Supplementary materials for:

Throughput enhancement of parallel step emulsifier devices by shear-free and efficient nozzle clearance

Supplementary Video description

Video name

Video description

SV1 Volcano device producing drops with diameter of 50 µm. The video shows a close-up view of all the nozzles in the device. Similar scan is performed during every experiment to verify all nozzles are in dripping mode.

SV2 Volcano device producing drops with diameter of ~80 µm, with average production rate of 40 drops per second for each nozzle. This movie was used to estimate the drops raising speed (Fig4). Video shows the drops are clearing off from the nozzle exit area. Video playback speed 33X slower.

SV3 SV3 is like video SV2, with average production rate of 130 drops per second for each nozzle.SV4 SV4 is like video SV2, with average production rate of 220 drops per second for each nozzle.SV5 SV5 is like video SV2, with average production rate of 330 drops per second for each nozzle.SV6 Volcano device producing drops with diameter of 1070 µm. The device has 120 nozzles

working in parallel and emulsify ~10 liter per hour of dispersed phase. SV7 Manually-driven volcano device producing drops with diameter of 1070 µm. The dispersed

phase is injected manually to demonstrate the device operation without pump. SV8 Volcano device constructed as a pipettor tip. Drop diameter is ~1000 µm. SV9 The experimental setup used to examine volcano devices with drop diameter of up to 100 µm.

SV10 Zoom-in on volcano device producing drops with diameter of 50 µm. The video shows a side view on the dispersed phase distribution channels.

SV11 Volcano device producing drops with diameter of 570 µm. The device has 135 nozzles working in parallel and emulsifies 3.6 liters per hour of dispersed phase.

SV12 Top view of volcano device producing drops with diameter of 1070 µm. SV13 Zoom-in on a volcano step emulsifier nozzle in dripping mode. Bottom view of horizontal

nozzle. The drops pushed to the side and then rising away from the focal plane. The step at the nozzle exit is marked with a yellow line. Nozzle height is 260 µm yielding drop diameters of 1070 µm. Video playback speed is 33X slower.

SV14 Zoom-in on a volcano step emulsifier nozzle in jetting mode. The video shows a bottom view of horizontal nozzle. The drops are pushed to the side and then rise above the focal plane. The step at the nozzle exit is marked with a yellow line. Nozzle height is 260 µm. Video playback speed is 33X slower.

SV15 Alternative configuration volcano device. In this “closed” volcano configuration the drops pushed out of the device into collection tube. Drops diameter is ~1100 µm.

Electronic Supplementary Material (ESI) for Lab on a Chip.This journal is © The Royal Society of Chemistry 2017

Figure S1: Drop diameter as a function of flow rate for a device with 135 nozzles and 135µm height. a) Probability density function (PDF) of drops diameter. b) Zoom-in of the PDF. Three regimes are observed: I. suboptimal working flow characterized by wide distribution (>4% CV); II. Optimal working flow result with lowest CV; III. Beyond the transition flow (black) part of the nozzle are in jetting mode. Therefore, in addition to the drops forming at 580 µm, a second peak at 1450 nm is emerged. Data is detailed in table S1.

Flow Rate

Mean Diameter CV

No. of fitted drops

Standard Deviation

Remark

[mL/Min] [µm] %0.5 538.5 4.15 208 22.33 561.5 5.29 665 29.71

12 570.1 2.18 7761 12.4350 561.1 3.04 2246 17.0660 570.9 2.5 6551 14.3070 572.9 2.08 9947 11.9380 591.7 15.59 2633 92.26 All drops80 578.8 4 2609 23.15 Drops smaller than 1000 µm80 1455 2.09 24 30.41 Drops bigger than 1000 µm

Table S1: Drop diameter and CV as a function of flow rate, for a device with 135 nozzles of 135µm height. Probability Density Function (PDF) of these data are plotted in figure S1.

