∼ 600 s) because of rotating flow in reactor [5]. Scale bar: 500 µm. Aqueous phase 1: 0.2 mM fluorescein sodium for (a)-(c) and 1 mM fluorescein sodium for (d) and (e). Aqueous phase 2: water for all. Oil phase: mineral oil with 0.5% Span80 for (a)–(c) and mineral oil with 5% Span80 for (d) and (e). Foil = 20 µL min−1 for (a) and (b), and 15 µL min−1 for (e). Foil = 15 µL min−1 (blue open square, w = 0.99 s), and 30 µL min−1 (red open circle, w = 0.40 s) for (d). Faq1 = Faq2 = 10 µL min−1 in all cases. (a) and (b) were captured using a high-speed CMOS camera (FASTCAM SA3 120K, Photron), (c) was captured using a digital camera (EOS 60D, Canon), and (d) and (e) was captured using a scientific CMOS camera (Zyla-5.5-CL3, Andor). Error bars of (c) and (d): s.d. Sample size of (c) and (d): 10 and 3 measurements, respectively.
4 Flag
Tjset
ON OFF
Time,
AC ON
AC
waiting ON OFF
t t
Fusion Fission
Nonfusion
Fusion
p (t ; T, w)
...
1 q 0
Tj
w Non-fusion Fusion
t
Non-fusion Fission
Fusion
Supplementary Figure 4. Control mechanism of fusion and fission by a droplet-fusion control program. T set j : set value of j-th fusion-fission interval; T j and w: actual interval and duration of j-th fusion-fission, respectively. p(t; T, w): pulse-train function expressing fusion-fission process. q: basal strength of chemical fluxes. First, a fusion flag in the droplet-fusion control program is turned ON by following T set j ; the droplet-fusion control program then waits for passing of a transporter to prevent unintended fusion, and AC voltage is turned ON; when the next transporter comes, the transporter fuses with the reactor; finally, just after the fission of the transporter, the flag and AC voltage are turned OFF; this cycle is repeated.
5
a
Chemicals
pH meter
b
Chemicals
7 6 pH
Exication LED light
5 4
Stirrer
Jacketed beaker
Emission filter
Normalized fluorescence [a.u.]
Water for thermal control
pH oscillation solution
Digital camera
3 1.0 0.8 0.6 0.4 0.2 0
10
20 30 Time [min]
40
Supplementary Figure 5. Comparison of pH changes and fluorescence intensity changes of BSF pH oscillation in beaker-sized open flowreactor. (a) Experimental setup. (b) Monitoring of BSF pH oscillation in beaker-sized open flow-reactor, based on fluorescence intensity (black line) and pH (red line). The experiments were carried out in a jacketed beaker (0065-01-13-01, Tokyo Glass Kikai). The total reaction volume was 18 mL, and 75 mM KBrO3 , 15 mM K4 Fe(CN)6 , 7.5 mM H2 SO4 , 100 mM Na2 SO3 , and 1 mM fluorescein sodium were flowed into the beaker at flow rates 0.9 mL min−1 using peristaltic pumps (MP-1000, EYELA). 40◦ C water was run into the beaker jacket to maintain the solution temperature. Fluorescence was observed using a digital camera (EX-F1, Casio). Excitation wavelength of light-emitting diode light: 470–475 nm. Emission filter wavelength > 540 nm. The pH was monitored using a pH meter (D-52LAB, Horiba).
6
b
c
D =100 min-1
D =1 min-1
q=0.5 6 4 2
q=0.2
6 4 2
Diffusion D Lower region (B)
Reactor
pH
Upper region (A)
q=0.14
6 4 2
q=0.1
6 4 2
q=0.2
6 4 2
pH
a
q=0.5 6 4 2
q=0.14
6 4 2
q=0.1
6 4 2
q=0.05
6 4 2
q=0.01
6 4 2 0
20 40 60 80 100
Time [min]
q=0.05
6 4 2
q=0.01
6 4 2 0
20 40 60 80 100
Time [min]
Supplementary Figure 6. Spatio-temporal analyses of droplet open-reactor system. (a) Simple two-region model considering diffusion of chemicals between upper and lower regions in the reactor. (b) and (c) Numerical analyses for (b) D = 100 min−1 and (c) D = 1 min−1 . Black line: upper region (A). Red line: lower region (B). Calculation parameters are the same as those in Supplementary Note 2.
