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Pressure and partial wetting effects on superhydrophobic friction reduction in microchannel flow
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Image of FIG. 1.
FIG. 1.

A 3D schematic view of a side trenched microchannel with liquid penetrating into the air cavities. More penetration is to be expected upstream of the microchannel than downstream since the pressure is higher.

Image of FIG. 2.
FIG. 2.

Schematic diagram of the experimental setup. Pressure drop, flow rate and temperature are measured during a microchannel sample experiment. The experiments were repeated 5–6 times for each micro-trench configurations, and newly fabricated PDMS microchannels were used for each trial. By using a new microchannel for each trial, contamination issues are minimized.

Image of FIG. 3.
FIG. 3.

Microscopic picture (M = 10×, NA = 0.3) of a trenched microchannel (a = 15 μm, b = 65 μm, c = 30 μm) at approximately 90% from the upstream. The outlet is connected to a vacuum line and the differential pressure was maintained at 6000 Pa.

Image of FIG. 4.
FIG. 4.

Microscopic images (M = 10×, NA = 0.3) of a micro-trenched microchannel (a = 15 μm, b = 65 μm, c = 120 μm) subject to different differential pressures. By observation, pressure is the largest near the inlet where water penetration is the deepest.

Image of FIG. 5.
FIG. 5.

Flow rate versus differential pressure for microchannels with (a) a = 55 μm, b = 65 μm (blue and green online) and (b) a = 15 μm, b = 65 μm (yellow and red online) for c = 30 μm, 60 μm, 120 μm, and 230 μm. The baseline plot is for a microchannel with no trenches on the side walls, and the error bars represent the standard deviation of 5 to 6 repeated experiments.

Image of FIG. 6.
FIG. 6.

Graph of fRe vs. Re for (a) a = 55 μm and (b) a = 15 μm, where the error bars represent the standard deviation among 5 to 6 similar samples (the error bars for Re are less than 5% and therefore obscured by the marker symbols). The theoretical fRe value for the baseline is ∼ 57.2. 46 In the lower Re, fRe starts off at a larger value and then levels off approximately at Re ∼ 10. The uncertainty due to the instrumental error specifications is less than 3.7% for fRe and 2.7% for Re. The uncertainty due to the measurement error is 1.8–6.4% for fRe and 1.3–6.1% for Re, which is consistent with the uncertainty from the standard deviation of the calculated fRe and Re values. The major and the minor losses from the external tubing are neglected since the combined losses account for 0.2–0.3% of the major loss in the microchannel.

Image of FIG. 7.
FIG. 7.

Graph of w eff vs. microchannel location. The w eff data is measured for all the microchannels experimented and is applied to the numerical simulation. Since the microchannel height is constant, the change in w eff represents the change in flow area (a = 15 μm, b = 65 μm, c = 60 μm).

Image of FIG. 8.
FIG. 8.

Comprehensive fRe vs Re graph for experimental and numerical results for a trenched microchannel (a = 15 μm, b = 65 μm, c = 60 μm). The numerical results are based on the actual w eff data, and the standard deviation of the results due to the fluctuations in water penetration from sample to sample are plotted as dotted lines above and below the averaged values. As expected, the experimental results are located between the two bounding numerical fRe limits (no-slip assumption and shear-free assumption at the air-water interface).

Image of FIG. 9.
FIG. 9.

Micrograph (M = 40×, NA = 0.60) of pinching effects in a micro-trench section (a = 15 μm, b = 65 μm, c = 30 μm) located at 70% from upstream. It is observed that the air layer protrudes more into the water layer if the inlet pressure (and hence Re) is lower.

Image of FIG. 10.
FIG. 10.

Fraction of trenches penetrated vs. Re for a single microchannel sample (left side of the trenches only). In the higher Re (or ΔP) range, the wetting of the trenches no longer increases significantly.

Image of FIG. 11.
FIG. 11.

Numerical results of the streamline deflection into a fully wet micro-trench element. The average deflection of the streamline is measured from the edge of the micro-trench land into the micro-trench gaps. As Re increases the streamline deflection into the micro-trench decreases.

Image of FIG. 12.
FIG. 12.

Comparison of friction in a microchannel between Cassie-Baxter state and Wenzel state (a = 15 μm, b = 65 μm, c = 60 μm). For the numerical fRe calculations, a rectangular cross-sectional area is assumed since the error in fRe due to the difference between the microchannel geometry measured in Table I and the rectangular cross-section is <0.5%.

Image of FIG. 13.
FIG. 13.

Absolute values of penetration depth (a = 15 μm) as a function of location at ΔP = 4000 Pa (Re ∼ 15) for a single microchannel sample. For each repeating trials, the slopes are similar regardless of different micro-trench depths. This suggests that the magnitude of penetration is similar regardless of the micro-trench depth.


Generic image for table
Table I.

Mean measured dimensions of the PDMS microchannel for each micro-trench configuration (N = 5) and the uncertainty due to instrument and measurement errors. Measurements were taken at different locations along the length of each microchannel sample. The land (a = 15 μm and a = 55 μm) represents the nominal distance between one edge to the other.

Generic image for table
Table II.

Comparison of the solid fraction ϕ S , estimated critical roughness factor r c , and the actual roughness factor r actual for different micro-trench configurations used in this study. When calculating the r c , the contact angle is assumed to be between θ Y = 110°–115°, hence the range of critical roughness values. The range in contact angle is attributed by the fact that pristine condition microchannels were used rather than microchannels with silanized walls.

Generic image for table
Table III.

The ratio of prematurely wetted trenches to the total number of trenches for both left and right side trenches combined. Since a = 15 μm, b = 65 μm, c = 30 μm configuration is well below the critical roughness factor, the number of prematurely wetted trenches is the greatest.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Pressure and partial wetting effects on superhydrophobic friction reduction in microchannel flow