Free-Flowing Shear-Thinning Liquid Film in Inclined μ-Channels
Abstract
:1. Introduction
2. Experimental Procedure
2.1. Experimental Setup
2.2. Measuring Procedure
3. Results and Discussion
3.1. Liquid Film Thickness Calculation
3.2. Effective Viscosity Prediction
3.3. Meniscus Shape
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
A | liquid phase cross section | μm2 |
Ca | capillary number | Dimensionless |
Fr | Froude number | Dimensionless |
g | acceleration of gravity | m/s2 |
Hf | height of the microchannel | μm |
Ho | height of the meniscus | μm |
H | liquid film thickness | μm |
L | length of the interface (meniscus) | μm |
M | objective lenses magnitude | Dimensionless |
m | mass flow rate | kg/s |
NA | numerical aperture | Dimensionless |
Q | volumetric flow rate | mL/h |
Re | Reynolds number | Dimensionless |
S | gas–liquid interfacial area | μm2 |
V | total fluid volume | μm3 |
X | distance from vertical wall | μm |
Y | distance from the channel bottom | μm |
WO | width of microchannel | μm |
Greek symbols | ||
α | specific surface | m2/m3 |
μ | liquid viscosity | Pa·s |
σ | surface tension | N/m |
τ | residence time/channel length | s/m |
ρ | liquid density | kg/m3 |
φ | inclination angle | ° |
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Index | Liquid | Refractive Index | Contact Angle | Density | Surface Tension | Viscosity |
---|---|---|---|---|---|---|
- | (°) | (kg/m3) | (mN/m) | (Pa·s) | ||
nW | 100% water + 0.03% xanthan gum | 1.340 | 74 | 998 | 72.1 | μ = 0.003698γ−1 + 0.004339γ−0.1819 |
nG20 | 75% water + 25% glycerol w/w + 0.03% xanthan gum | 1.360 | 74 | 1059 | 66.7 | μ = 0.002952γ−1 + 0.006295γ−0.1535 |
Fluid | μ∞ (Pa·s) | μave (Pa·s) | % Difference |
---|---|---|---|
nG20_80 | 0.0025 | 0.00260 | 4.0 |
nG20_40 | 0.0025 | 0.00270 | 8.0 |
nW_80 | 0.0014 | 0.00145 | 4.0 |
nW_40 | 0.0014 | 0.00150 | 7.1 |
Constants for Equation (1) | Present Work | Previous Work [13] |
---|---|---|
a | 0.50 | 0.50 |
b | 0.01 | 0.01 |
c | 3.90 | 2.04 |
d | −0.56 | −0.56 |
f | −0.86 | −0.86 |
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Koupa, A.T.; Stergiou, Y.G.; Mouza, A.A. Free-Flowing Shear-Thinning Liquid Film in Inclined μ-Channels. Fluids 2019, 4, 8. https://doi.org/10.3390/fluids4010008
Koupa AT, Stergiou YG, Mouza AA. Free-Flowing Shear-Thinning Liquid Film in Inclined μ-Channels. Fluids. 2019; 4(1):8. https://doi.org/10.3390/fluids4010008
Chicago/Turabian StyleKoupa, Angeliki T., Yorgos G. Stergiou, and Aikaterini A. Mouza. 2019. "Free-Flowing Shear-Thinning Liquid Film in Inclined μ-Channels" Fluids 4, no. 1: 8. https://doi.org/10.3390/fluids4010008