7
0.41 0.33
0.5
0.0 1.0
0.5
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1.0
[mM]
110
120
0 20 40 60 80 100
0.0
cSO32-
0 20 40 60 80 100
0.0
100
0 20 40 60 80 100
0.0 0 20 40 60 80 100
0.0 0 20 40 60 80 100
90
0.0
80
0.0
Time [min]
0 20 40 60 80 100
70
0 20 40 60 80 100
130
Supplementary Figure 7. Time-course data for 2D bifurcation diagram in Fig. 3f.
2.4
3
4
5
30
20
15
10
8
6
Tjset[s]
0.25 0.20 0.17
0.033
0.050
0.067
0.099
0.12
q Norm. Fl. Int. [a.u.]
8
a
Transporter
c
q = 0.085
800 μm
Reactor #1
#2
300 μm
#3
#4
b
800 μm
Norm. fl. int. [a.u.]
d 1
Normalised fluorescence intensity [a.u.]
1
No.1 #1 No.2 #2 #3 No.3 #4 No.4 0
0
100 200 Time [sec]
300
0 1
q = 0.057
0 1
q = 0.043
0 1
q = 0.034
No.1 #1 No.2 #2 #3 No.3 #4 No.4
0 1
q = 0.021 0 0
20 40 Time [min]
60
Supplementary Figure 8. Droplet open-reactor system with arrayed multiple reactors. (a) Design of the arrayed multiple reactors (reactors #1–#4). Except for the arrayed reactors, the microfluidic configuration is the same as that displayed in Supplementary Fig. 2a. (b) Fluorescent image of the arrayed multiple reactors captured during the experiment presented in (c). (c) Control of the BSF reaction in the droplet openreactor system with arrayed multiple reactors. Faq1 = Faq2 = 2 µL min−1 , and Foil = 26 µL min−1 . In this flow-rate, w was 0.35 s. T = 4 s for q = 0.085, T = 6 s for q = 0.057, T = 8 s for q = 0.043, T = 10 s for q = 0.034, and T = 16 s for q = 0.021. cSO2− = 130 mM. 3 The concentrations of the other chemicals were the same as those described in the Methods section in the main text. The AC voltage for the droplet fusion (300 V (peak-to-peak), 1 kHz) was simultaneously applied to the four reactors using the droplet-fusion control program. (d) Time courses of the fluorescence intensity increase when droplet fusion occurred every ∼ 2 s. The flow rates and chemical concentrations were the same as those used in the experiments (c). Reactor #1 exhibited a higher rate of increase than the other reactors, suggesting that the chemical fluxes of reactor #1 were greater than those of the other reactors. This difference is probably the cause of the different reaction behaviour observed in reactor #1 in (c).
9 1 0 0.10 0.05 0.00
p
c 2 min
p q
p
20
0
30
e q
p
10
20
Time [min]
0
g q
20
0
i q
p
0
10
20
Time [min]
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30
10
20
30
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20
30
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30
Time [min]
1 0 0.10 0.05 0.00
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10
Time [min]
1 0 0.10 0.05 0.00
30
p
10
Time [min]
1 0 0.10 0.05 0.00
p
q q q q
10
Time [min]
1 0 0.10 0.05 0.00 0
h
Time [min]
30
1 0 0.10 0.05 0.00 0
f
20
1 0 0.10 0.05 0.00 0
d
10
p
0
b
enlarged view
Time [min]
1 0 0.10 0.05 0.00
p
q
a
0
Time [min]
Supplementary Figure 9. Generation of p and q by pulse-density modulation control. Blue lines: pulse trains of p(t; T, w). Black lines: (a)–(g) theoretical curves, (h)–(i) theoretical averages. Red dots and lines: q generated in experiments, calculated as q = w j /T j . w j = 0.99 s (fixed). (a) Constant function (ZC (t)). (b) and (c) Sinusoidal wave functions (ZS (t), Aq = 0.45, T q = 3 and 10 min). (d) and (e) Square wave functions (ZSq (t), Aq = 0.45, T q = 3 and 10 min). (f) and (g) Saw-tooth wave functions (ZSt (t), Aq = 0.45, T q = 3 and 10 min). (h) and (i) White noise functions (ZN (t), Aq = 0.2 and 0.45). q = w/T = 0.066 (w = 0.99 s, T = 15 s). Solutions in the transporter and reactor were 0.1 mM fluorescein sodium. ZC (t), ZS (t), ZSq (t) ZSt (t), and ZN (t) are described in Supplementary Note 4.
10
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