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Effect of electro-osmotic flow on energy conversion on superhydrophobic surfaces
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10.1063/1.4802044
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Affiliations:
1 Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
2 Center of Smart Interfaces, Petersenstr. 17, 64287 Darmstadt, Germany
Phys. Fluids 25, 042002 (2013)
/content/aip/journal/pof2/25/4/10.1063/1.4802044
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/4/10.1063/1.4802044
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Figures

FIG. 1.

Schematic diagram of the superhydrophobic surface. Within the grooves air is entrapped and we assume the air-liquid interface to remain ideally flat. The length of the channel is assumed to be and consists of two parallel surfaces at distance 2. The surfaces are periodically structured with groves of width δ and periodicity .

FIG. 2.

Output power density for varying free surface charge density, σ, for different values of the free surface fraction, δ. The solid line is calculated based on our analytical expression , and the crosses (×) are calculated based on the more exact semi-analytic expressions . Pluses (+) and circles (o) are numerical results using the nonlinear Poisson-Boltzmann equation, differing in the evaluation of the conduction current by, respectively, a constant and variable charge density according to Eqs. . The dotted line shows the behavior when the electro-osmotic flow is not accounted for (at δ = 0.7). The figure was plotted assuming = = 100 μm, σ = 0.1 μS/cm, λ = 1 μm, μ = 1 mPa s and σ = 2.

FIG. 3.

Relative drop of streaming potential for increasing free surface charge density, σ, for different values of the free surface fraction, δ. The solid line is calculated based on our analytical expression , and the crosses (×) are calculated based on the more exact expressions . The figure was plotted assuming = = 100 μm, σ = 0.1 μS/cm, λ = 1 μm, μ = 1 mPa s and σ = 2.

FIG. 4.

Variation of efficiency with free surface charge density, σ, both for varying values of bulk conductivity σ and free surface fractions δ = 0.4 and δ = 0.9. Lines are calculated based on the analytical expressions . Circles (o) are numerical results obtained using the nonlinear Poisson-Boltzmann equation. The dashed lines shows the maximum theoretical efficiency predicted for such systems. Here = = 100 μm, λ = 1 μm, μ = 1 mPa s and σ = 2.

FIG. 5.

(a) Variation of maximum efficiency with free surface charge density, σ, for values of λ/ between 0.01 and 0.1, fixing the geometry length scale and varying λ. Lines are calculated based on the analytical expressions . Circles (o) are numerical results obtained using the nonlinear Poisson-Boltzmann equation. Here = = 100 μm, δ = 0.9, μ = 5.43 × 10 m/(Vs), μ = 1 mPa s and σ = 2. (b) Variation of maximum efficiency as a function of λ/ at fixed λ = 1 μm, σ = 0.1 μS/cm and variable length-scale for several values of surface charge density σ. Circles (•) are numerical results obtained using the nonlinear Poisson-Boltzmann equation and the dotted line is the analytical expression . Here = , δ = 0.9, μ = 1 mPa s, and σ = 2.

/content/aip/journal/pof2/25/4/10.1063/1.4802044
2013-04-29
2014-04-21

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