All device Single nozzleNozzle height

Average drop size

CV No. of

fitted drops

Number of

nozzles

Total device area

Max. flow rate

Max Flow rate

Max drops

per second

[µm] [µm] % [mm2] [L/hour] [mL/hour] [Hz]6 30 5.2 6414 384 280 0.03 0.078 1500

12 51 4.8 5174 192 280 0.05 0.262 106320 96 2.6 1953 160 231 0.09 0.566 341

134 573 2.1 9947 135 3750 4.2 31.1 88263 1071 4.3 970 120 3750 9.9 82.5 36

Table S2: Maximum measured production rate, per device.

Figure S2: power law plots

The transition flow rates (a-c) and number of drops (d-f) at each nozzle, as a function of drop diameter (a,d), drop surface area (b,e) and drop volume (c,f). All plots are fitted by a power law as indicated by inset equations.

Nozzle height

Nozzle Width

Drop diameter

Max Flow

rate per Nozzle

Max no. of drops per

second per nozzle

Effective nozzle cross

section

Critical nozzle flow

velocity

Critical Capillary

no.Ca*

Critical Weber

no.We*

Critical Bond no.Bo*

Critical Reynold

noRe*

[µm] [µm] [µm] [µL/hour] [µm2] [m/s] [] [] [] []

6 35 30 78 1,500 201 0.108 3.36E-02 1.95E-02 1.40E-03 8.05E-01

12 70 51 260 1,063 615 0.118 3.67E-02 4.24E-02 3.94E-03 1.60E+00

20 100 96 563 341 1,874 0.083 2.59E-02 3.41E-02 1.40E-02 1.83E+00

134 1,000 573 31,111 88 76,925 0.112 3.49E-02 4.24E-01 5.03E-01 1.69E+01

263 1,700 1,071 82,500 36 281,673 0.081 2.53E-02 4.35E-01 1.76E+00 2.39E+01

Table S3: The critical nozzle flow velocity, capillary, Weber, Bond and Reynolds numbers for devices with nozzle heights between 6 and 263 µm. The effective nozzle cross section is the product of the nozzle height and the drop diameter. The critical nozzle flow velocity is calculated by dividing the max flow rate per nozzle by the effective nozzle cross section.

Where:

𝐶𝑎 ∗ =𝜇𝑐𝑜𝑛𝑈𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙

𝛾

𝑊𝑒 ∗ =𝜌𝑑𝑖𝑠𝑈𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙

2𝐷 ∗

𝛾

𝐵𝑜 ∗ =Δ𝜌𝑔𝐷 ∗ 2

𝛾

𝑅𝑒 ∗ =𝑊𝑒 ∗

𝐶𝑎 ∗

Ucritical is the critical velocity of the dispersed phase

D* is the drop diameter at the critical velocity.

g is the gravitational acceleration constant.

μ is the dispersed phase dynamic viscosity. 0.0008937 [Pa sec]μcon is the continuous phase dynamic viscosity.

0.00124278 [Pa sec]γ is the surface tension between the continuous and dispersed phases. 0.004 [N/m]ρdis is the density of the dispersed phase.

1000 [kg/m3]ρ is density of the continuous phase 1614 [kg/m3]Δρ is the density difference between the dispersed and continuous phases. 614 [kg/m3]

0 50 100 150 200 250 3000

200

400

600

800

1,000

1,200

Drop Diameter Vs Nozzle Height

Nozzle Height [µm]

Drop

Dia

met

er [µ

m]

Figure S3: Drop diameter at highest production rates, as a function of nozzle height. Ratio between nozzle height and drop diameter is 4.116, as deduced from fitted slope. Error bars are standard deviation of the measurements.

Fig S4: Drop image is captured in real-time by video. Schematic view of the experimental setup is illustrated in the inset; drops produced by volcano device rise along the surface of a transparent box. The box serves as a ‘swim mask’ for visualizing drops and analyzing dispersity. Examples are available in online videos SV11-12.

Fig S5: Drop size distribution obtained by a home-made image analysis software. Top: Fitted drops are labeled in red. Bottom: images taken by an optical microscope.