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Anisotropic flow in striped superhydrophobic channels
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10.1063/1.4718834
/content/aip/journal/jcp/136/19/10.1063/1.4718834
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/19/10.1063/1.4718834
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Sketch of the symmetric striped channel (a) Θ = π/2 corresponds to transverse stripes, Θ = 0 to longitudinal stripes; (b) situation in (a) is approximated by a periodic cell of size L, with equivalent flow boundary conditions on the gas-liquid and solid-liquid interfaces.

Image of FIG. 2.
FIG. 2.

The relation between the slip length b and the wall friction parameter γ L , for a wall interaction cutoff 2.0σ. The inset shows an enlarged portion of the region where the slip length is zero. The no-slip boundary condition can be implemented by using . Dashed curves show analytical predictions.37

Image of FIG. 3.
FIG. 3.

Typical density (a) and velocity (b) profiles simulated for a longitudinal flow and a texture with L = H = b = 50σ, ϕ2 = 0.5.

Image of FIG. 4.
FIG. 4.

The effective downstream slip length, , as a function of tilt angle Θ for a pattern with L = b = 50σ and ϕ2 = 0.5. Symbols are simulation data. Solid lines are theoretical values calculated using Eq. (54) with eigenvalues obtained by a numerical solution of Eqs. (19), (20), (30), and (31), (a) H = 50σ. The thick channel limit (dashed line) is calculated with Eqs. (22) and (38). (b) H = 10σ. The thin channel limit (dashed line), is calculated with Eqs. (21) and (35).

Image of FIG. 5.
FIG. 5.

The ratio ⟨Q z /⟨Q x as a function of the tilt angle Θ obtained with Eq. (39) for the data sets from Fig. 4 for (a) H = 50σ and (b) H = 10σ. Symbols are simulation data, solid curves represent theoretical values, and dashed curves show asymptotic predictions in the limit of thick channels (a) and thin channels (b).

Image of FIG. 6.
FIG. 6.

The eigenvalues of the effective slip length tensor (symbols) as a function of ϕ2. Solid curves are theoretical values obtained by a numerical solution of Eqs. (19), (20), (30), and (31). Calculations were made for a pattern with L = b = 50σ, (a) H = 50σ. Dashed curves are calculated with Eqs. (22) and (38), (b) H = 10σ. Dashed curves are computed with Eqs. (21) and (35).

Image of FIG. 7.
FIG. 7.

The ratio ⟨Q z /⟨Q x as a function of ϕ2 obtained with Eq. (39) for Θ = π/4 by using the data sets from Fig. 6 (a) H = 50σ and (b) H = 10σ. Symbols are simulation data, solid curves represent theoretical values, and dashed curves show asymptotic predictions in the limit of thick channels (a) and thin channels (b).

Image of FIG. 8.
FIG. 8.

The longitudinal (a) and transverse (b) effective slip lengths as a function of the channel height H for a texture with L = b = 50σ and ϕ2 = 0.5. The theoretical curves are obtained by a numerical solution of Eqs. (19), (20), (30), and (31). Dashed lines show expected asymptotics in the limit of thin and thick channels.

Image of FIG. 9.
FIG. 9.

The ratio between the transverse and longitudinal flow rates ⟨Q z /⟨Q x as a function of channel thickness H for a pattern with L = b = 50σ, ϕ2 = 0.5, and Θ = π/4. Symbols are simulation data and the lines represent theoretical values obtained using Eq. (39). Dashed lines show expected asymptotics in the limit of thin and thick channels.

Image of FIG. 10.
FIG. 10.

The velocity profile across the channel at Θ = π/4, (a) H = 10σ, y from −5σ to 5σ, (b) H = 50σ, y from −25σ to 25σ, (c) H = 50σ, y from 15σ to 25σ, enlarged part near the striped-pattern, and (d) H = 50σ, y from −5σ to 5σ, enlarged part near the channel center. The z components in (c) and (d) have been increased five times for better demonstration.

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/content/aip/journal/jcp/136/19/10.1063/1.4718834
2012-05-18
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Anisotropic flow in striped superhydrophobic channels
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/19/10.1063/1.4718834
10.1063/1.4718834
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