Micro Fluid i Que

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Supporting Information

Bhargava et al. 10.1073/pnas.1414764111

Note S1

See www.dolomite-microfluidics.comand www.micronit.comfortwo examples of proprietary solutions to standardized jumper-

cable-based interconnects and monolithic microfluidic devices.Note S2

All resistors in the equivalent circuit model (Fig. 2B) wereapproximated by series addition of their contributing elementresistances in the actual component assembly (Eqs. S1S3; seeTable S2 for subscript nomenclature):

R=RI+RT;750 + 3RC;1;000 +RL;750 +RSP;750 =Rstruct+Rref [S1]

Rs =RI+RT;750 + 3RC;1;000 +RL;750 +Rselect =Rstruct+Rselect [S2]

Ro =RT;750 +RC;1;000 +RI;750: [S3]

Here R is the resistance on the reference branch, Rs is theresistance on the variable branch with the selected resistor,and Ro is the outlet resistance. The component reference re-

sistor Rref and variable resistor Rselec t uniquely control howmuch blue and yellow dye enter the outlet T junction by throt-tling the action of the pressure source differently in their re-spective branches. This action is analogous to the use of acurrent divider in electronic circuit design to deduce an un-known resistance with respect to known resistance. Nodalanalysis was applied in the T junction to calculate the pressure

wher e the two dye stre ams were comb ined. The contributionof each dye stream to the outlet streams was then computedby simple application of Poiseuilles Law to each branch re-sistor (Eqs. S4 and S5).

Qy =P

R

RRs +RoRs +RoR

[S4]

Qb =P Rs

RRs +RoRs +RoR: [S5]

Eq. 2is obtained by dividing Eq. S4 by Eq. S5.

Bhargava et al. www.pnas.org/cgi/content/short/1414764111 1 of 6
http://www.dolomite-microfluidics.com/http://www.micronit.com/http://www.pnas.org/cgi/content/short/1414764111http://www.pnas.org/cgi/content/short/1414764111http://www.micronit.com/http://www.dolomite-microfluidics.com/


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Reservoir1 Reservoir 2

Negative Displacement Pump

Collector 2

Collector 1

R1 Rs1

Rs,n=Rstruct+Rselect,n

Rn=Rstruct+Rref,n

R2 Rs2

Qo2Qo1 RoRo

R1 Rs1 R2 Rs2 R3 Rs3

Ro Qo1 Qo2 Qo3Ro Ro

R1 Rs1 R2 Rs2 R3 Rs3 R4 Rs4

Ro Qo1 Ro Qo2 Ro Qo3 Ro Qo4

Fig. S2. Comparison of equivalent circuit models for (Top) two-, (Middle) three-, and (Bottom) four-outlet parallelized configurations of the tunable mixer

system (appearing left to right in Fig. 4). Each single-outlet subcircuit is appended to the inlet reservoirs such that the mixing ratio mo,nof outlet streamsQo,n,

where n = 14, is independently controlled by the ratio of Rs,n/Rn. The system was constructed with rotational symmetry around a cylindrical axis so that

no additional resistance due to excess components contributed to the branch resistances despite the expansion of operational capabilities, ensuring that the

ratio of select and reference resistorsRselect,n and Rref,n remained the only throttles on the distribution of pressures (and thus flow rates) in single-outlet

subcircuit branches.

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50 k375 k

Output

+5V

Infrared LEDIR sensitive

phototransistor

Fig. S3. Electrical circuit diagram depicting the operation of the near-infrared droplet measurement element. LED, light-emitting diode.

Fig. S4. Contact angle was measured between a water droplet surrounded by oil and an (A) uncoated and (B) coated channel surface, showing effective

modification of the channel hydrophobicity by initiated chemical vapor deposition.



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Fig. S5. Potting of joints between components and connectors by direct application of (A) epoxy and (B) silicone pipe sealant. (C) A T-junction emulsification

device was connected to breather tubing and completely encased in poly(dimethylsiloxane).

Table S1. Library of constructed circuit elements and their

designed segment cross-sectional side length h, reference label

for circuit analysis, theoretical hydrodynamic resistance Ras due

to designed side length, and expected resistance due tomanufacturing imperfection Rexp (presented with percentile SD)

Element h, m Label R, MPasm3

Rexp, MPasm3

Connector 1,000 RC,1000 227.20 223.1 5.5%

Straight pass 500 RSP,500 2,726.40 2,720.41 3.7%

750 RSP,750 5 38.55 525.69 6.2%

1,000 RSP,1000 170.40 169.67 3.1%

L joint 500 RL,500 2,726.40 2,720.41 3.7%

750 RL,750 538.55 525.69 6.2%

1,000 RL,1000 1 70.40 169.67 3.1%

Mixer 635 RM,635 16,227.00 17,708.04 4.2%

750 RL,750 6,395.30 6218.5 7.2%

1,000 RL,1000 1,846.00 1838.1 3.1%

T junction 500 R(T),500 1,363.20 1,360.21 3.7%

750 R(T),750 269.28 262.85 6.2%

1,000 R(T),1000 85.20 84.835 3.1%

X junction 500 R(X),500 1,363.20 1,360.21 3.7%750 R(X),750 269.28 262.85 6.2%

1,000 R(X),1000 85.20 84.835 3.1%

Interface 750 RI,750 448.79 438.08 6.2%

XT junction 750 R(XT),750 269.28 262.85 6.2%

XX junction 750 R(XX),750 269.28 262.85 6.2%

IR sensor 642.5 RIR,642.5 999.95 993.57 0.99%

In devices with multiple outlets, R is presented as the internal segment

resistance contributed by the equivalent circuit diagram from that particular

element in Table S3. The labels used during circuit analysis are placeholders

for the numerical averages presented in their corresponding row values

ofRexp.



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Table S2. Comparison of intended and measured side length of

segments (h and hmeasured, respectively) with corresponding SD

h, m hmeasured, m n

1,000 1,001 8 75

750 754 12 100

642.5 644 2 12

635 621 7 12

500 500 5 36

The number of samples measured for a particular category of h is given

byn.

Table S3. Catalogue of components and their associated names, CAD drawings, orientationvisual cues, and internal equivalent circuit diagrams

tiucriCtnenopmoCeuCtnemelE

Connector

Straight Pass

L-Joint

Mixer

T-Junction

X-Junction

Interface

XT-Junction

XX-Junction


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