Kosmas Ellinas, Angeliki Tserepi, Evangelos Gogolides*

Superhydrophobic, passive microvalves with controllable opening threshold: Exploiting plasma nanotextured microfluidics for a programmable flow switchboard

Kosmas Ellinas, Angeliki Tserepi, Evangelos Gogolides*

Institute of Microelectronics, NCSR “Demokritos”, PO BOX 60228, 153 10 Aghia Paraskevi, Greece

*corresponding author email:

Supporting information

S1. Hot embossing process for microchannel fabrication

Profilometer characterization of both the master and the microfluidic channel was performed to find the optimal embossing conditions. For PMMA with Tg ~105 0C, the pressing time is approximately 5 min at 130 0C. Three different pressures 35×105Pa, 40×105 Pa and 50×105 Pa were tested, the optimum being the 40×105 Pa. After embossing, temperature is set to 900C and the sample is left to cool down. The pressure is released when the temperature decreases below Tg. Different release different temperatures (e.g. 90 and 1000C) were also tried.. The whole process lasted about 30 min. Table 1 summarizes the embossing tests.

Table 1. Silicon Master and PMMA microfluidic profiles for different applied pressure and different release temperature.

Master
(Trapezoidal Crossection with small and large base) / Microchannel Applied pressure 35×105 Pa release temperature 1000C : / Microchannel Applied pressure 40×105 Pa release temperature 1000C : / Microchannel
Applied pressure 50×105 Pa release temperature 900C :
Slopes:
Left: 0.8,
Right: 0.94 / Corresponding imprinted Slopes: Left: 0.64
Right: 0.71 / Corresponding imprinted Slopes: Left: 0.79
Right: 0.83m, / Corresponding imprinted Slopes: Left: 0.84
Right: 0.94,
Small Base: 181μm,
Large base: 221 μm / Small base :168μm,
Large base: 221 μm / Small base: 175 μm Large base: 217 μm, / Large base: 206 μm, Small base:165 μm

S2. Pressure drop calculations and measurements inside 20 μm flat, non-plasma treated microchannels

The Hagen–Poiseuille equation for rectangular microchannel was used to calculate the pressure drop across the microchannel. and verify that the pressure drop is smaller than the threshold pressure in all cases studied. It is perhaps a surprising fact that no analytical solution is known to the Poiseuille-flow problem with a rectangular coss-section(Bruus, 2007). The following approximate solution can be written: .

Factor C value is 84.7 for a rectangular microchannel with aspect ratio 0.1 (depth/width~0.1 of the microchannel), Q the volumetric flow rate in m3/s, Rh the hydraulic radius for a rectangular microchannel and ν the kinematic viscocity in S.I. Using Eq. (1) we calculate the pressure drop for a 20μm deep, 175μm wide untreated microchannel. For a typical constant flow rate of 1 μl/min, the pressure drop is: . This result is close to the experimental value referred in our recent work (Papageorgiou et al., 2013) and lower than the values for the theoretical pressure thresholds given from Table 1 in the main text. The pressure drop of the non-plasma treated channel was measured approximately 30 mbar for a length of approximately 2cm, which is very close to the analytically calculated value for constant flow rate of 1μl/min. In figure S1 the pressure rise curve measurement for the 20μm deep, 175μm wide untreated microchannnel is given, showing the pressure drop which develops in this channel.

Figure S1. Pressure drop inside a 20 μm deep microchannel. Flow rate is kept constant at 1 μl/min. Pressure rises versus time as liquid fills the microchannel, and stabilizes to the pressure drop value.

S.3 Optical visualization of the valve reusability

The reusability of the valves is visualized in the following figure, which shows the valve drain effect after flow is stopped in the channel and pressure is released. Figure S2 is complementary to figure 6 of the main text in which pressure is released several times and the experiment is repeated. Each time pressure is released, water moves away from both ways of the patch leaving it dry. Release of the pressure is required to stop the flow and reinitialize the valve operation.

Figure S2. Magnified image (×5) of the hydrophobic patch. Valve drains after the flow is stopped and pressure is released. Dry hydrophobic patch looks blurred, while the remaining channel is non-visible (transparent) due to wetting. Red arrows indicate valve draining in both directions away from the patch.

S5 Pressure threshold calculation using a superhydrophobic patch

Care must be taken in defining the parameters that affect the pressure threshold of a superhydrophobic valve, especially for the complex nanotexture produced by plasma. Let us assume a superhydrophobic surface in which θc is the Cassie-state static contact angle for water, and let θ0 (θ0~1150) be the initial static contact angle for water on a flat, smooth C4F8 plasma deposited surface. The total energy of a system with solid-liquid, liquid-gas and gas-solid interfaces is given as: (S1), where Αsl, Asv and Alv are solid-liquid, solid-vapor, and liquid-vapor interface areas, γsl, γsv, γlv its corresponding surface energies per unit area and (S2). The surface energies are related to the equilibrium contact angle θc, by the Young equation: (S3). Using Eq. (S1),(S2),(S3) yields the reduced expression: (S4). The energy becomes function of the injected liquid volume. Pressure can be written as (S5). Inserting Eq. (S4) to the right-hand side of Eq. (S5) we obtain a new expression for the pressure:

(S6)

Figure S3. Rectangular channel cross-section with geometrical features (width-W0, and height-h) and roughness height hroughness.

For a rectangular crossection microchannel as shown in figure S3 and nanotextured Superhydrophobic bottom, we estimate each interfacial areas ALV, ASL ASV, as follows:

ALV=(h-hroughness)Wo+(1-Φs)Wodx

ASL=[(2h- hroughness) +Wo]dx+rfΦsWodx

ASV= -[(2h- hroughness) +Wo]dx+(r-Φs)Wodx

Incorporating these expressions for the liquid-vapor, solid-liquid and solid-vapor area in equation S6 we obtain the final equation (S7) for the pressure threshold as a function of factors (φs, θo, r, rf, hroughness) and geometrical features (width-W0, and height-h):

(S7)

Equation S7 highlights the role of plasma nanotexturing in the valve operation through surface fraction given by the Cassie equation, roughness height hroughness,,contact angle of the coating θo, roughness surface area r and roughness wetted area factor rf.

The roughness wetted area in our case was estimated as follows. Let us assume we have a conical shape pillar as shown in figure S3. Roughness wetted area factor rf is the ratio of the peripheral of the cone divided by the base area, this leads us to rf=πbλ/πb2=λ/b=1/sinθ. Assuming that the aspect ratio is 2:1 we yield that θ=26.50 and thus the roughness wetted area factor is calculated to be 2.3.

S6. Valve working principle video

The supporting information video S1 highlights the working principle of the hydrophobic valve. The microfluidic flow is kept constant at 1 μl/min. Notice the stopped flow in the middle of the channel when the liquid front meets the hydrophobic valve. The valve opens when pressure exceeds the threshold pressure value of the valve and fills up the microchannel.

S7. Switchboard working video

The supporting information video S2 highlights the working principle of the switchboard. The fluid flow is first set to 1 μl/min and it is gradually increased to 5 μl/min. The wells are filled in a predesigned sequence.

Reference

Bruus H (2007) Theoretical Microfluidics. In press Ou (ed.), (ed.), Vol. pp.

Papageorgiou DP, Tsougeni K, Tserepi A, and Gogolides E (2013) Superhydrophobic, hierarchical, plasma-nanotextured polymeric microchannels sustaining high-pressure flows. Microfluidics and Nanofluidics 14, 247-55.