Microfluidics and Nanofluidics
Supplementary Information
Experimental Procedure, Auxiliary Data
Title:Global Network Design for Robust Operation of Microfluidic Droplet Generators with Pressure Driven Flow
Authors:Tomasz Glawdel, Carolyn L. Ren
S.1Chip Designs
Three designs are chosen which vary the relative length of the inlet/outlet branches to each other as shown in Figure S.1. The purpose is to test whether the global network design influences the droplet breakup process under constant pressure control. The three designs correspond to relative channel lengths of (Ld:Lc:Lm) (a) 1:1:5, (b) 1:5:2, (c) 5:1:2. The minimum length is 1 cm for the inlet oil/water channels. More important than the length ratio, is the hydrodynamic resistance ratio between the channels as this directly influences the pressure field within the chip. The actual hydrodynamic resistance depends on the viscosities as well as the channel dimensions, and therefore the ratio changes with each chip type and oil/water combination.
Fig.S.1 Diagram of the three different chip designs with different channel lengths. Type 1- 1:1:5, Type2- 1:5:2, and Type 3-5:1:2. A close up of the intersection design is also included for the three types of intersections (wd:wc) 1:1, 1:2 and 1:3. Outside the intersection area, the channel width is 100 µm and the height is uniform.
S.2Velocity Fluctuation Experiments
Table S.1 summarizes the conditions for the velocity fluctuations data presented in the manuscript (Figure 4). For each experiment, 16 different pressure combinations of PdandPc were applied to vary the size, speed and spacing of droplets.Prior to each experiment the hydrodynamic resistance of the network channels was measured. This was accomplished by using a calibrated micro-flow sensor (SLG 1430-4870, Sensirion) and pressure controller to measure the equivalent hydrodynamic resistance (Rhyd=P/Q) of each channel.
TableS.1 Table listing the order in which experiments were performed. The five independent factors are listed in columns 2-5. The three right hand side columns are the viscosity (µd/µc), network channel lengths (Lc:Ld:Lm) and hydrodynamic resistances (Rc:Rd:Rm) ratios. All values shown are nominal.
Exp # / C.Ph / D.Ph/Surf / C. Typ / W.R / H.R / µd/µc / Lc:Ld:Lm / Rc:Rd:Rm1 / Silicone Oil / Water / Type 2 / 1:1 / 1:5 / 1:10 / 1:5:2 / 10:5:20
2 / Silicone Oil / Water / Type 3 / 1:2 / 1:3 / 1:10 / 5:1:2 / 50:1:20
3 / Silicone Oil / Water / Type 1 / 1:3 / 1:2 / 1:10 / 1:1:5 / 10:1:50
4 / Silicone Oil / Water +1%SDS / Type 1 / 1:1 / 1:5 / 1:10 / 1:1:5 / 10:1:50
5 / Silicone Oil / Water +1%SDS / Type 2 / 1:2 / 1:3 / 1:10 / 1:5:2 / 10:5:20
6 / Silicone Oil / Water +1%SDS / Type 3 / 1:3 / 1:2 / 1:10 / 5:1:2 / 50:1:20
7 / Hexadecane / Water / Type 2 / 1:3 / 1:5 / 1:3 / 1:5:2 / 3:5:6
8 / Hexadecane / Water / Type 3 / 1:1 / 1:3 / 1:3 / 5:1:2 / 15:1:6
9 / Hexadecane / Water / Type 1 / 1:2 / 1:2 / 1:3 / 1:1:5 / 3:1:15
10 / Hexadecane+1% Span 80 / Water / Type 3 / 1:3 / 1:5 / 1:3 / 5:1:2 / 15:1:6
11 / Hexadecane+1% Span 80 / Water / Type 1 / 1:1 / 1:3 / 1:3 / 1:1:5 / 3:1:15
12 / Hexadecane+1% Span 80 / Water / Type 2 / 1:2 / 1:2 / 1:3 / 1:5:2 / 3:5:6
13 / FC-40 / Water +10%PFO / Type 3 / 1:2 / 1:5 / 1:5 / 5:1:2 / 25:1:10
14 / FC-40 / Water +10% PFO / Type 1 / 1:3 / 1:3 / 1:5 / 1:1:5 / 5:1:25
15 / FC-40 / Water +10% PFO / Type 2 / 1:1 / 1:2 / 1:5 / 1:5:2 / 5:5:10
16 / FC-40 / 35%Gly+10% PFO / Type 1 / 1:2 / 1:5 / 1:2 / 1:1:5 / 5:2.5:25
17 / FC-40 / 35%Gly +10% PFO / Type 2 / 1:3 / 1:3 / 1:2 / 1:5:2 / 5:12.5:10
18 / FC-40 / 35%Gly +10% PFO / Type 3 / 1:1 / 1:2 / 1:2 / 5:1:2 / 10:2.5:4
S.3Validation of Working Range Prediction
Table S2 lists the results for six T-junction designs with different intersection and network configurations. Experiments were performed, with and without surfactants, using silicon oil as the continuous phase and water as the dispersed phase. Measurements were made by fixing Pc and slowly lowering Pd until the interface remained fixed just inside the dispersed channel inlet. This was done at two different levels of Pc. The two columns on the left of Table S2 summarize the comparison. Overall, the correlation is good as the prediction is generally within 2% of the measured value.
Table S2Experimental results for prediction of Pdmin. Data is presented for 6 different chip designs with various local and global geometries, with and without surfactants.
Exp # / C.Ph / D.Ph/Surf / wd(µm) / wc
(µm) / h
(µm) / PLp
(mBar) / Rc:Rd:Rm / Pc
(mBar) / Pdmin
(exp) / Pdmin
(calc)
1 / Si Oil / Water / 98 / 98 / 42 / 15.3 / 10:1:50 / 400 / 0.885 / 0.872
500 / 0.884 / 0.864
2 / Si Oil / Water / 91 / 91 / 31 / 19.5 / 10:7:20 / 400 / 0.713 / 0.709
500 / 0.700 / 0.699
3 / Si Oil / Water+1%SDS / 46 / 94 / 43 / 4.05 / 10:1:50 / 400 / 0.838 / 0.842
500 / 0.830 / 0.840
4 / Si Oil / Water+1%SDS / 92 / 92 / 41 / 3.2 / 10:1:50 / 400 / 0.838 / 0.832
500 / 0.830 / 0.830
5 / Si Oil / Water+1%SDS / 92 / 92 / 41 / 3.2 / 10:20:20 / 400 / 0.688 / 0.675
500 / 0.660 / 0.673
S.4Numerical Simulation Results Noise Absent
Figure S2 presents the transient droplet spacing, and the correspond FFT analysis, for the case of Rc:Rd:Rm=10:1:50, with Pc=500 mBar, γ=50 mN m, with the absence of noise in Pc, and Pd. The response follows an exponentially decaying sinusoidal signal. FFT analysis of the signal confirms that the oscillations in spacing have a period matching closely to the residence time of droplets in the channel, τ/ndrop~1. When Rd is increased from 1→7 the decay rate increases and the overall magnitude of the oscillations decreases (see Figure S2c,d). Similarly, the FFT analysis confirms a peak near τ/ndrop~1. A strong peak near the residence time was confirmed for every numerical simulation even when ndrop and Lm were varied. If the simulation is run for a long-enough time oscillations eventually subside to a constant output in droplet spacing.
Fig.S2Time-trace and FFT analysis of droplet spacing for two numerical simulations (a, b) Rc:Rd:Rm=10:1:50, with Pc=500 mBar, γ=50 mN m and (c, d) with Rc:Rd:Rm= 10:7:50 and for both casesλ~10wc, Gc=3.
S.5Case Study
Consider an application that uses a T-junction generator with silicon oil (µc=10mPas) and water (µd=1mPas) as the two phases without a surfactant (γ~50mN/m). All channels have the same cross-sectional dimension of wc=100 µm and h=35 µm. The pressure system in use has an available range from 0-1000mBar with a resolution of 0.5mBar.
Calculations are based on using the midpoint of the pressure systemPc=500mBar. Because surfactants are not used and the surface tension is relatively high, a 1:1 inlet geometry is chosen to limit interface shape distortion during the formation process. A gradual taper can be added to the end of the channel to reduce pressure pulses as the droplets exit.The pressure drop across the interface as it resides in the dispersed channel is PLp=20mBarand. Assuming a maximum droplet spacing of 10wc=1 mm, with a minimum of 50 droplets, the main channel length should be design to be Lm=50mm.
Generally, Lc should be as small as possible, however, for practical reasons it is better to make the length slightly larger. During start up sometimes the two phases may reverse flow and the dispersed phase may enter into the continuous phase channel. If this happens, then we do not want dispersed phase to reach all the way into the reservoir of Rc causing it to be trapped and ejected later during operation. A reasonable length to help reduce the probability of this happening is Lc=10 mm, and thus.
The next step is to make an assumption on the droplet resistance Rdrop. For this example, it is assumed that droplets will have a real length ofLdrop~1.5wc and a hydrodynamic resistance ofLhdrop~3Ldrop., thus. Hence at maximum spacing, the contribution to the total resistance of Rmfrom the droplets is 31% (nRdrop/Rm), and the change in Rm for one droplet leaving is ~0.6%. Following the suggested design of Rm=Rd, the length of dispersed inlet Ld would need to be 50cm when considering the viscosity contrast. This is an extremely long channel to fit on a chip. Typically, a long capillary with a small inner diameter would be attached to the inlet to increase the channel length. The best way to achieve the same effect without the long capillary is to create a two-level microchannel design where a portion of the dispersed inlet is much shallower than the rest of the network. Channel resistance scales with h-3, and therefore reducing the height by half will require a channel only 1/8th the length (Ld~60mm), a size far more manageable to fit directly on the chip. Smaller channels are more favourablethan a long capillary because they also reduce the dead volume in the system thereby decreasing the time it takes to reach steady state.
Based on this setup the pressure range for is 0.87→2.04 or in real terms 436→1020 mbar. The offset from the minimum pressure needed to generate a continuous stream of droplets is approximately 10mBar, so that the lower limit is now 446mbar. Assuming that 1/3rd of the pressure range is actually used since only smaller droplets are desired, then there are (1020-446)/(3∙0.5)=382 discrete system points that can be used to tune droplet generation. Additionally, the flow rates can also be estimated using Eqn. (11). For a pressure setup of Pc=500mBar and Pd=600mBar, flow rates are estimated (without consideration of Rdrop) to beQd=0.6 µl/min and Qc=1.20 µL/min for a flow ratio of approximately φ=0.5.
For this geometry and setup, calculations for the expected fluctuations in Pj are only 0.75%, and udroponly0.81%. If Pc is increased to 800 mBar, these fluctuations reduce to 0.48% and 0.51% respectively. If the same system setup is used, but surfactant is added (γ=10mN/m), the fluctuations are reduced to 0.14% and 0.16%. In this case, the original dispersed channel can be replaced with a shorter channel still with good performance (0.65%,0.71% respectively). This example demonstrates the application of the design rules to a specific T-junction generator design.